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Statistical investigation of breakdown in cryogenic liquids
Journal of Electrostatics, 13 (1982) 85--89 Elsevier Scientific Publishing Company, Amsterdam - - Printed in The Netherlands
85
Short Communication STATISTICAL INVESTIGATION OF B R E A K D O W N IN CRYOGENIC LIQUIDS
C. F R E I and M. NITTMANN
Section de Physique, Universit$ de Gen~ve, 1211 Geneva 4 (Switzerland) (Received December 16, 1981; accepted January 26, 1982)
Introduction The great majority of breakdown studies on dielectric liquids have been performed by measuring their dielectric strength with a steadily rising voltage ramp and by determining the voltage at which breakdown occurs. Indeed, cryogenic liquids are no exception to this rule. An influence of liquid motion on the b r e a k d o w n behaviour of liquid nitrogen has been made evident using this technique [1]. Under the conditions given in [1] for the geometry of the electrodes and the applied voltages, the mean breakdown strength of liquid nitrogen increases from 180 kV/cm to 230 kV/cm when the liquid is caused to flow with a velocity of 2.6 m/s. In addition the statistical distribution of the individual values of breakdown strength, which conforms to that of extreme values when the liquid is stationary, becomes Gaussian when the liquid moves past the electrodes. Similar findings have previously been reported for a hydrocarbon oil [2]. We have been able to show that by measuring the breakdown time lags the influence of liquid motion on breakdown can be viewed in terms of a simple statistical description [ 3 ] : In a motionless hydrocarbon liquid the time lags to breakdown are distributed according to an exponentially decreasing function which suggests a mechanism based on a Poisson process. On the other hand, when the dielectric liquid is moving with respect to the electrode surfaces, the exponentially distributed time lags become convoluted with a Gaussian function. Such a Gaussian c o m p o n e n t would result from a formative process. It is the purpose of our present investigation to see whether or n o t electric breakdown in cryogenic liquids fits into the same framework.
Experimental arrangement In our first approach to the question we have built a cryogenic system for liquid nitrogen. The design of the apparatus corresponds to standard practice and is shown schematically in Fig. 1. The electrodes (12, 13) are made of copper tubing (outside diameter 4 cm), m o u n t e d coaxiaUy. This geometry
0304-3886/82/0000--0000/$02.75
© 1982 Elsevier Scientific Publishing Company
86
® • ,\\ ,\
~\\
\ "\
",\
\
",\
(
Fig. 1. Schematic view of cryostat for time lag measurements: (1) dewar and vessel for outer bath, (2) copper vessel for inner bath, (3) supporting structure, (4) dielectric liquid reservoir, (5) liquid nitrogen inlet of outer bath, (6) liquid nitrogen inlet of inner bath, (7) liquid nitrogen inlet of reservoir, (8) high voltage connection, (9) step motor drive for upper electrode, {10) sapphire guides, (11 ) inductive transducer for gap size measurement, (12) upper electrode (Cu), (13) lower electrode (Cu), (14) dielectric liquid inlet, (15) stirrer.
enables the dielectric liquid to flow radially between the electrodes when a pressure difference is applied between the inner bath (2) and the reservoir (4). The reservoir contains the dielectric liquid to be tested; in accordance with our previous practice, we use a suspension of fine conductive particles of a few pm in diameter. These are introduced into the reservoir through one of the tubes of the supporting structure (3). A stirrer (15) keeps the powder in suspension. Working with conductive-particle suspensions makes the use of low voltages and high test rates possible. Rectangular pulses of 600 V are applied from a transistor generator which quenches approximately 1 ps after voltage collapse. The gap between the electrodes is adjusted externally.
87
The size of the gap, assuming a few tens of ~m, is measured by an inductive transducer (11) with a precision of about 2 p m that is m o u n t e d in the immediate proximity of the electrodes and submerged in liquid nitrogen. The intervals between successive tests are in the millisecond range. The time lags, r, defined by the period from the application of the step voltage until the onset of the discharge current, are recorded by means of a data acquisition system which also calculates and plots their statistical distribution (Fig. 2).
100!N .:"
r.~.
10-
(a) •
•
0@••
•
•
•
T
0
1000
2000
ps
3000
N
100
(b)
10 : ' ~ , . . . . . .
