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Contribution to the optimization of the electrical performance of a superhydrophobic insulation covered with water drops under DC voltage
Journal of Electrostatics 102 (2019) 103375
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Review
Contribution to the optimization of the electrical performance of a superhydrophobic insulation covered with water drops under DC voltage Khaled Hamour a, Sarah Soudani a, Bahia Smati a, Fatma Bouchelga a, b, *, Rabah Boudissa a, Stefan Kornhuber c, Klaus Dieter Haim a a b c
Laboratory of Electrical Engineering, Department of Electrical Engineering, University A. Mira of Bejaia, 06000, Bejaia, Algeria University of Ghardaia, Algeria University of Applied Sciences, Theodor - Koerner - Allee 16, Zittau, 8800, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Superhydrophobic insulation Bridge electrodes Arrangement of water drops Expulsion voltage of drops Pollution DC performance
In this study, a superhydrophobic insulation and a suitable electrode profile are developed to eject the water drops outside surface, with preventing any development of electrical discharges and/or the flashover of its surface under DC voltage. The effect of geometrical and electrical parameters of the water drops on its perfor mance was quantified. Also, the evacuation of water drops using bridge-shaped electrodes without creating any electrical discharges is demonstrated. As well, the expulsion voltage is less than half of its flashover in dry case, and therefore, the superhydrophobicity of the insulation is better conserved and its longevity is optimized.
1. Introduction Disruptions are affecting the power transmission and distribution networks in the world, due to the flashover of their hydrophilic in sulators, under the effect of a wet layer of pollution covering them [1,2]. In order to limit these disruptions, insulating surface’s scientists, in consultation with the operators of these electrical networks, for more than six decades, have been developing hydrophobic insulations, [3,4]. This polymer insulation is light with a very high long-term water proofing power. Therefore, the moisture persists very long on its surface in the form of discrete water drops [5,6]. This last advantage allows the minimization of tracking currents and inhibits the evolution of dis charges due to flashover, even if it is heavily contaminated, because the silicone transfers its hydrophobicity to the polluting deposits that cover its surface [7]. Despite the elevation of their electrical performance compared to that of ceramics, when put under voltage these polymer insulations are not immune to alteration under severe humidity condi tions [8–11]. Indeed, in highly humid environment, the persistence of a deposit of resulting water drops causes the elevation of the electric field prevailing between the ends of these insulations under voltage. As result, this can lead with the elongation of water drops to short-circuit of their dry leakage path and consequently their flashover by electrical discharges. The recurring heating of their surface by these electric arcs can lead to
their irreversible failure resulting in cracks and surface erosions [8–11]. Among the new solutions brought by some researchers to this problem, we can speak of the addition of some adjuvants to the composition of this polymer. As a first adjuvant, we mention aluminum trihydrate for the inhibition of the occurrence of superficial cracks in the insulation [12]. Moreover, The other elements added concern either silicon oxide for the growth of resistance to the deterioration of its surface [13], or the operation of the very good thermal conductivity of boron nitride for a fast dissipation of the heat released by the flashover arc of the insulation, and therefore contribute to the improvement of its resistance to heating [14]. Finally, the addition of melamine cyanurate to this polymer allows the extinction of the flashover arc in case of its appearance on the surface of the polymer [15]. Inspired by the effect of the lotus, several researchers have taken other tracks, including the development of superhydrophobic surfaces already exploited in some industrial fields [16–19]. Their design is mainly based on the absence of adhesion of any form of moisture coming into contact with their surface, which allows it to maintain its drought. Therefore, in case of their use as electrical insulators, they will keep their electrical insulation resistance and their dielectric strength constant regardless of the humidity’s degree of their environment use. Nowadays, there are few results of published works to inhibit the occurrence of electrical discharges on the superhydrophobic insulation’s surface by ejection outside it of any kind of humidity covering its surface under the
* Corresponding author. Laboratory of Electrical Engineering, Department of Electrical Engineering, University A. Mira of Bejaia, 06000, Bejaia, Algeria. E-mail address: [email protected] (F. Bouchelga). https://doi.org/10.1016/j.elstat.2019.103375 Received 22 April 2019; Received in revised form 25 September 2019; Accepted 27 September 2019 Available online 3 October 2019 0304-3886/© 2019 Elsevier B.V. All rights reserved.
