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Onset mechanism and development of corona discharge on water drops dripping from a conductor under high direct voltage
Journal of Electrostatics, 9 (1981) 339--353 Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
339
ONSET MECHANISM AND DEVELOPMENT OF CORONA DISCHARGE ON WATER DROPS DRIPPING FROM A CONDUCTOR UNDER HIGH DIRECT VOLTAGE
MASANORI H A R A
Department of Electrical Engineering, Faculty of Engineering, Kyushu University, Fukuoka (Japan) and M A S A N O R I A K A Z A K I
Department of Energy Conversion Engineering, Graduate School of Engineering Sciences, Kyushu University, Fukuoka (Japan) (Received June 30, 1980; accepted in revised form January 6, 1981)
Summary Corona onset mechanism was studied by an analytical method and onset and development of corona discharge on water drops dripping from a conductor under high direct voltages were investigated by simultaneous recordings of the light emission, corona current and drop profile. The analytical study shows that corona onset mechanism depends on the drop size and the ambient air pressure. Although at about atmospheric air pressure the electrostatic instabilitycauses discharge on the surface of a water drop dripping from a conductor with a d.c. high voltage, in a higher electric field,beyond the corona onset voltage, corona can develop on a stable surface of the water drop whose radius is smaller than a criticalvalue depending on the ambient air pressure. The criticalradius for the appearance of this corona discharge mechanism could be related to the radius for the transition between two corona onset mechanisms: pure corona onset and onset caused by the surface-disruption of the drop at a given air pressure. Time-resolved photographs of corona discharge support descriptions of the corona discharge mechanism discussed in previous papers.
1. Introduction The onset mechanism of corona discharge on a water drop in an electric field has been investigated by English [3], Arai and Tsunoda [4] and Dawson [5, 6]. According to them, there axe two modes of the corona onset mechanism: (1) surface-disruption mode: the onset of corona discharge from a water drop at a b o u t atmospheric pressure is determined by the electrostatic instability of the drop surface; (2) pure corona mode: at reduced pressure, positive corona onset can occur on the stable drop surface. The criterion for the transition b e t w e e n these two modes, however, is n o t fully understood. As is the case for a water drop on a transmission c o n d u c t o r in foul weather when the drop hangs from the c o n d u c t o r under high direct voltages, the shape
0304-3886/81/0000---0000/$02.50 © 1981 Elsevier Scientific Publishing Company
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and size of the pendent drop change with the extent of its disintegration and the applied voltage. At a low voltage, the drop consists of the head and neck which turn into a mother and satellites when the drop breaks away. With increasing voltage, the drop becomes slender and it becomes difficult to distinguish between the head and the neck. Hence, in a study of the onset mechanism and development of corona discharge it may be necessary to consider the effect of the changing radius of the drop-tip curvature with the applied voltage, on the onset field strength of pure corona and on that of the surface instability on the drop. The purpose of this paper is to show the corona onset mechanism on a water drop dripping from a high voltage conductor as a function of the air pressure and the drop size and to clarify the relationship between the shape of the droptip in corona discharge and the corona onset mechanism. Moreover, discharge processes described in a previous paper [2] are confirmed to be correct by using time-resolved photographs of corona discharge. 2. Onset mechanism of corona discharge on water drop
2.1 Criterion for electrostatic surface instability When an electric field acts on the surface of a water drop, two types of surface instability, Rayleigh and Taylor instabilities [7, 8], or in a more general case a combination of the two, can develop if electrical corona on the drop is suppressed. Dawson appiied Rayleigh's and Taylor's criteria to compare the field strengths for their instabilities at the drop surface and showed the critical field strengths (in kV/cm) were given as follows [5] : (a) for the Rayleigh instability of a charged drop, Es~ = 18.07/~/r~
(1)
where r~ (in cm) is the radius of the undistorted drop; and (b) for the Taylor instability of an uncharged drop, Est = 14.6/~/r~
(2)
where r~ (in cm) is the polar radius of the spheroidal drop having a distortion ratio of 1.9. In most cases, for a mixture of the above instabilities, the critical field strength lies between E~ and Est. Moreover, the experimental values using the drop point to plane gap agree reasonably well with the eqn. (2) [5, 6]. Therefore, although eqn. (2) is the critical field strength for the uncharged drop, Est will be used later to discuss experimental data on the drop shape at corona onset.
2.2 Threshold field strength o f pure corona Threshold field strength of pure corona on the positive drop surface may be determined by the streamer breakdown criterion,
~
2
Xi
(a -- fl)dx = K
K = 10 ~ 20
(3)
341
where a and ~ are the first Townsend ionization coefficient and the electron attachment coefficient respectively, xl is the position in a gap where the electric field strength is the highest and x2 is the position where ~ = ~. This is based on the fact that the positive drop at pure corona onset exhibits the corona onset phenomena observed with a metal point. Only a little analytical study has been made concerning the criterion of corona discharge from a particle or water drop in the presence of the electric field. Hara and Akazaki [10] pointed out that the critical field strength of discharge onset (in kV/cm) on a metallic spherical particle moving in a parallel plane gap can be predicted accurately by the following semi~mpirical equation: Ec = 31.05p (1 + 0 . 3 0 1 / q ~ o )
(4)
where p (in atm) is the air pressure. Although the distribution of electric field around the sphere is not exactly the same as that around the spheroid under the Taylor condition, eqn. (4) will be used to discuss later the corona onset mechanism on the water drop because the value obtained from eqn. (4) is near ly equal to that obtained by the well known Peek formula [11] which can be used for a smooth cylindrical electrode. (kVlcm) 140
120
i00
,,..
80 L
~60
.... .__
40
I~
20
-
Ec(O'6°tm)~
~Ec(P=lotm)
.......
Est
0
I 1
0
I 2 (film)
rd
0 I ]
I
I
I
1
2 b
3
I 2
t 3 ro
(rr~)
I 4
(ram)
Fig. I. Onset field strengths of corona discharge, Ec, and electrostatic surface instability, Est. p, air pressure; rd, radius of the drop tip; b and r0, minor semi-axis and undistorted radius of the spheroid assumed to be under the Taylor condition.