..'-[. •
0
500
o,,o
ps
•
•
1000
Fig. 2. E x a m p l e o f t i m e lag d i s t r i b u t i o n s o f liquid n i t r o g e n n e a r boiling t e m p e r a t u r e w i t h 0 . 0 8 g/l g r a p h i t e , r e c t a n g u l a r t e s t pulses UB = 6 0 0 V, g = 55 urn, (a) liquid nitrogen flowing, rf = 4 6 0 us, rs = 7 6 0 us, ( b ) s t a t i o n a r y , ~s = 2 4 0 us.
Results
The first results of time lag measurements with a cryogenic liquid demonstrate that such liquids behave essentially like other room-temperature insulating liquids. T h e y exhibit statistically distributed time lags whereby the frequency of occurrence of long delays fades away exponentially. Qualitatively this was shown to be true for u n c o n t a m i n a t e d liquid nitrogen. However, the high breakdown strength and the low voltage level with which we work at present imply that gap sizes are too small to enable reliable measurements. As we have n o t e d before, a suspension of conductive particles greatly reduces the experimental difficulties without changing the basic features of breakdown in liquids. The time lag distributions of Fig. 2 have been obtained
88 with a volume concentration of approximately 0.003% of graphite powder in liquid nitrogen. They closely resemble the distributions we recorded with hydrocarbon oil or water [ 3 ] . Measurements in a moving liquid were always easier to perform than in immobile liquid; this is mainly due to sedimentation of the suspended particles. In liquid nitrogen the effect is worse, so that stable discharge conditions are difficult to obtain with the liquid at rest. Therefore the presence of a Gaussian c o m p o n e n t in the time lag distribution of flowing liquid nitrogen shows up clearly (Fig. 2a). Its absence in the stationary liquid could only be ascertained in a few cases (Fig. 2b) and remains to be confirmed by further experiments. The results of the measurements with liquid nitrogen moving with respect to the electrodes are shown in Fig. 3. A plot of the characteristic time, %,
10-3!
%
S 10-4. 10-5 . 10-6 .
UB
(Q) 0
260
16o
360
10-3! Tf S
46o c m //
lO-k
J f
lo-6. o
2o
4'o
6'o
Fig. 3. Plot of (a) characteristic time, rs, versus applied mean field strength, UB/g, (b) formative time, rf, versus gap, g, for flowing liquid nitrogen near boiling temperature with 0.4 g/l graphite, rectangular test pulses, UB = 600 V.
of the exponential part of the time lag distributions as a function of the apparent field strength, UB/g, is shown in Fig. 3a. Although the characteristic times on the plot show much scatter they essentially follow the well known pattern of an exponential law with respect to the inverse of the gap, g. Also the formative times, rf (Fig. 3b), behave similarly to those for hydro-
89
carbon liquids. As a matter of fact, they almost coincide with the formative times for paraffinic oils [3]. D i s c u s s i o n and c o n c l u s i o n
It is our main concern to emphasize the similarity which exists, with respect to the statistics of the breakdown time lags, between liquid nitrogen and the more c o m m o n liquids like h y d r o c a r b o n oils, alcohols, water, etc., so far studied. This is, of course, complementary to the similarity which exists for the statistics of dielectric strength measurements with a steadily rising voltage. The argument is weighty considering the drastic change which occurs when a liquid, initially immobile, is caused to flow (typically at velocities, in m/s, of a few tenths). At rest, breakdown voltages are known to o b e y the statistics of extreme values. This fact, however, appears to be purely accidental, since it can be shown that the assumption of a statistical behaviour of time lags according to a Poisson process and the further assumption of an exponential dependence of the mean time lag on the electric field lead to a Fisher---Tippett t y p e probability density distribution of the b r e a k d o w n strength. Our experimental results seem to corroborate these premises, so that the time lag measurements of liquid nitrogen strengthen the idea of a general breakdown mechanism, valid for dielectric liquids of various composition (a restriction to short timescale breakdown events should be made, however). The formative process which occurs whenever a dielectric liquid is perturbed, for instance as a consequence of motion, invariably modifies the statistics and brings it close to the Gaussian law. Acknowledgements
It is a pleasure to acknowledge the continuing interest and financial support of the Ateliers des Charmilles S.A. We would like to thank R. Martin for contributing the transistorized high-voltage pulse generator and G. R e y Mermier for most of the remaining electronic circuitry. References 1 L. Centurioni, G. Molinari and A. Viviani, L'Energia Elettrica, 2 (1975) 102. L. Centurioni, B. Delfino, G. Molinari and A. Viviani, Proc. of 5th Int. Conf. on Conduction and Breakdown in Dielectric Liquids, 1975, p. 221. 2 J.K. Nelson, B. Salvage and W.A. Sharpley, Proc. IEE, 118 (1971) 388. 3 B. Bommeli, C. Frei and A. Ratajski, J. Electrostatics, 7 (1979) 123.