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action of a weak direct electrical field [20–23]. For the reasons given, we opted, initially, for the making of a superhydrophobic insulation based on silicone. In a second step, we looked for a suitable electrode profile allowing the expulsion of all water drops outside the insulation in horizontal position, and consequently contributing to prevent the appearance of electrical discharge in order to optimize its longevity. Finally, this study is completed by the quantifi cation of the ratio of the evacuation voltages of all water drops outside the superhydrophobic insulation and its flashover without these drops according to some of its electro-geometrical parameters. These results will bring great contribution to the HDVC network in the world. 2. Experimental model and technique of measurement The main steps of a superhydrophobic coating of glass insulation are summarized in Fig. 1. The glass plate has the dimensions: 10 cm � 10 cm x 0.5 cm. Its upper surface is manually coated with two stacking layers which are composed of two different materials. The first layer of silicone gel is taken from a commercial product (Fig. 1a). The second layer is composed mainly of soot. This one is obtained by carbonization of some amount of silicone gel from the same product and sprayed with iso propanol alcohol (Fig. 1b). Its contribution on the fresh layer of silicone gel covering the glass (Fig. 1c) is possible by bringing it closer momentarily to the flame (Fig. 1b). The soot is applied on the fresh layer of silicone gel so that the carbon produced can adhere well on the sili cone coating. Fig. 1d reflects the image of the upper surface of the glass, blackened with soot and washed with tap water. A micropipette, equipped with an adjustable volume counter be tween 0 and 100 μl, is illustrated in Fig. 2. A well-defined quantity of water can be drawn from the solution contained in a beaker (Fig. 2a). This is deposited as a water drop on its surface (Fig. 2b). The measure ment of its contact angle on the insulation’s surface is determined using of a goniometer (Fig. 2d). The value of the static contact angle of a water drop, with 20 μl of volume, is in the order of 160 � (Fig. 2e). Its sliding angle on the same inclined surface compared to the horizontal is less than 2 � . These values are in accordance with those obtained by other researchers on a surface of a different nature [21,22]. Fig. 3 reflects the images of three geometries each of them repre senting a set of electrodes, respectively, full parallelepiped with rounded ends (Fig. 3a), cylindrical with five teeth in each electrode (Fig. 3b) and cylindrical in the shape of a bridge (Fig. 3c). The third profile is obtained from the second one after eliminating the internal teeth. The purpose of these configurations is to find a suitable profile facilitating the expulsion of water drops outside the insulation, without their attachment to the HV and ground electrodes. Their definitive disappearance from the insulation contributes very strongly in preventing the appearance of partial electrical discharges and/or the flashover of the material thus optimizing its longevity.
Fig. 2. Micropipette and goniometer for measuring the volume and the angle of contact of water drop on a superhydrophobic surface.
The number, volume, viscosity, arrangement and electrical conduc tivity of water drops were considered in this study. For reasons of simulation of condensation’s phenomena and natural rain, the number of water drops, deposited on the surface of the superhydrophobic insu lation, is varied between 1 and 25. The water drops are deposited in the form of several rows at the rate of 4 or 5 water drops per row and following the modes of zigzag (Fig. 4a) or straight line arrangements (Fig. 4b). Their choice maybe justified by the fact that the first type of arrangement is similar to that found during the condensation phenom enon [24] and the second because of the elevation of water drops’ evacuation voltage because of their mutual attraction during their expulsion outside the surface. The constellation of water drops is described by the following four parameters: Ldv, Ldd, Ldg and lrr (Fig. 4). In this study, their values are maintained equal to 0.8 cm for the first three sizes and 1 cm for the fourth. The device supporting the super hydrophobic insulation is illustrated in Fig. 4c. Its mobile upper arma ture is positioned horizontally during all tests. This arrangement is taken for reasons of reproduction of the most unfavorable situation, corre sponding to the lowest electrical performance of the superhydrophobic insulation. This is due precisely to the very low mobility of the water drops in this position and the high probability of the insulation’s flashover by electrical discharges, generated by these water drops, following their coalescence and their elongation under the action of an electrical field [21,22]. The size of the water drops formed during the phenomenon of condensation or natural rain is very different [24]. In order to consider this fact, the volume of water drops was varied be tween 20 and 100 μl. According to the environmental conditions, the purity and the conductivity of water formed on the insulating surface differ from one place to another, so the solution used is a mixture of distilled water, and neutral kaolin with a mass varied between 0 and 100 g for thickening the polluting layer and sodium chloride so as to modify its electrical conductivity. The electrical conductivity’s interval of the polluting solution is varied between 10 μS/cm and 20 mS/cm in order to simulate the pollution levels of the sites between a very low level of contamination and a very heavily contaminated one. The con ductivity of each prepared polluting solution is measured using an electrical conductivity meter with moving probe. The measuring station, illustrated in Fig. 5, consists of a step-up transformer delivering at its secondary a maximum AC voltage of 135 kV and a current of 80 mA. This voltage is rectified by diode (D) in direct (positive polarity: 1) or indirect (negative polarity: 2). The Vcr displays the real voltage applied to the superhydrophobic insulation. The applied insulation voltage is raised manually in steps of 0.5 kV
Fig. 1. Main steps in the manufacture of a silicone superhydrophobic insu lating surface. 2
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Journal of Electrostatics 102 (2019) 103375
Fig. 3. Geometries and characteristics of the electrodes delimiting the superhydrophobic insulating surface.