342
2.3 Onset mechanism o f corona discharge on water drop The primary process for corona onset from the pendent drop can be determined by a comparison between the values of Est and Ec on the drop tip. But the shape of the drop tip during its elongation changes in a complicated fashion with time and the applied voltage. Then the critical field strengths of the surface instability and corona onset on the tip of the pendent drop are approxiI t mated by eqns. (2) and (4) where rp and r0 are replaced by the radius of curvature r d of the drop tip. Est and Ee axe illustrated at pressures of 0.6, 0.8 and 1 atm as a function of rd in Fig. 1. If the drop shape is spheroidal under Taylor's condition, the abscissa rd can be converted to the semi-axis b or the undistorted drop radius r0 by the equation b -- 1.9rd or r0 -- 2.353rd. Since the pure corona onset mode appears in the region where Ec is less than Est, the thin full and broken curves in the figure show the regions for the pure corona mode and the surface disruption mode for corona onset respectively. The boundary between these modes depends on the air pressure and the drop size as shown in Fig. 2. This figure also shows that the pure corona mode may develop at about atmospheric air pressure if the radius r0 of the drop tip becomes smaller than 0.674 ram. 4 (ran)
ro
2
Pure Corona Mode
0 0,5
i 0,6
i 0.7
I 0.8 P
I 0.9
I 1.0
I l.l (atm)
Fig. 2. Transition c o n d i t i o n s b e t w e e n t w o c o r o n a onset modes. - - , calculated value for the b o u n d a r y ; • e, e x p e r i m e n t a l value of the limit for t h e pure c o r o n a m o d e by English [3] ; • . . . . •, e x p e r i m e n t a l value o f the limit for the pure c o r o n a m o d e by Dawson [5] ; ×, e x p e r i m e n t a l value for t h e surface-disruption m o d e by Macky [ 15]; o, present results for c o r o n a d e v e l o p m e n t o n t h e stable drop surface, i.e. p u r e c o r o n a m o d e for c o r o n a onset.
343 3. Onset and development o f corona discharge on a water drop dripping from a d.c. energized conductor
3.1 Observation of drop profile and corona discharge Experimental apparatus Corona discharge is photographed by a still camera combined with an imageintensifier tube (Hitachi, HS-690) having a maximum gain of 8.2 × 104. To take a streak photograph showing the discharge process, the camera was also used as a rotating camera which was mounted loosely on the tripod and was rotated manually. The streak speed of the camera was not measured but can be found from a comparison of the deformation process of the pendent drop, the waveform of the corona current and the streak photograph. Since the mechanism of corona discharge is affected by the water resistivity, either distilled water or tap water was used to study the relationship between the corona discharge process and the drop profile. ACSR conductor of 810 mm 2 was used as an inner conductor of the coaxial cylindrical electrode. The remainder of the apparatus has been described in previous papers [1, 2].
Drop profile and onset and development of corona discharge Typical photographs of corona discharge are shown together with the corona current and drop profile for various values of the applied voltage in Figs. 3--5, where the size of the object taken in photographs has nearly the same dimension in each item. But the streak photograph is slightly distorted due to aberration in the image intensifier. Details of the relationship between corona current and the deformation process of the drop can be seen for a wide range of the applied voltage in the Hara et al. [2]. When the applied voltage is about 1% higher than the corona onset voltage, the light emission from the main drop tip and from the region between the main drop and the neck is observed as given in Fig. 3 (2). As the voltage increases, the corona discharge appears on the drop tip elongating from the conductor and on both terminals of the drop disconnecting from the conductor (Fig. 4). It is confirmed from this figure that the current pulses appearing during the period of the current decay are mainly due to the corona after the drop parts from the conductor. As seen in (2) of Fig. 4 (c), discharge ceases temporarily during the period of the current decrease in each current loop in which the drop tip has a rounded shape [2]. This event can clearly be observed for distilled water at a field strength on the conductor of about 7 kV/cm. The drop shape in the corona zone is always conical and its conical tip has a sharp edge or a short thin filament. When the field strength on the conductor becomes greater than about 15 kV/cm, the drop profile in the corona discharge zone is.affected by the water resistivity and the voltage polarity. Figs. 5 and 6 show the drop profiles and the appearance of corona discharge at the same applied voltage. The tip of an elongated negative drop always has a rounded shape and corona appears on
344
tI
t2
t3
(i)
tI
tI
t4
(2)
t2
t4
(I)
(2)
tI
t 2 t 3 t4
t3
t2t 3 t 4
(3) R=220kQ, 5ms/dJv, 0. 909~]A/dJ v
(3) R=220k~, 5ms/dJv, 0.909UA/dJv
(a)
(b)
tI
t2
t3
(1)
t4
(2)
tI
t2
•
•
(i)
t3 0.
t4 Q
(2)
O_ tI
t2t3t 4
(3) R=220k~, 5ms/div, 0. 909UA/dJ v (c)
(3)
R=220k~, 5ms/dJv, 0. 909~]A/dJv
(d)
Fig. 3. Drop profile, c o r o n a appearance and c u r r e n t waveform a r o u n d the c o r o n a onset voltage ( V = 1.01V¢, Vc: c o r o n a onset voltage). (1) drop profile; (2) still photographs; (3) c o r o n a current. (a) positive tap water-drop (t~ - t 3 = 550 ~s); (b) negative tap-water drop ( t 2 - t~ : 960 ~s); (c) positive distilled-water drop (t2 -- t3 : 550 ~s), (d) negative distilledwater drop (t2 - t3 = 1100 ~s), R : c u r r e n t measuring resistor.
345
°
0 •
o
0 f'-I
11
v
T
0 ..c
0
.~.
t~
0 f...~
0
~'~
I!