85
Short Communication STATISTICAL INVESTIGATION OF B R E A K D O W N IN CRYOGENIC LIQUIDS
C. F R E I and M. NITTMANN
Section de Physique, Universit$ de Gen~ve, 1211 Geneva 4 (Switzerland) (Received December 16, 1981; accepted January 26, 1982)
Introduction The great majority of breakdown studies on dielectric liquids have been performed by measuring their dielectric strength with a steadily rising voltage ramp and by determining the voltage at which breakdown occurs. Indeed, cryogenic liquids are no exception to this rule. An influence of liquid motion on the b r e a k d o w n behaviour of liquid nitrogen has been made evident using this technique [1]. Under the conditions given in [1] for the geometry of the electrodes and the applied voltages, the mean breakdown strength of liquid nitrogen increases from 180 kV/cm to 230 kV/cm when the liquid is caused to flow with a velocity of 2.6 m/s. In addition the statistical distribution of the individual values of breakdown strength, which conforms to that of extreme values when the liquid is stationary, becomes Gaussian when the liquid moves past the electrodes. Similar findings have previously been reported for a hydrocarbon oil [2]. We have been able to show that by measuring the breakdown time lags the influence of liquid motion on breakdown can be viewed in terms of a simple statistical description [ 3 ] : In a motionless hydrocarbon liquid the time lags to breakdown are distributed according to an exponentially decreasing function which suggests a mechanism based on a Poisson process. On the other hand, when the dielectric liquid is moving with respect to the electrode surfaces, the exponentially distributed time lags become convoluted with a Gaussian function. Such a Gaussian c o m p o n e n t would result from a formative process. It is the purpose of our present investigation to see whether or n o t electric breakdown in cryogenic liquids fits into the same framework.
Experimental arrangement In our first approach to the question we have built a cryogenic system for liquid nitrogen. The design of the apparatus corresponds to standard practice and is shown schematically in Fig. 1. The electrodes (12, 13) are made of copper tubing (outside diameter 4 cm), m o u n t e d coaxiaUy. This geometry
0304-3886/82/0000--0000/$02.75
© 1982 Elsevier Scientific Publishing Company
86
® • ,\\ ,\
~\\
\ "\
",\
\
",\
(
Fig. 1. Schematic view of cryostat for time lag measurements: (1) dewar and vessel for outer bath, (2) copper vessel for inner bath, (3) supporting structure, (4) dielectric liquid reservoir, (5) liquid nitrogen inlet of outer bath, (6) liquid nitrogen inlet of inner bath, (7) liquid nitrogen inlet of reservoir, (8) high voltage connection, (9) step motor drive for upper electrode, {10) sapphire guides, (11 ) inductive transducer for gap size measurement, (12) upper electrode (Cu), (13) lower electrode (Cu), (14) dielectric liquid inlet, (15) stirrer.
enables the dielectric liquid to flow radially between the electrodes when a pressure difference is applied between the inner bath (2) and the reservoir (4). The reservoir contains the dielectric liquid to be tested; in accordance with our previous practice, we use a suspension of fine conductive particles of a few pm in diameter. These are introduced into the reservoir through one of the tubes of the supporting structure (3). A stirrer (15) keeps the powder in suspension. Working with conductive-particle suspensions makes the use of low voltages and high test rates possible. Rectangular pulses of 600 V are applied from a transistor generator which quenches approximately 1 ps after voltage collapse. The gap between the electrodes is adjusted externally.
87
The size of the gap, assuming a few tens of ~m, is measured by an inductive transducer (11) with a precision of about 2 p m that is m o u n t e d in the immediate proximity of the electrodes and submerged in liquid nitrogen. The intervals between successive tests are in the millisecond range. The time lags, r, defined by the period from the application of the step voltage until the onset of the discharge current, are recorded by means of a data acquisition system which also calculates and plots their statistical distribution (Fig. 2).
100!N .:"
r.~.
10-
(a) •
•
0@••
•
•
•
T
0
1000
2000
ps
3000
N
100
(b)
10 : ' ~ , . . . . . .
..'-[. •
0
500
o,,o
ps
•
•
1000
Fig. 2. E x a m p l e o f t i m e lag d i s t r i b u t i o n s o f liquid n i t r o g e n n e a r boiling t e m p e r a t u r e w i t h 0 . 0 8 g/l g r a p h i t e , r e c t a n g u l a r t e s t pulses UB = 6 0 0 V, g = 55 urn, (a) liquid nitrogen flowing, rf = 4 6 0 us, rs = 7 6 0 us, ( b ) s t a t i o n a r y , ~s = 2 4 0 us.
