Analysis of Air Bubble Deformation Subjected to Uniform Electric Field in Liquid Dielectric

Transcription

1 International Journal of Eletromagnetis and Appliations 01, (1): 4-10 DOI: /j. ijea Analysis of Air Bubble Deformation Subjeted to Uniform Eletri Field in Liquid Dieletri M. Talaat *, A. El-Zein Eletrial Power & Mahines Department, Faulty of Engineering, Zagazig University, Zagazig, Postode 44519, Egypt Abstrat A new numerial analysis has been arried out in order to determine the eletrostati pressure ating on the liquid-air interfae. Also by aid of photographi reording the surfae tension at the equator and poles is determined, the internal pressure is alulated and the relationship with the voltage square is enlightened. The analysis of the unstable bubble ejeted or ompressed against the sphere eletrode with sharp edge protrusion, is explained and the values of harge under an applied eletrial field at ejetion ondition are given. The breakdown eletri field of the transformer oil is alulated, and a new breakdown voltage equation linking the ompressed onduting bubble to the breakdown field is proposed. A new ratio of alulated eletri harge at ejetion mode relative to the value of ejeted eletri field is ahieved. Also the breakdown voltage an be estimated by knowing the value of the voltage at ompressed mode, using a new addressed spae harge formation fator whih is equal to 1.1. The results have been assessed through omparison with available analytial and experimental data. Keywords Deformed Air Bubble, Uniform Eletri Field, Dieletri Liquid, Breakdown in Liquid Dieletri, Sphere to Plane Gap, Spae Charge Calulation, Streamer Formation 1. Introdution Liquid dieletri improvement is a very interesting subjet for the development of higher voltage levels of transmission system and orresponding omponents suh as transformers, iruit breakers, apaitors, et. Also, the required "rep-rate swith using high pressure dieletri liquids is essential for future direted energy appliations[1]. Thus, the pressure analysis is a very important way for determining the ondition of our liquids. The interfae problem is also an important item to study the pressure stability analysis[]. Therefore, the study of air bubbles existing in dieletri liquid medium, and their effet on the breakdown harateristis were arried out by many authors[3-14]. Also, the stressed liquid volume and stressed eletrode area for ryogeni liquids were reported by[15]. These authors showed that the breakdown inreased with larger stressed liquid volume, whih means, minimum air voids size. And the area effet under the existene of miro-protrusion on the eletrode surfae dominated the breakdown strength for eletrodes with small stressed liquid volume or rough surfae [15]. The indued eletri pressure harateristis under applied voltage are similar to that of urrent[16,17]. The effet of additives to dieletri liquids plays an important role in its * Corresponding author: m_mtalaat@zu.edu.eg (M. Talaat) Published online at Copyright 01 Sientifi & Aademi Publishing. All Rights Reserved harateristis. For example the urrent and indued pressure an be raised linearly by the inrease of moisture ontent till 5 and 3. respetively[17]. The pressure has been taken to support the theory, that liquid dieletri breakdown is started by the formation of gas bubbles in the liquid medium. Then, the bubble breakdown is onsidered the ineption event leading to liquid breakdown[18]. Also, transformer oil with pressure up to.4 MPa showed a breakdown strength gain of up to 35%-40%, inrease above the atmospheri pressure[19]. In this work, the role of bubbles in the streamer generation in liquid dieletris subjeted to an eletri field is studied. It is intended to use the deformation of an air bubble loated in a non-uniform eletri field with different spaes between eletrodes and different high voltage eletrode diameter to study the pre-breakdown behavior and to explore whih theory ould explain our experimental results.. Experimental Tehniques Figure 1, shows the tehnique used for experimental reording [0,1]. The test ell onsists of a transparent glass ontainer of m. The upper Perspex over of the ell supports the inlet opper pipe of 6 mm with inner diameter of 3 mm; this pipe is srewed externally to 5 mm from one side. The over also supports an inlet, for dieletri liquid input. The pipe arries a high voltage sphere termination whih is open till the sphere tip and srewed internally to 5 mm to be ereted in the mentioned opper pipe. The other