I
0
346
"e'l
2~ C,l
0
0
II
I 0
~a
<
0
0 ~'~ c~ tl 0
0
I
347
(i)
(2)
~ er]od stage
of drop elongation of figure (i)]
196]]A/dJ v
(a)
(i)
(2)
period of conical drop tip
(i)
(2)
19.6~]A/dJ v
(c)
39.2]/A/d~ v
(d)
Fig. 5. Drop profile, corona appearance and current waveforrn in the case of corona discharge appearing on a non~onical drop tip (E c = 18.4 kV/cm). (1) drop profile; (2) still photograph of corona discharge; (3) corona current. (a) positive tap-water drop, (2-1): weak streamer corona or pulseless corona, (2-2): streamer corona; (b) negative tap-water drop; (c) positive distilled-water drop; (d) negative distilled-water drop.
348
conductor surface
~.
conductor surface
Fig. 6. Streak photographs of corona discharge under the same applied voltage as that of Fig. 5. (a) positive tap-water drop; (b) negative tap-water drop; (c) positive distilled-water drop ; (d) negative tap-water drop.
the tip as seen in (b) and (d) of Figs. 5 and 6. On the other hand, the shape of the positive drop in the pulseless corona zone is a tapered cylinder for distilled water (Figs. 5(c) and 6 (c)). In the case of a positive tap-water drop, corona discharge manifests two types: one is weak streamers developing from the bright base and the other is vital streamers (Figs. 5(a) and 6(a)). The drop tip in the weak streamer ejects a fine droplet continuously. However, the drop tip becomes conical if the water supply is stopped. At a higher applied voltage, near the flashover voltage, water drips in a manner shown in Figs. 5(b) and (d) and the positive corona becomes vital streamers (Figs. 7(a) and (c)). Negative corona is essentially the same as that at relatively low applied voltage (Figs. 7(b) and (d)). GeneraUy, light emission from the positive drop of tap water shows a long branched streamer during the pulsative current and the emission is confined to a narrow region around the tip of the positive water drop during the pulseless current and of the negative water drop during any waveform of the corona current. In the case of a distilled-water drop, whereas the appearance of corona discharge is almost the same as that for the tap-water drop, the light intensity and propagation length of corona discharge are less than those for tap water.
349 tJme-~
(a) time-~
(c)
conductor surface
time-,,-
(b) conductor surface
time-,-
(d)
Fig. 7. Streak photograph of corona discharge at a higher appled voltage (24.9 kV/cm). (a) positive tap-water drop; (b) negative tap-water drop; (c) positive distilled-water drop; (d) negative distilled-water drop.
These light measurements of corona discharge support the results in the previous paper [2] where corona discharge was investigated from a viewpoint of the current waveform.
350 4. Discussion The head part of the p e n d e n t drop hanging from the conductor in the absence of an applied voltage has an approximately spherical shape at the m o m e n t of its removal from the conductor. Increasing voltage changes its shape so that it becomes close to prolate spheroid (Fig. 3(1)). The distortion ratio of the drop is illustrated as a function of the relative applied voltage to the corona onset as shown in Fig. 8. The disintegration is developed remarkably when the applied voltage reaches the corona onset value. The radius of an equivalent spherical drop at corona onset voltage is about 3.2 m m [1] and is in the region of the surface-disruption mode for the corona onset of Fig. 2. These facts mean that the surface instability is predominant for corona onset in the present experiment. But the vibration of drop surface may also contribute to building the Taylor cone at the drop tip since corona discharge is always developed on the drop during the first period of the drop's oscillation after separating from the neck. From Figs. 3 to 5 three patterns of the drop profile in corona discharge during its disintegration are recognized as shown in Fig. 9 with an increase of the voltage further beyond the corona onset. If the thickness 2t of the p e n d e n t drop is greater than the critical radius for pure corona mode shown by the solid thick line in Fig. 2, the drop tip is always conical as shown in Figs. 9(a) and (b), which means the development of the electrostatic surface instability on the drop. Sometimes the filament is drawn from the conical tip of a highly resistive water drop. On further increasing the applied voltage, a thinner cylindrical drop with an approximately constant radius and hemispherical tip appears (Fig. 9(d)) or a tapered thread-like stream with an atomized region appears (Fig. 9(c), Fig. 5(b), (c) and (d)). Corona discharge for the case of Fig. 9(c) develops around the filament part and the junction of the filament and the conical
2 a/b
I'
0
I
P
I
0.5
1.0
1.5
V/V c
VC: cororla onset voltage, Fig. 8. D i s t o r t i o n r a t i o o f a main d r o p as a f u n c t i o n o f a p p l i e d voltage.
351
'~~"t~pendent' drop
~ flloment
conl~
... " ......
: .........
/
otomlzed
/ region
'/~//~:corona zone
~wrconlcol
tlP
(a)
(b)
(c)
(d)
Fig. 9. Drop profile and its shape i n c o r o n a d i s c h a r g e z o n e . (a) and (b) conical tip produced by the electrostatic instability; (c) and (d) stable surface in c o r o n a z o n e .