Fig. 4. Arrangements’ modes for water drops on the surface of the insulation and its support.
Uiem is the applied voltage obtained from the test in the time of i (kV); N is the total times of the valid test, N ¼ 20; RSD is the relative standard deviation of the test result. Since the evacuation voltage of the water drops is related to the ambient temperature, the pressure and the humidity of the air prevailing in the laboratory and that the various tests were not carried out during the same period, in order to compare the direct voltage of water drops’ ejection for the two polarities, all the results obtained were brought back to the normal conditions of temperature θ0, pressure P0 and humidity H0 (θ0 ¼ 20 � C, P0 ¼ 100 kPa and H0 ¼ 11 g/m3) using the following re lationships [25]:
Fig. 5. Diagram for measuring the direct voltage of water drops’ ejection and visualization of their expulsion outside the insulation.
until the last water drop is ejected from the insulation surface. This voltage creates an electric field between the electrodes that generates forces on the drops. Because this voltage is not applied directly to the drops, it is considered an ‘‘indirect voltage of expulsion (Uie)’’, which we will simply call the ‘‘expulsion voltage’’ (Ue) in this document. The display device for the expulsion of water drops outside the material and partial discharges and/or of flashover is shown in Fig. 5. It consists of a camera (Cam) at 1000 photos/s for the recording of the various steps of water drops’ evacuation and a PC for image processing using video studio software 11. For each parameter of influence investigated in this paper, a series of 20 tests were carried out and the retained value of the expulsion voltage of each of water drops, is the arithmetic average of all those obtained on the same series of measurement. The average value and standard devi ation formulas of the ejection voltage of water drops are shown in Formula 1 and 2: N 1 X Uem ¼ Uiem N i¼1
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uN uP u ðUiem Uem Þ2 t1 100% RSD ¼ : Uem N 1
Ue ¼
KH Uem Kd
(3)
With: Uem: Expulsion voltage of the water drops, measured at the tem perature θ and the pressure P and the humidity H; Ue: Ejection voltage of the water drops under normal conditions (θ0, P0 and Hr0); Kd: Correction factor relating to the temperature and the pressure whose expression has the form: Kd ¼
2:93P ð273 þ θÞ
(4)
Where:
(1)
P (pressure) is in kPa and θ (temperature) in � C; KH: Correction factor relating to humidity. Its value is deduced from the charts given in Ref. [25]. The good repetition of the measurement techniques allowed us to have maximum relative RSD equal to 5%.