Results
The first results of time lag measurements with a cryogenic liquid demonstrate that such liquids behave essentially like other room-temperature insulating liquids. T h e y exhibit statistically distributed time lags whereby the frequency of occurrence of long delays fades away exponentially. Qualitatively this was shown to be true for u n c o n t a m i n a t e d liquid nitrogen. However, the high breakdown strength and the low voltage level with which we work at present imply that gap sizes are too small to enable reliable measurements. As we have n o t e d before, a suspension of conductive particles greatly reduces the experimental difficulties without changing the basic features of breakdown in liquids. The time lag distributions of Fig. 2 have been obtained
88 with a volume concentration of approximately 0.003% of graphite powder in liquid nitrogen. They closely resemble the distributions we recorded with hydrocarbon oil or water [ 3 ] . Measurements in a moving liquid were always easier to perform than in immobile liquid; this is mainly due to sedimentation of the suspended particles. In liquid nitrogen the effect is worse, so that stable discharge conditions are difficult to obtain with the liquid at rest. Therefore the presence of a Gaussian c o m p o n e n t in the time lag distribution of flowing liquid nitrogen shows up clearly (Fig. 2a). Its absence in the stationary liquid could only be ascertained in a few cases (Fig. 2b) and remains to be confirmed by further experiments. The results of the measurements with liquid nitrogen moving with respect to the electrodes are shown in Fig. 3. A plot of the characteristic time, %,
10-3!
%
S 10-4. 10-5 . 10-6 .
UB
(Q) 0
260
16o
360
10-3! Tf S
46o c m //
lO-k
J f
lo-6. o
2o
4'o
6'o
Fig. 3. Plot of (a) characteristic time, rs, versus applied mean field strength, UB/g, (b) formative time, rf, versus gap, g, for flowing liquid nitrogen near boiling temperature with 0.4 g/l graphite, rectangular test pulses, UB = 600 V.
of the exponential part of the time lag distributions as a function of the apparent field strength, UB/g, is shown in Fig. 3a. Although the characteristic times on the plot show much scatter they essentially follow the well known pattern of an exponential law with respect to the inverse of the gap, g. Also the formative times, rf (Fig. 3b), behave similarly to those for hydro-
89
carbon liquids. As a matter of fact, they almost coincide with the formative times for paraffinic oils [3]. D i s c u s s i o n and c o n c l u s i o n
It is our main concern to emphasize the similarity which exists, with respect to the statistics of the breakdown time lags, between liquid nitrogen and the more c o m m o n liquids like h y d r o c a r b o n oils, alcohols, water, etc., so far studied. This is, of course, complementary to the similarity which exists for the statistics of dielectric strength measurements with a steadily rising voltage. The argument is weighty considering the drastic change which occurs when a liquid, initially immobile, is caused to flow (typically at velocities, in m/s, of a few tenths). At rest, breakdown voltages are known to o b e y the statistics of extreme values. This fact, however, appears to be purely accidental, since it can be shown that the assumption of a statistical behaviour of time lags according to a Poisson process and the further assumption of an exponential dependence of the mean time lag on the electric field lead to a Fisher---Tippett t y p e probability density distribution of the b r e a k d o w n strength. Our experimental results seem to corroborate these premises, so that the time lag measurements of liquid nitrogen strengthen the idea of a general breakdown mechanism, valid for dielectric liquids of various composition (a restriction to short timescale breakdown events should be made, however). The formative process which occurs whenever a dielectric liquid is perturbed, for instance as a consequence of motion, invariably modifies the statistics and brings it close to the Gaussian law. Acknowledgements
It is a pleasure to acknowledge the continuing interest and financial support of the Ateliers des Charmilles S.A. We would like to thank R. Martin for contributing the transistorized high-voltage pulse generator and G. R e y Mermier for most of the remaining electronic circuitry. References 1 L. Centurioni, G. Molinari and A. Viviani, L'Energia Elettrica, 2 (1975) 102. L. Centurioni, B. Delfino, G. Molinari and A. Viviani, Proc. of 5th Int. Conf. on Conduction and Breakdown in Dielectric Liquids, 1975, p. 221. 2 J.K. Nelson, B. Salvage and W.A. Sharpley, Proc. IEE, 118 (1971) 388. 3 B. Bommeli, C. Frei and A. Ratajski, J. Electrostatics, 7 (1979) 123.