pendent drop. Houburg and Melcher [12] showed by using controlled-potential apparatus that corona discharge could occur as a result of the reduction of the filament radius. Calculating the value of the electric field on the stream surface by the charge simulation method, the luminous region of corona discharge in Fig. 5(c) coincides reasonably well with an area where the calculated value becomes larger than the value given by eqn. (4). In the field calculation the equipotential on the filament and the distribution of space charge predicted from the photograph of droplets in the atomized region and the specific charge on the droplet are assumed. It is therefore conceivable that the filament surface behaves essentially as a metallic electrode as stated by Houburg and Melcher and is very stable. Let us now discuss factors determining the tip shape of the elongated pendent drop in corona. Suppose both critical field strengths given by eqns. (2) and (4) axe achieved on the drop, the field strength at the drop surface in corona will remain a constant at its onset level [13, 14]. Therefore the drop surface in corona will always experience the corona onset field. Electric field strengths for the surface instability, Est, and for pure corona onset, Ec, can be predicted for a given radius of a stable drop. When the stable drop is placed in a field beyond the values of Est and Ec, ifEst is greater than Ec, corona discharge will appear on a stable and rounded drop tip. If Ec is greater than Est, two possible cases may be considered: (1) corona discharge occurs on the unstable drop surface since the criterion of the surface instability is lower than the field strength around the drop; and (2) corona discharge will unify the field distribution along the drop surface and may result in the rounded shape of the drop tip. Observation shows that the tip shape of an unelongated drop
352 with large volume in corona is always conical with a sharp tip for a positive c o n d u c t o r and with a slightly r o u n d e d tip for a negative conductor, even if the applied voltage is m u c h higher than the corona onset voltage. It can be argued from the above discussion that if Ec is greater than Est, the above item (1) may occur easily. Therefore, it m a y be concluded that the onset mechanism of corona discharge on a drop is the pure corona m o d e if its tip radius is the same as that of the r o u n d e d tip in corona. Then the radius of the drop having an approximately hemispherical tip in corona was plotted as circles in Fig. 2 which shows the m o d e of the corona onset. All measured values are in the pure corona mode. This is precisely as expected. The measured radius was hardly affected by the water resistivity and the polarity of the conductor. The radius of the undistorted drop at the transition between two corona onset modes, from English and Dawson, with positive polarity was plotted in Fig. 2, where it is assumed that the drop supported on the end of the capillary has Taylor's distortion ratio and that its minor semi-axis o r t h e polar radius is the same as the capillary radius. Except for Dawson's data with a small capillary, the experimental values agree reasonably with the estimation according to the above calculation. Macky [15] has confirmed that the critical field for the surface instability of the drop with 0.835 m m radius is lower than that for pure corona onset and that its radius is also in the region of the surface-disruption mode, as expected (the cross in Fig. 2). Formation of the r o u n d e d tip in corona m a y be important to understand the characteristics of the specific charge in the region of high electric field on the c o n d u c t o r surface. Measurement of the specific charge on a water drop [1, 2] shows that if the filament, as shown in Fig. 9{c), does not appear and corona discharge occurs on the r o u n d e d drop tip, the increasing rate of specific charge with the applied field tends to decrease as compared with that in the case of the conical tip. A possible explanation for this characteristic is the corona effect weakening of the electric field around the drop tip ,and the large drop resulting from the formation of the r o u n d e d tip in the high applied field. 5. Conclusion
Corona onset mechanism on a water drop in the presence of an electric field was discussed to take into account, in addition to air pressure, the drop size. Corona behavior on water drops dripping from a d.c. energized c o n d u c t o r was observed by a rotating camera combined with an image intensifier with a very high gain. The results m a y be summarized as follows. (1) The boundary conditions between two corona onset mechanisms, pure corona onset and onset caused by the surface
353 (3) T h e c o r o n a discharge m e c h a n i s m a n d t h e r e l a t i o n s h i p b e t w e e n t h e m a n n e r in w h i c h a w a t e r d r o p drips a n d t h e c o r o n a b e h a v i o r described in t h e p r e v i o u s p a p e r were c o n f i r m e d t o be c o r r e c t f r o m a v i e w p o i n t o f t h e light emission f r o m c o r o n a discharge.
Acknowledgements T h e a u t h o r s wish t o t h a n k Mr. Y a m a s h i t a f o r his t e c h n i c a l assistance. This w o r k was s u p p o r t e d in p a r t b y a G r a n t - i n - A i d f o r Scientific R e s e a r c h f r o m t h e Ministry o f E d u c a t i o n , Science a n d Culture, J a p a n .
References 1 M. Hara, S. Ishibe and M. Akazaki, Corona discharge and electrical charge on water drops dripping from dc transmission conductors -- An experimental study in laboratory, J. Electrostatics, 6 (1979) 235. 2 M. I-lara, S. Ishibe, S. Sumiyoshitani and M. Akazaki, Electrical corona and specific charge on water drops from a cylindrical conductor with high dc voltage, J. Electrostatics, 8 (1980) 239. 3 W.N. English, Corona discharge from a water drop, Phys. Rev., 74 (1948) 179. 4 K. Arai and Y. Tsunoda, Deformation and discharge of water drop in electric field, Memoirs of the Faculty of Engineering, Kobe University, No. 14 (1968) 61. 5 G.A. Dawson, Pressure dependence of water-drop corona onset and its atmospheric importance, J. Geophysical Res., 74 (1969) 6859. 6 G.A. Dawson, Electrical corona from water-drop surfaces, J. Geophysical Res., 75 (1970) 2153. 7 L. Rayleigh, On the equilibrium of liquid conducting masses charged with electricity, Phil. Mag., 14 (1882) 184. 8 G. Taylor, The disintegration of water drops in an electric field, Proc. R. Soc., Lond., A280 (1964) 383. 9 M.A. Abbas and J. Latham, The disintegration and electrification of charged water drops falling in an electric field, Qt. J. R. Meteorol. Soc., 95 (1969) 63. 10 M. Hara and M. Akazaki, A method for prediction of gaseous discharge threshold voltage in the presence of a conducting particle, J. Electrostatics, 2 (1976) 223. 11 F.W. Peek, Jr., Dielectric Phenomena in High Voltage Engineering, 3rd edn., McGraw Hill, New York, 1929, p. 77. 12 J.F. Hoburg and J.R. Melcher, Current-driven, corona-terminated water jets as sources of charged droplets and audible noise, IEEE Paper No. C73 165-8, IEEE PES Winter Meeting, New York, 1973. 13 R.T. Water, T.E.S. Rickard and W.B. Stark, Electric field measurement in dc corona discharges, 2nd Int. Conf. on Gas Discharge, London, 1972, p. 188. 14 R.T. Water, T.E.S. Rickard and W.B. Stark, Direct measurement of electric field at line conductors during ac corona, Proc. IEE, 119 (1972) 717. 15 W.A. Macky, Some investigations on the deformation and breaking of water drops in electric fields, Proc. R. Soc., Lond., A133 (1931) 565.