(2)
Where: Uem is the average of the measured expelling voltage of each of the water drops (kV);
3
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3. Results and discussion
evacuation is one by one expulsion of all the water drops. Finally, the groupo-individual mode of ejection is the combination of the two pre ceding types and consists of successive evacuation of a set of small water drops, sometimes; each of them is accompanied by an individual water drop. With regard to the direction of the drops’ movement, their moving is either only done in one direction (towards the high voltage or the grounded electrode), or bidirectional (towards the high voltage or the grounded electrode), regardless of their location on the leakage path of the insulation. It results from the visualization of the electro hydrodynamic behavior of the water drops more frequent appearance of the groupo-individual and bidirectional expulsion mode of these water drops despite the nature of their arrangement and the polarity of the applied voltage. Regarding the hydrodynamic and electrical forces governing the expulsion of water drops outside the insulation’s surface, we relied on the Navier - Stockes equation, based on the conservation of motion forces and modeling the motion of an incompressible water drop ac cording to relation 5:
3.1. Electrical performance of superhydrophobic insulation without water drops Fig. 6 gives the flashover voltage histogram of the superhydrophobic insulation without water drops as a function of the profile (Pf) of the electrodes delimiting the same surface between electrodes having a total leakage path Lf equal to 4 cm. The value of the mentioned magnitude will serve as a reference to the expulsion voltage of water drops outside the insulation’s surface after they have been deposited on it while it is switched off. As a result, the flashover voltage of the dry insulation under bridge electrodes is greater than that obtained under electrodes with teeth or full electrodes. The maximum relative difference between the insulation’s flashover voltages under bridge and full electrode is about 13%. This can be explained by the decreasing of the contact surface of each of the electrodes with the insulation’s superhydrophobic surface going from full electrodes to those with bridge. Indeed, the flashover path of the insulation, under full or toothed electrodes, is performed at the base of the HV and ground electrodes in contact with the surface of the insulation. This explains the imprint left by the elec trical flashover discharge on this surface. On the other hand, in the case of bridge electrodes, the path of the electrical flashover discharge of the insulation is practically in the air at the height of the bridges, which explains the absence of the discharge’s trace on its surface. For that reason, the place of birth and the length of flashover discharge of the insulation differ from the bridge electrodes compared to the full ones. The maximum relative difference between the negative and the positive DC voltage is about 3%. This difference is negligible, since it is less than the maximum RSD find in this study (ffi 5%). Therefore, the polarity has no effect on the insulation’s flashover voltage, since this is always governed by two negative and positive discharges regardless of the po larity of the DC voltage applied to the dry insulation.
� ! � ∂V ! ! ! ! rPΔ þ μr2 V þ F ¼ d þ V :r V ∂t
(5)
Where: - d, V and μ respectively represent fluid density, velocity and viscosity; ! ! - The three terms: rPΔ , μr2 V and F respectively represent the ef fects of forces due to the pressure, the viscosity and the electrostatic force exerted on the water drop; - The right member of the equality 5 designates the acceleration of the water drop under the three forces’ action. Assuming that the drop retains its spherical shape during its motion and that the surface is superhydrophobic (θ¼ 160� ), the electrostatic ! force F plays a predominant role in the movement of the drop on the superhydrophobic insulation’s surface [26–28]. For an individual water drop, placed on a superhydrophobic surface and put under the action of an electric field, the expression of this electric force is of the form [29]: � � 1 2 1 2 dε F ¼ ρt E (6) ρm jEj rε þ r jEj 2 2 d ρm
3.2. Electrical performance of superhydrophobic insulation covered with water drops 3.2.1. Expulsion mode of water drops from the insulation Regarding the number of expelled water drops and the linking of their evacuation from the surface of the insulation to the electrodes or their ejection bluntly outside the surface, 3 distinct modes were iden tified regardless of the arrangement mode of water drops and the po larity of the applied voltage: individual, with group, or groupoindividual ejection of water drops. The group mode of expulsion means that it takes the form of a set of small water drops leaving sepa rately and successively the surface of the insulation. The individual
Where: E, ρt, ε and ρm respectively represent the electric field, the total charge, the dielectric permittivity of water and the voluminal density. The three terms of the right member of equation (6) represent respectively the Coulomb force, the dielectrophoretic force, and the electrostriction pressure. In this study, the last two terms are neglected because of the uni formity of the electric field prevailing in the planar electrode system and the keep of the spherical shape of the water drop during its expulsion from the insulation. Therefore, the ejection of a single water drop outside the insulation is practically caused by the Coulomb force. In the case of several water drops, the expulsion of water drop from a row which is parallel to the electrodes and very close to them is gov erned by the resultant Coulomb forces and mutual forces of drops’ attraction along the creepage distance of the insulation and of repulsion, perpendicular to the creepage distance in the plane of the insulation [30, 31]. As the water drops in a row move in parallel to the direction of the applied field, so the repulsive forces are considered negligible in this case. In summary, the ejection outside the insulation of the water drops of each row is governed mainly by the resultant Coulomb force directed to the nearest electrode (HV or ground) and the force of mutual attraction directed towards the row of adjacent drops and the force of Coulomb is the most dominant in this case. Fig. 7 summarize some important phases of the group and
Fig. 6. Flashover voltage of superhydrophobic insulation without drops as a function of electrodes’ profile (Lc ¼ 4 cm, Ef: Full electrodes, Et: Tooth elec trodes, Eb: Bridge electrodes, Pf: profile of high voltage electrodes and ground). 4
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Fig. 7. Groups and bidirectional evacuation stages of 25 zigzag water drops of the insulation surface with full electrodes (Ua: Applied voltage, Vd ¼ 60 μl, σv ¼ 10 μS/cm).