2 International Journal of Eletromagnetis and Appliations: 01; (1): side of the pipe is onneted to the injetion air bubble system. Also the bottom of the test ell is made of Perspex and supports the grounded plane, 3 m in diameter. The grounded plane position an be hanged to adjust the tested gap against high voltage sphere eletrode. In the present experiment one sphere termination of 11.8 mm diameter has been used. Transformer oil H.V. Sphere eletrode Injeted bubble Test ell At equator, σγ Pi = Pep + + Phe (1) b ( + 1) σ γ Pi = Peq + + P e () bγ where, P i is the internal pressure of the bubble, P ep is the eletrial pressure at the pole, P eq is the eletrial pressure at the equator, P h is the hydrostati pressure above the bubble, σ is the surfae tension of the dieletri medium, γ is the ratio of the bubble elongation and b is the minor semi-axis.. The ross setion area of the bubble an be also alulated from the photographi reording by the aid of ellipse area equation. Area = π a b (3) where, a is the major semi-axis and b is the minor semi-axis Camera Plane eletrode 3. Method of Analysis 3.1. Deformed Air Bubble Figure 1. Sheme of a bubble immersed in a liquid dieletri under a sphere-to-plane onfiguration The tests were arried out using 0~60kV D.C. power supply with negative polarity. The high voltage D.C. supply was onneted to the sphere eletrode, using 0.5 MΩ series resistor..1. Experimental Proedures 1. The high voltage eletrode was terminated with the required sphere eletrode. The grounded plane was adjusted to the required distane by using the speial srewing rod, whih passed through the lower termination. After that, the glass test ell ontainer was filled to a required hydrostati head above sphere tip. The test gap was adjusted to required distane.. The injetion system was adjusted to initial ondition by the aid of oarse syringe adjustment, and stopoks system ontaining valves. After that the air bubble was injeted by using mirometer loaded syringe. 3. The high voltage D.C starts to rise gradually with kv step. At eah voltage step the air bubble shape was photographed. 4. This photograph reording was performed by inreasing the applied voltage until the air bubble ompressed or ejeted from the sphere tip... Experimental Calulation 1. The internal pressure of the bubble an be alulated by knowing the minor and major semi-axis from photographi reording using Krasuki equations for the pressure at the poles, and at the equator [6]. At poles, Stable Air Bubble The stable air bubble ase is taken in the low voltage region, where the relation between the voltage inreasing and elongation of air bubble is in the linear region. ε Sphere eletrode ε 1 Stable bubble Dieletri liquid Figure. Table bubble immersed in a dieletri medium The average eletrostati pressure (P e ) is used as an effetive eletrostati tration ating on the boundary of a spherial bubble [14]. This pressure given as: 3 ε ε1 Pe = εε oe (4) ε + ε1 where, ε 1 and ε are the relative permittivity of the air and dieletri liquid respetively, i.e., ε > ε 1. For stable air bubble, P e, tends to press the bubble against the sphere eletrode Unstable air bubble For unstable bubble, the aumulated harge on the air-liquid interfae inreases.

3 6 M. Talaat et al.: Analysis of Air Bubble Deformation Subjeted to Uniform Eletri Field in Liquid Dieletri Sphere eletrode Sphere eletrode ε ε 1 Unstable bubble E ej q a Dieletri liquid Figure 3. Unstable bubble immersed in a dieletri medium This harge, whih has the same sign of the spherial eletrode, inreases the Columbi pressure (P ) Sphere eletrode ε Ph Pi ε 1 Pe Ps P Figure 4. Pressure analysis for unstable bubble For more bubble analysis, we must notie the following for air bubble balaned pressures. P + P + P = P + P (5) e h s i where, P h, P s and P i are hydrostati pressure, surfae tension pressure and internal air bubble pressure respetively. By inreasing the applied voltage, P inreases also, and if we assumed that P h + P s = P i whih is orret at the instant of zero applied voltage. Therefore, P P e for unstable bubble whih will be ompressed or ejet aording to relative value of P with respet to P e i.e., three modes arises: First mode: Pe > P the bubble ompressed. Seond mode: P e < P the bubble ejeted. Third mode: P e = P the bubble beomes unstable. whih an be onsidered as a new finding for delaration of what happen to injeted air bubble under different experimental high voltage onditions. 3.. Spae Charge Calulation If the spae harge is (q) then the fore on this harge due to applied eletri field (E) will be, F = qe (6) b Figure 5. Unstable bubble in a dieletri medium for ejetion ase This fore an be alled the Columbi fore, whih an be given at the equator as follows: F = P area (7) If the bubble is unstable, Pe = P, the following equation an be given: 1 3 ε ε1 qe ej = εε oeej (8) πb ε + ε1 where, πb is the elliptial elongated bubble ross setion area and E ej is the value of the applied eletri field at instane of bubble ejetion. 3 ε ε1 q = εε oeejπb (9) ε + ε1 where, ε 1 = 1 for air bubble and ε =.1 for transformer oil. The spae harge under the ase of transformer oil, 1 q = ( πb ) E ej (10) 3.3. Breakdown Analysis If the unstable bubble was not ejeted, with further inreasing of the applied voltage, the ionization inside bubble inreases also. At higher voltages this bubble will be onverted to onduting one, and ompressed against the sphere eletrode with sharp end protrusion. The eletri field intensity ahead this protrusion tip will at to push off the liquid from this tip. At balane ondition this eletrial indued pressure must overome the hydrostati and atmospheri pressures. When the bubble is onverted from dieletri to onduting medium the eletri pressure P e ould be given aording to equation, 3 Pe = εε oet (11) where, E t is the eletri field at the tip of the ompressed air bubble i.e., onduting medium. At this ondition, Pe = Ph + Pa (1) where, P a is the atmospheri pressure whih equal 10 5 N/m