339
ONSET MECHANISM AND DEVELOPMENT OF CORONA DISCHARGE ON WATER DROPS DRIPPING FROM A CONDUCTOR UNDER HIGH DIRECT VOLTAGE
MASANORI H A R A
Department of Electrical Engineering, Faculty of Engineering, Kyushu University, Fukuoka (Japan) and M A S A N O R I A K A Z A K I
Department of Energy Conversion Engineering, Graduate School of Engineering Sciences, Kyushu University, Fukuoka (Japan) (Received June 30, 1980; accepted in revised form January 6, 1981)
Summary Corona onset mechanism was studied by an analytical method and onset and development of corona discharge on water drops dripping from a conductor under high direct voltages were investigated by simultaneous recordings of the light emission, corona current and drop profile. The analytical study shows that corona onset mechanism depends on the drop size and the ambient air pressure. Although at about atmospheric air pressure the electrostatic instabilitycauses discharge on the surface of a water drop dripping from a conductor with a d.c. high voltage, in a higher electric field,beyond the corona onset voltage, corona can develop on a stable surface of the water drop whose radius is smaller than a criticalvalue depending on the ambient air pressure. The criticalradius for the appearance of this corona discharge mechanism could be related to the radius for the transition between two corona onset mechanisms: pure corona onset and onset caused by the surface-disruption of the drop at a given air pressure. Time-resolved photographs of corona discharge support descriptions of the corona discharge mechanism discussed in previous papers.
1. Introduction The onset mechanism of corona discharge on a water drop in an electric field has been investigated by English [3], Arai and Tsunoda [4] and Dawson [5, 6]. According to them, there axe two modes of the corona onset mechanism: (1) surface-disruption mode: the onset of corona discharge from a water drop at a b o u t atmospheric pressure is determined by the electrostatic instability of the drop surface; (2) pure corona mode: at reduced pressure, positive corona onset can occur on the stable drop surface. The criterion for the transition b e t w e e n these two modes, however, is n o t fully understood. As is the case for a water drop on a transmission c o n d u c t o r in foul weather when the drop hangs from the c o n d u c t o r under high direct voltages, the shape
0304-3886/81/0000---0000/$02.50 © 1981 Elsevier Scientific Publishing Company
340
and size of the pendent drop change with the extent of its disintegration and the applied voltage. At a low voltage, the drop consists of the head and neck which turn into a mother and satellites when the drop breaks away. With increasing voltage, the drop becomes slender and it becomes difficult to distinguish between the head and the neck. Hence, in a study of the onset mechanism and development of corona discharge it may be necessary to consider the effect of the changing radius of the drop-tip curvature with the applied voltage, on the onset field strength of pure corona and on that of the surface instability on the drop. The purpose of this paper is to show the corona onset mechanism on a water drop dripping from a high voltage conductor as a function of the air pressure and the drop size and to clarify the relationship between the shape of the droptip in corona discharge and the corona onset mechanism. Moreover, discharge processes described in a previous paper [2] are confirmed to be correct by using time-resolved photographs of corona discharge. 2. Onset mechanism of corona discharge on water drop
2.1 Criterion for electrostatic surface instability When an electric field acts on the surface of a water drop, two types of surface instability, Rayleigh and Taylor instabilities [7, 8], or in a more general case a combination of the two, can develop if electrical corona on the drop is suppressed. Dawson appiied Rayleigh's and Taylor's criteria to compare the field strengths for their instabilities at the drop surface and showed the critical field strengths (in kV/cm) were given as follows [5] : (a) for the Rayleigh instability of a charged drop, Es~ = 18.07/~/r~
(1)
where r~ (in cm) is the radius of the undistorted drop; and (b) for the Taylor instability of an uncharged drop, Est = 14.6/~/r~
(2)
where r~ (in cm) is the polar radius of the spheroidal drop having a distortion ratio of 1.9. In most cases, for a mixture of the above instabilities, the critical field strength lies between E~ and Est. Moreover, the experimental values using the drop point to plane gap agree reasonably well with the eqn. (2) [5, 6]. Therefore, although eqn. (2) is the critical field strength for the uncharged drop, Est will be used later to discuss experimental data on the drop shape at corona onset.
2.2 Threshold field strength o f pure corona Threshold field strength of pure corona on the positive drop surface may be determined by the streamer breakdown criterion,
~
2
Xi
(a -- fl)dx = K
K = 10 ~ 20
(3)
341
where a and ~ are the first Townsend ionization coefficient and the electron attachment coefficient respectively, xl is the position in a gap where the electric field strength is the highest and x2 is the position where ~ = ~. This is based on the fact that the positive drop at pure corona onset exhibits the corona onset phenomena observed with a metal point. Only a little analytical study has been made concerning the criterion of corona discharge from a particle or water drop in the presence of the electric field. Hara and Akazaki [10] pointed out that the critical field strength of discharge onset (in kV/cm) on a metallic spherical particle moving in a parallel plane gap can be predicted accurately by the following semi~mpirical equation: Ec = 31.05p (1 + 0 . 3 0 1 / q ~ o )
(4)
where p (in atm) is the air pressure. Although the distribution of electric field around the sphere is not exactly the same as that around the spheroid under the Taylor condition, eqn. (4) will be used to discuss later the corona onset mechanism on the water drop because the value obtained from eqn. (4) is near ly equal to that obtained by the well known Peek formula [11] which can be used for a smooth cylindrical electrode. (kVlcm) 140
120
i00
,,..
80 L
~60
.... .__
40
I~
20
-
Ec(O'6°tm)~
~Ec(P=lotm)
.......
Est
0
I 1
0
I 2 (film)
rd
0 I ]
I
I
I
1
2 b
3
I 2
t 3 ro
(rr~)
I 4
(ram)
Fig. I. Onset field strengths of corona discharge, Ec, and electrostatic surface instability, Est. p, air pressure; rd, radius of the drop tip; b and r0, minor semi-axis and undistorted radius of the spheroid assumed to be under the Taylor condition.