bidirectional expulsion mode of a multitude of water drops, arranged in zigzag under negative DC voltage (Fig. 7). Their evacuation from the insulation surface under full electrodes is established completely in 3 steps in the case of their arrangement in zigzag (Fig. 7). Fig. 7a illustrates the zigzag arrangement of 25 water drops covering the surface of the superhydrophobic insulation without voltage (Ua ¼ 0 kV). The image of Fig. 7b corresponds to a phase where small group of water drops is attracted by the HV electrode after coalescence of some of the other persistent drops (Ua ¼ 5 kV). Fig. 7c shows the presence of 4 drops on the surface of the insulation (Ua ¼ 10 kV). Some of the missing drops were attracted to the grounded electrode and the others were ejected squarely outside the insulation. Fig. 7d shows the image of a surface clear of all its drops (Ua ¼ 13.5 kV); their distribution is almost equitable on the high voltage and grounded electrodes. Finally, it appears from Fig. 7 a taper of some drops held by the HV and ground electrodes especially those at their ends. Such deformation of these water drops generally results short-circuit of the leakage path of the insulation, which can lead to partial electrical discharges that can evolve to flashover of the material’s surface. This constitutes a defect characterizing the profile of the full parallelepiped electrodes. The evolution of the expulsion voltage outside the insulation of a set of water drops as a function of their rank is illustrated by Fig. 8. The latter gives histogram characterizing the ratio
water drops from the surface of the insulation to the HV electrode in a ratio
Fig. 8.
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Fig. 9. Partial expulsion of the water drops from the insulation’s surface with full electrodes and the flashover of it (Vd ¼ 40 μl, mk ¼ 0 g/l, σv ¼ 10 μS/cm).
Fig. 10. Partial evacuation of water drops from the surface of the insulation with tooth electrodes and the flashover of it (Vd ¼ 40 μl, Ck ¼ 40 g/l, σv ¼ 10 μS/cm).
Fig. 11. Complete ejection of water drops outside the insulation with bridge electrodes (Vd ¼ 40 μl, Ck ¼ 40 g/l, σv ¼ 10 μS/cm).
visualization of the electrohydrodynamic behavior of the water drops show that the frequency of occurrence of the partial electrical discharges and the insulation’s flashover with tooth electrodes (Fig. 9) is weaker than under full electrodes (Fig. 10). This is almost zero under bridge electrodes (Fig. 11). This is justified by the fact that the full and rounded electrodes retain all the water drops. Because of their small radius of curvature, they taper it and the two partial nets, formed in the vicinity of the two electrodes, meet and short-circuit the leakage distance of the insulation and cause the flashover of the material. The problem of tooth electrodes is explained by their sharp geometry, that favors the attrac tion and trapping of a number of water drops very reduced compared to that collected by the full electrodes. On the other hand, the bridge electrodes with high radius of curvature eject practically all the water drops from the surface of the insulation and rarely one or two drops hang
on their ends, but without causing any electric discharges. Whatever the mode of water drops’ arrangement (Fig. 9a1–b1) and the polarity of the voltage applied to the insulation, leaving the surface of the material under the effect of an electrical field, the first water drops are hooked onto the HV and grounded electrodes respectively (Fig. 9a1–b2). Following their accumulation and their taper with the growth of the electrical field, they succeed with the other drops not yet evacuated or those pushed back by the electrodes, to short-circuit most of the insulation’s dry leakage path, which generates, the formation of partial electrical discharges between the partial water nets (Fig. 9a3–b3), that develop with the increase of the applied voltage, then eventually cause the material’s flashover (Fig. 9a4–b4). In the case of toothed electrodes (Fig. 10a1–b1), some drops are able to escape by passing between the teeth, but others hitched up on the 6
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teeth while attracting others (Fig. 10a2–b2). Their accumulation at the vicinity of the electrodes and the coalescence of some drops not yet expelled from the surface, cause the reduction of the dry leakage path of the insulation (Fig. 10a3–b3). This results an incomplete evacuation of the water drops and the birth of partial electrical discharges between the drops. This discharges progress with the increase of the applied voltage and can lead to the flashover of the material with a lower probability than previously (Fig. 10a4–b4), regardless of the type of water drops’ arrangement with or without kaolin and the polarity of the applied voltage. Fig. 11 gives the essential steps of a complete expulsion, according to groupo-individual and bidirectional mode, of a multitude of water drops with kaolin, deposited on the surface of a superhydrophobic insulation with bridge electrodes (Fig. 11a1–b1). In a ratio
3.2.3. Number of water drops’ rows and their arrangement mode on the insulation In this section, we are particularly interested in the effect of the number of water drops’ rows (Nr) and the mode of their arrangement (Ar) on the electrical performance of the superhydrophobic insulation. The results obtained are illustrated in Fig. 13, giving the characteristic
Fig. 12.