4 r p International Journal of Eletromagnetis and Appliations: 01; (1): Sphere eletrode bubble under asending mode against applied voltage, for 3, 4, 5, 6, 7, 8 and 13 mm gap distanes. d Figure 6. Compressed bubble in a dieletri for breakdown ase Figure 8. Deformation proess of air bubble for gap 6mm sphere 11.8mm The applied voltage required to produe this value of field an be alulated from the following equation: V Et = (13) r ln 4d P r p where, r p is the radius of the ompressed air bubble tip, d is the distane from bubble tip to plane eletrode and V is the applied voltage Compressed Air Bubble Tip Radius Estimation The tip radius of the ompressed air bubble an be measured from the photographi reording analysis as following: Figure mm Deformation proess of air bubble for gap 8mm sphere Figure mm Deformation proess of air bubble for gap 14mm sphere Figure 7. Shemati figure for radius alulation of ompressed air bubble We an onsider the protrusion tip as a one with base "y" as shown, at /3 the height of the one we an onsider the distane "x" as the diameter of the tip as shown in the shemati figure. From this Figure rp = x/ and y = 3x = 6r p. Aordingly the voltage at whih the gap breaks down an be alulated from equation (13) by the measured experimental values of y as follows: y 4d 6 Vb = ln E (14) t 1 y where, V b is the breakdown voltage. From Figures 8, 9 and 10, it is lear that the bubble assumes nearly a spheroid shape at low applied voltage and then it starts to elongate assuming an elliptial shape. With further inreases of the applied voltage the bubble enter the sphere tip eletrode, Figure 10, or ejet from the gap, Figure 11, or beomes unstable bubble, Figure 1. Figure 11. Compressed air bubble for gap 6mm sphere 15.8 mm 4 Results and Disussion 4.1. Experimental Results Sphere eletrodes of 10, 11.8, 13., and 15.8 mm diameter with a hydrostati pressure of 4 m oil were used. The test has been arried out to detet the behavior of air Figure 1. Ejeted air bubble for gap 4mm sphere 10 mm