342
2.3 Onset mechanism o f corona discharge on water drop The primary process for corona onset from the pendent drop can be determined by a comparison between the values of Est and Ec on the drop tip. But the shape of the drop tip during its elongation changes in a complicated fashion with time and the applied voltage. Then the critical field strengths of the surface instability and corona onset on the tip of the pendent drop are approxiI t mated by eqns. (2) and (4) where rp and r0 are replaced by the radius of curvature r d of the drop tip. Est and Ee axe illustrated at pressures of 0.6, 0.8 and 1 atm as a function of rd in Fig. 1. If the drop shape is spheroidal under Taylor's condition, the abscissa rd can be converted to the semi-axis b or the undistorted drop radius r0 by the equation b -- 1.9rd or r0 -- 2.353rd. Since the pure corona onset mode appears in the region where Ec is less than Est, the thin full and broken curves in the figure show the regions for the pure corona mode and the surface disruption mode for corona onset respectively. The boundary between these modes depends on the air pressure and the drop size as shown in Fig. 2. This figure also shows that the pure corona mode may develop at about atmospheric air pressure if the radius r0 of the drop tip becomes smaller than 0.674 ram. 4 (ran)
ro
2
Pure Corona Mode
0 0,5
i 0,6
i 0.7
I 0.8 P
I 0.9
I 1.0
I l.l (atm)
Fig. 2. Transition c o n d i t i o n s b e t w e e n t w o c o r o n a onset modes. - - , calculated value for the b o u n d a r y ; • e, e x p e r i m e n t a l value of the limit for t h e pure c o r o n a m o d e by English [3] ; • . . . . •, e x p e r i m e n t a l value o f the limit for the pure c o r o n a m o d e by Dawson [5] ; ×, e x p e r i m e n t a l value for t h e surface-disruption m o d e by Macky [ 15]; o, present results for c o r o n a d e v e l o p m e n t o n t h e stable drop surface, i.e. p u r e c o r o n a m o d e for c o r o n a onset.
343 3. Onset and development o f corona discharge on a water drop dripping from a d.c. energized conductor
3.1 Observation of drop profile and corona discharge Experimental apparatus Corona discharge is photographed by a still camera combined with an imageintensifier tube (Hitachi, HS-690) having a maximum gain of 8.2 × 104. To take a streak photograph showing the discharge process, the camera was also used as a rotating camera which was mounted loosely on the tripod and was rotated manually. The streak speed of the camera was not measured but can be found from a comparison of the deformation process of the pendent drop, the waveform of the corona current and the streak photograph. Since the mechanism of corona discharge is affected by the water resistivity, either distilled water or tap water was used to study the relationship between the corona discharge process and the drop profile. ACSR conductor of 810 mm 2 was used as an inner conductor of the coaxial cylindrical electrode. The remainder of the apparatus has been described in previous papers [1, 2].
Drop profile and onset and development of corona discharge Typical photographs of corona discharge are shown together with the corona current and drop profile for various values of the applied voltage in Figs. 3--5, where the size of the object taken in photographs has nearly the same dimension in each item. But the streak photograph is slightly distorted due to aberration in the image intensifier. Details of the relationship between corona current and the deformation process of the drop can be seen for a wide range of the applied voltage in the Hara et al. [2]. When the applied voltage is about 1% higher than the corona onset voltage, the light emission from the main drop tip and from the region between the main drop and the neck is observed as given in Fig. 3 (2). As the voltage increases, the corona discharge appears on the drop tip elongating from the conductor and on both terminals of the drop disconnecting from the conductor (Fig. 4). It is confirmed from this figure that the current pulses appearing during the period of the current decay are mainly due to the corona after the drop parts from the conductor. As seen in (2) of Fig. 4 (c), discharge ceases temporarily during the period of the current decrease in each current loop in which the drop tip has a rounded shape [2]. This event can clearly be observed for distilled water at a field strength on the conductor of about 7 kV/cm. The drop shape in the corona zone is always conical and its conical tip has a sharp edge or a short thin filament. When the field strength on the conductor becomes greater than about 15 kV/cm, the drop profile in the corona discharge zone is.affected by the water resistivity and the voltage polarity. Figs. 5 and 6 show the drop profiles and the appearance of corona discharge at the same applied voltage. The tip of an elongated negative drop always has a rounded shape and corona appears on
344
tI
t2
t3
(i)
tI
tI
t4
(2)
t2
t4
(I)
(2)
tI
t 2 t 3 t4
t3
t2t 3 t 4
(3) R=220kQ, 5ms/dJv, 0. 909~]A/dJ v
(3) R=220k~, 5ms/dJv, 0.909UA/dJv
(a)
(b)
tI
t2
t3
(1)
t4
(2)
tI
t2
•
•
(i)
t3 0.
t4 Q
(2)
O_ tI
t2t3t 4
(3) R=220k~, 5ms/div, 0. 909UA/dJ v (c)
(3)
R=220k~, 5ms/dJv, 0. 909~]A/dJv
(d)
Fig. 3. Drop profile, c o r o n a appearance and c u r r e n t waveform a r o u n d the c o r o n a onset voltage ( V = 1.01V¢, Vc: c o r o n a onset voltage). (1) drop profile; (2) still photographs; (3) c o r o n a current. (a) positive tap water-drop (t~ - t 3 = 550 ~s); (b) negative tap-water drop ( t 2 - t~ : 960 ~s); (c) positive distilled-water drop (t2 -- t3 : 550 ~s), (d) negative distilledwater drop (t2 - t3 = 1100 ~s), R : c u r r e n t measuring resistor.
345
°
0 •
o
0 f'-I
11
v
T
0 ..c
0
.~.
t~
0 f...~
0
~'~
I!