Fig. 13.
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Fig. 14.
Fig. 16.
insulation, this causes the elevation of its expulsion voltage, which in volves the growth of the
In order to study the electrohydrodynamic behavior of water drops on a superhydrophobic insulation under DC voltage, a super hydrophobic insulating surface, based on silicone, was made. The static contact angle of a water drop, placed in a horizontal position on this surface, is of the order of 160� . The sliding angle on this surface, inclined compared to the horizontal, is less than 2� . The visualization of the electrohydrodynamic phenomenon of water drops has highlighted the most frequent apparition of a groupoindividual and bidirectional expulsion mode of these water drops outside the insulation’s surface, regardless of the geometrical and electrical parameters of water drops and the polarity of the applied voltage. Among the three selected electrode geometries, the bridge electrode set has a better profile, allowing easy and fast ejection of all water drops squarely outside the insulation under the application of a voltage which can, in the most unfavorable case, exceed slightly half of that causing its flashover without these water drops, which pass under the bridges constituting the two electrodes without any clinging to their feet. Thus, the formation of any partial electrical discharge and/or of the material’s flashover is inhibited by such a profile and therefore, the super hydrophobicity of the insulation is preserved and its longevity is optimized. Deposition of water drops in straight lines requires a greater evacu ation voltage than under a zigzag arrangement regardless of their vol ume, viscosity and electrical conductivity. The variation of the electrical conductivity of water drops covering the insulation does not in any way affect its electrical performance, on the other hand, the effects exerted by their volume and the amount of kaolin added to the polluting solution on the superhydrophobicity of this material are respectively positive and negative. Finally, the polarity has no influence on the direct expulsion voltage
polarization time constant τ ¼ εσa decreases from 708 μs (εa ¼ 80 � 8.8 e 12 F/m and σ 1 ¼ 10 7 S/m) to 0.35 μs (εa ¼ 80 � 8.8 e 12 F/m and σ 2 ¼ 2.10 2 S/m) is very small in front of the time application of the electric field or of expulsion of the last drop from the insulation (te ffi 10 s) that the water drops’ ejection voltage is not influenced by their electrical conductivity. This result is in very good agreement with those obtained under DC with a superhydrophobic surface delimited by non-uniform electric field electrodes and on which a water drop of electrical conductivity varying between 20 μS/cm and 3 mS/cm [20,33] or between 1 and 107 μS/cm [27]. In addition, the curves of the expul sion voltage of water drops as a function of their electrical conductivity are almost identical for the two polarities of the applied voltage stress. 3.2.6. Kaolin concentration of the water solution Fig. 16 shows the appearance of the characteristic of the ratio
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of the water drops as a function of their electro-geometrical parameters investigated in this study.