5 8 M. Talaat et al.: Analysis of Air Bubble Deformation Subjeted to Uniform Eletri Field in Liquid Dieletri Figure 13. Unstable air bubble for gap 8mm sphere 10 mm 4.. Spae Charge Calulation In order to demonstrate the proposed approah, Table 1 desribed the ejetion or unstable bubble data obtained from experimental, these data required for alulating the spae harge using equation (10). Table 1. Voltage values in ase of (ejeted or unstable bubble modes) for different gap spaing using various sphere diameters Gap Sphere diameter ( mm ) distant ( mm ) kV unstable 8 17 kv unstable 0 kv ejet 9 18 kv unstable 18 kv ejet kv ejet 18 kv ejet kv ejet 0 kv unstable 1 1 kv unstable kv unstable 13 0 kv ejet 3 kv unstable 3 kv unstable 14 8 kv ejet 4 kv unstable 34 kv ejet The values of the spae harge is alulated for transformer oil using equation (10) for different sphere terminations and tabulated in Table. From Table, the required harge value (q) for bubble ejetion related to ejetion eletri field (q/e ej ) is nearly 13 equals to.4 10 C.m/kV. Sphere diameter Table. Spae harge alulation Parameters required for equation (10) Gap distant Ejetion voltage (kv) E ej (kv/ m) b Spae harge (C) q/e ej C.m/k V Eletri Field Calulation Streamer Formation For streamer formation the number of eletrons per avalanhe, ne, needed are 108 < n e < 109 as given by[]. From the previous values of q at ejetion ondition the number of equivalent eletrons ranges between at gap 8 mm and at gap 14 mm, for sphere 15.8 mm and at gap 13 mm, and at gap 14 mm, for sphere 10 mm. Therefore if we onsider the number of eletrons per avalanhe equal to 10 9 eletrons for streamer formation, then 9 the harge will equal to q = e 10, where e is the eletron 19 e = C, then q = C. harge value, Under our ondition this harge may be ahieved at fields equal to 59.9 kv/m and kv/m for gap distane of 8 and 14 mm respetively sphere 15.8 mm. Also this field equal to kv/m for gap distanes of 13 and 14 mm sphere 10 mm Breakdown Analysis When the bubble is onverted from dieletri to onduting medium the eletri pressure P e ould be given aording to equation (1), using h = 40 mm.oil, g = 9.81m/s, ρ = 880 kg/m 3, ε =.1for transformer oil to determine the value of Ph = ρ gh = N/m, from equation (1) the value 5 of P e = 10 N/m, using this value in equation (11), then 3 5 εε oet = 10 E t = kv/m, whih is in aordane with that given to be 570 kv/m by[3-5]. The voltage at whih the gap breaks down an be alulated from equation (14). Table 3 shows the experimental measured voltage at ompressed bubble ondition, V, and the breakdown voltage V b given by equation (14). From this Table it is lear that the average value of the ratio V b /V is higher than one, this value an be alled a spae harge formation fator (m), whih reahes a mean value of 1.1 Table 3. The experimental measured V and the alulated V b Gap distant ( mm ) V (kv) y Sphere diameter (15.8 mm ) x r p V b (kv) m =V b/v Conlusions In this paper, an effort was made to outline the different stages of pre-breakdown in dieletri liquid, "transformer oil", by using the deformation of an artifiial air bubble injeted at high voltage eletrode between different gaps, and different high voltage eletrodes diameters with onstant hydrostati head in a non-uniform eletri field. Based on the finding of the present work the following salient points may onlude this paper: 1. The injeted air bubble under existing hydrostati head

6 International Journal of Eletromagnetis and Appliations: 01; (1): and no applied voltage has a prolate spheroid shape, with the elongation of bubble in the horizontal axis.. As the voltage inrease the internal pressure of the bubble also inrease as approximately linear relation until a ertain value for whih the bubble ompressed and the non-onduting bubble onvert to a onduting one. After that, the spheroid shape assumes a onial shape. At this value, there is no air bubble but a onduting gas medium. 3. For unstable bubble, the aumulated harge on the air-liquid interfae inreases. This harge, whih has the same sign of the spherial eletrode, inreases the oulombi pressure (P ). So that the analysis of the unstable bubble an be represented as: when the eletrostati pressure is higher than oulombi pressure the bubble ompressed (first mode), and when it beomes smaller than it the bubble will be ejet (seond mode), also, when they are equal the bubble beomes unstable (third mode). 4. Under the analysis of unstable bubble, the alulated harge under applied eletrial fields at ejetion ondition reveals that its ratio equals C.m/kV. 5. When the bubble not ejeted and with further applied voltage inrease, till it ompressed against the sphere eletrode, a sharp end protrusion appears. The estimated breakdown field intensity reahes a value of 598.8kV/m. 6. A new equation of breakdown voltage inside the dieletri liquid has been dedued, by knowing the length of the ompressed air bubble base. 7. The new spae harge formation fator (m), whih approximately equals 1.1, used to desribe the ompressed and breakdown voltage for unstable ompressed bubble. REFERENCES [1] Joshua J. lekbee, Randy D. Curry, Kenneth F. M Dorald, W. Ray Cravey, Glenn Anderson and Susan Heidyer "Design, Modeling, and Verifiation of a High Pressure Liquid Dieletri Swith for Direted Energy Appliations" IEEE Transations on Plasma siene Vol. 3, No.5, pp , 004. [] F. Vega Reyes and A. 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