I
0
346
"e'l
2~ C,l
0
0
II
I 0
~a
<
0
0 ~'~ c~ tl 0
0
I
347
(i)
(2)
~ er]od stage
of drop elongation of figure (i)]
196]]A/dJ v
(a)
(i)
(2)
period of conical drop tip
(i)
(2)
19.6~]A/dJ v
(c)
39.2]/A/d~ v
(d)
Fig. 5. Drop profile, corona appearance and current waveforrn in the case of corona discharge appearing on a non~onical drop tip (E c = 18.4 kV/cm). (1) drop profile; (2) still photograph of corona discharge; (3) corona current. (a) positive tap-water drop, (2-1): weak streamer corona or pulseless corona, (2-2): streamer corona; (b) negative tap-water drop; (c) positive distilled-water drop; (d) negative distilled-water drop.
348
conductor surface
~.
conductor surface
Fig. 6. Streak photographs of corona discharge under the same applied voltage as that of Fig. 5. (a) positive tap-water drop; (b) negative tap-water drop; (c) positive distilled-water drop ; (d) negative tap-water drop.
the tip as seen in (b) and (d) of Figs. 5 and 6. On the other hand, the shape of the positive drop in the pulseless corona zone is a tapered cylinder for distilled water (Figs. 5(c) and 6 (c)). In the case of a positive tap-water drop, corona discharge manifests two types: one is weak streamers developing from the bright base and the other is vital streamers (Figs. 5(a) and 6(a)). The drop tip in the weak streamer ejects a fine droplet continuously. However, the drop tip becomes conical if the water supply is stopped. At a higher applied voltage, near the flashover voltage, water drips in a manner shown in Figs. 5(b) and (d) and the positive corona becomes vital streamers (Figs. 7(a) and (c)). Negative corona is essentially the same as that at relatively low applied voltage (Figs. 7(b) and (d)). GeneraUy, light emission from the positive drop of tap water shows a long branched streamer during the pulsative current and the emission is confined to a narrow region around the tip of the positive water drop during the pulseless current and of the negative water drop during any waveform of the corona current. In the case of a distilled-water drop, whereas the appearance of corona discharge is almost the same as that for the tap-water drop, the light intensity and propagation length of corona discharge are less than those for tap water.
349 tJme-~
(a) time-~
(c)
conductor surface
time-,,-
(b) conductor surface
time-,-
(d)
Fig. 7. Streak photograph of corona discharge at a higher appled voltage (24.9 kV/cm). (a) positive tap-water drop; (b) negative tap-water drop; (c) positive distilled-water drop; (d) negative distilled-water drop.
These light measurements of corona discharge support the results in the previous paper [2] where corona discharge was investigated from a viewpoint of the current waveform.
350 4. Discussion The head part of the p e n d e n t drop hanging from the conductor in the absence of an applied voltage has an approximately spherical shape at the m o m e n t of its removal from the conductor. Increasing voltage changes its shape so that it becomes close to prolate spheroid (Fig. 3(1)). The distortion ratio of the drop is illustrated as a function of the relative applied voltage to the corona onset as shown in Fig. 8. The disintegration is developed remarkably when the applied voltage reaches the corona onset value. The radius of an equivalent spherical drop at corona onset voltage is about 3.2 m m [1] and is in the region of the surface-disruption mode for the corona onset of Fig. 2. These facts mean that the surface instability is predominant for corona onset in the present experiment. But the vibration of drop surface may also contribute to building the Taylor cone at the drop tip since corona discharge is always developed on the drop during the first period of the drop's oscillation after separating from the neck. From Figs. 3 to 5 three patterns of the drop profile in corona discharge during its disintegration are recognized as shown in Fig. 9 with an increase of the voltage further beyond the corona onset. If the thickness 2t of the p e n d e n t drop is greater than the critical radius for pure corona mode shown by the solid thick line in Fig. 2, the drop tip is always conical as shown in Figs. 9(a) and (b), which means the development of the electrostatic surface instability on the drop. Sometimes the filament is drawn from the conical tip of a highly resistive water drop. On further increasing the applied voltage, a thinner cylindrical drop with an approximately constant radius and hemispherical tip appears (Fig. 9(d)) or a tapered thread-like stream with an atomized region appears (Fig. 9(c), Fig. 5(b), (c) and (d)). Corona discharge for the case of Fig. 9(c) develops around the filament part and the junction of the filament and the conical
2 a/b
I'
0
I
P
I
0.5
1.0
1.5
V/V c
VC: cororla onset voltage, Fig. 8. D i s t o r t i o n r a t i o o f a main d r o p as a f u n c t i o n o f a p p l i e d voltage.
351
'~~"t~pendent' drop
~ flloment
conl~
... " ......
: .........
/
otomlzed
/ region
'/~//~:corona zone
~wrconlcol
tlP
(a)
(b)
(c)
(d)
Fig. 9. Drop profile and its shape i n c o r o n a d i s c h a r g e z o n e . (a) and (b) conical tip produced by the electrostatic instability; (c) and (d) stable surface in c o r o n a z o n e .
pendent drop. Houburg and Melcher [12] showed by using controlled-potential apparatus that corona discharge could occur as a result of the reduction of the filament radius. Calculating the value of the electric field on the stream surface by the charge simulation method, the luminous region of corona discharge in Fig. 5(c) coincides reasonably well with an area where the calculated value becomes larger than the value given by eqn. (4). In the field calculation the equipotential on the filament and the distribution of space charge predicted from the photograph of droplets in the atomized region and the specific charge on the droplet are assumed. It is therefore conceivable that the filament surface behaves essentially as a metallic electrode as stated by Houburg and Melcher and is very stable. Let us now discuss factors determining the tip shape of the elongated pendent drop in corona. Suppose both critical field strengths given by eqns. (2) and (4) axe achieved on the drop, the field strength at the drop surface in corona will remain a constant at its onset level [13, 14]. Therefore the drop surface in corona will always experience the corona onset field. Electric field strengths for the surface instability, Est, and for pure corona onset, Ec, can be predicted for a given radius of a stable drop. When the stable drop is placed in a field beyond the values of Est and Ec, ifEst is greater than Ec, corona discharge will appear on a stable and rounded drop tip. If Ec is greater than Est, two possible cases may be considered: (1) corona discharge occurs on the unstable drop surface since the criterion of the surface instability is lower than the field strength around the drop; and (2) corona discharge will unify the field distribution along the drop surface and may result in the rounded shape of the drop tip. Observation shows that the tip shape of an unelongated drop
352 with large volume in corona is always conical with a sharp tip for a positive c o n d u c t o r and with a slightly r o u n d e d tip for a negative conductor, even if the applied voltage is m u c h higher than the corona onset voltage. It can be argued from the above discussion that if Ec is greater than Est, the above item (1) may occur easily. Therefore, it m a y be concluded that the onset mechanism of corona discharge on a drop is the pure corona m o d e if its tip radius is the same as that of the r o u n d e d tip in corona. Then the radius of the drop having an approximately hemispherical tip in corona was plotted as circles in Fig. 2 which shows the m o d e of the corona onset. All measured values are in the pure corona mode. This is precisely as expected. The measured radius was hardly affected by the water resistivity and the polarity of the conductor. The radius of the undistorted drop at the transition between two corona onset modes, from English and Dawson, with positive polarity was plotted in Fig. 2, where it is assumed that the drop supported on the end of the capillary has Taylor's distortion ratio and that its minor semi-axis o r t h e polar radius is the same as the capillary radius. Except for Dawson's data with a small capillary, the experimental values agree reasonably with the estimation according to the above calculation. Macky [15] has confirmed that the critical field for the surface instability of the drop with 0.835 m m radius is lower than that for pure corona onset and that its radius is also in the region of the surface-disruption mode, as expected (the cross in Fig. 2). Formation of the r o u n d e d tip in corona m a y be important to understand the characteristics of the specific charge in the region of high electric field on the c o n d u c t o r surface. Measurement of the specific charge on a water drop [1, 2] shows that if the filament, as shown in Fig. 9{c), does not appear and corona discharge occurs on the r o u n d e d drop tip, the increasing rate of specific charge with the applied field tends to decrease as compared with that in the case of the conical tip. A possible explanation for this characteristic is the corona effect weakening of the electric field around the drop tip ,and the large drop resulting from the formation of the r o u n d e d tip in the high applied field. 5. Conclusion
Corona onset mechanism on a water drop in the presence of an electric field was discussed to take into account, in addition to air pressure, the drop size. Corona behavior on water drops dripping from a d.c. energized c o n d u c t o r was observed by a rotating camera combined with an image intensifier with a very high gain. The results m a y be summarized as follows. (1) The boundary conditions between two corona onset mechanisms, pure corona onset and onset caused by the surface
353 (3) T h e c o r o n a discharge m e c h a n i s m a n d t h e r e l a t i o n s h i p b e t w e e n t h e m a n n e r in w h i c h a w a t e r d r o p drips a n d t h e c o r o n a b e h a v i o r described in t h e p r e v i o u s p a p e r were c o n f i r m e d t o be c o r r e c t f r o m a v i e w p o i n t o f t h e light emission f r o m c o r o n a discharge.
Acknowledgements T h e a u t h o r s wish t o t h a n k Mr. Y a m a s h i t a f o r his t e c h n i c a l assistance. This w o r k was s u p p o r t e d in p a r t b y a G r a n t - i n - A i d f o r Scientific R e s e a r c h f r o m t h e Ministry o f E d u c a t i o n , Science a n d Culture, J a p a n .
References 1 M. Hara, S. Ishibe and M. Akazaki, Corona discharge and electrical charge on water drops dripping from dc transmission conductors -- An experimental study in laboratory, J. Electrostatics, 6 (1979) 235. 2 M. I-lara, S. Ishibe, S. Sumiyoshitani and M. Akazaki, Electrical corona and specific charge on water drops from a cylindrical conductor with high dc voltage, J. Electrostatics, 8 (1980) 239. 3 W.N. English, Corona discharge from a water drop, Phys. Rev., 74 (1948) 179. 4 K. Arai and Y. Tsunoda, Deformation and discharge of water drop in electric field, Memoirs of the Faculty of Engineering, Kobe University, No. 14 (1968) 61. 5 G.A. Dawson, Pressure dependence of water-drop corona onset and its atmospheric importance, J. Geophysical Res., 74 (1969) 6859. 6 G.A. Dawson, Electrical corona from water-drop surfaces, J. Geophysical Res., 75 (1970) 2153. 7 L. Rayleigh, On the equilibrium of liquid conducting masses charged with electricity, Phil. Mag., 14 (1882) 184. 8 G. Taylor, The disintegration of water drops in an electric field, Proc. R. Soc., Lond., A280 (1964) 383. 9 M.A. Abbas and J. Latham, The disintegration and electrification of charged water drops falling in an electric field, Qt. J. R. Meteorol. Soc., 95 (1969) 63. 10 M. Hara and M. Akazaki, A method for prediction of gaseous discharge threshold voltage in the presence of a conducting particle, J. Electrostatics, 2 (1976) 223. 11 F.W. Peek, Jr., Dielectric Phenomena in High Voltage Engineering, 3rd edn., McGraw Hill, New York, 1929, p. 77. 12 J.F. Hoburg and J.R. Melcher, Current-driven, corona-terminated water jets as sources of charged droplets and audible noise, IEEE Paper No. C73 165-8, IEEE PES Winter Meeting, New York, 1973. 13 R.T. Water, T.E.S. Rickard and W.B. Stark, Electric field measurement in dc corona discharges, 2nd Int. Conf. on Gas Discharge, London, 1972, p. 188. 14 R.T. Water, T.E.S. Rickard and W.B. Stark, Direct measurement of electric field at line conductors during ac corona, Proc. IEE, 119 (1972) 717. 15 W.A. Macky, Some investigations on the deformation and breaking of water drops in electric fields, Proc. R. Soc., Lond., A133 (1931) 565.