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Declaration of competing interestCOI The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The authors would like to express their deepest gratitude to all of the members of the laboratory of HV in Bejaia. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.elstat.2019.103375. References [1] Z. Jiang, X. Jiang, Z. Zhang, Y. Guo, Y. Li, Investigating the effect of rainfall parameters on the self-cleaning of polluted suspension insulators: insight from southern China, Energies 10 (2017) 1–13, 601. [2] M. Dimitropoulou, D. Pylarinos, K. Siderakis, E. Thalassinakis, M. Danikas, Comparative investigation of pollution accumulation and natural cleaning for different HV insulators, Eng. Technol. Appl. Sci. Res. 5 (2015) 764–774. [3] Z. Jia, C. Chen, X. Wang, H. Lu, C. Yang, T. Li, Leakage current analysis on RTV coated porcelain insulators during long term fog experiments, IEEE Trans. Dielectr. Electr. Insul. 21 (No. 4) (2014) 1547–1553. [4] F. Yin, M. Farzaneh, X.L. Jiang, Electrical performance of composite insulators under icing conditions, IEEE Trans. Dielectr. Electr. Insul. 21 (2014) 2584–2593. [5] G.X. Xie, F. He, X. Liu, L.N. Si, D. Guo, Sessile multidroplets and salt droplets under high tangential electric fields, Sci. Rep. 6 (2016) 25002–25003. [6] C. Baer, R. Baersch, A. Hergert, J. Kindersberger, Evaluation of the retention and recovery of the hydrophobicity of insulating materials in high voltage outdoor applications under AC and DC stresses with the dynamic drop test, IEEE Trans. Dielectr. Electr. Insul. 23 (1) (2015) 294–303. [7] D.A. Swift, C. Spellman, A. Haddad, Hydrophobicity transfer from silicone rubber to adhering pollutants and its effect on insulator performance, IEEE Trans. Dielectr. Electr. Insul. 13 (No. 4) (2006) 820–829. [8] al T. Sakoda, Discharge behavior and dielectric performance of artificially polluted hydrophobic silicone rubber, J. Electrost. 93 (2018) 97–103. [9] A. Ren, H. Liu, J. Wei, Q. Li, Natural contamination and surface flashover on silicone rubber surface under haze-fog environment, Energies 10 (2017) 1–18, 1580. [10] al. D.M. Soares, Electrical field on non-ceramic insulators and its relation to contact angles for constant volume droplets J. Electrost. 84 (2016) 97–105. [11] M.A. Douar, A. Beroual, X. Souche, Assessment of the resistance to tracking of polymers in clean and salt fogs due to flashover arcs and partial discharges degrading conditions on one insulator model, IET Gener., Transm. Distrib. 10 (4) (2016) 986–994. [12] N. Yoshimura, S. Kumagai, B. Du, Research in Japan on the tracking phenomenon of electrical insulating materials, IEEE Electr. Insul. Mag. 13 (5) (1997) 8–19.
9
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Journal of Electrostatics journal homepage: http://www.elsevier.com/locate/elstat
Review
Contribution to the optimization of the electrical performance of a superhydrophobic insulation covered with water drops under DC voltage Khaled Hamour a, Sarah Soudani a, Bahia Smati a, Fatma Bouchelga a, b, *, Rabah Boudissa a, Stefan Kornhuber c, Klaus Dieter Haim a a b c
Laboratory of Electrical Engineering, Department of Electrical Engineering, University A. Mira of Bejaia, 06000, Bejaia, Algeria University of Ghardaia, Algeria University of Applied Sciences, Theodor - Koerner - Allee 16, Zittau, 8800, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Superhydrophobic insulation Bridge electrodes Arrangement of water drops Expulsion voltage of drops Pollution DC performance
In this study, a superhydrophobic insulation and a suitable electrode profile are developed to eject the water drops outside surface, with preventing any development of electrical discharges and/or the flashover of its surface under DC voltage. The effect of geometrical and electrical parameters of the water drops on its perfor mance was quantified. Also, the evacuation of water drops using bridge-shaped electrodes without creating any electrical discharges is demonstrated. As well, the expulsion voltage is less than half of its flashover in dry case, and therefore, the superhydrophobicity of the insulation is better conserved and its longevity is optimized.
1. Introduction Disruptions are affecting the power transmission and distribution networks in the world, due to the flashover of their hydrophilic in sulators, under the effect of a wet layer of pollution covering them [1,2]. In order to limit these disruptions, insulating surface’s scientists, in consultation with the operators of these electrical networks, for more than six decades, have been developing hydrophobic insulations, [3,4]. This polymer insulation is light with a very high long-term water proofing power. Therefore, the moisture persists very long on its surface in the form of discrete water drops [5,6]. This last advantage allows the minimization of tracking currents and inhibits the evolution of dis charges due to flashover, even if it is heavily contaminated, because the silicone transfers its hydrophobicity to the polluting deposits that cover its surface [7]. Despite the elevation of their electrical performance compared to that of ceramics, when put under voltage these polymer insulations are not immune to alteration under severe humidity condi tions [8–11]. Indeed, in highly humid environment, the persistence of a deposit of resulting water drops causes the elevation of the electric field prevailing between the ends of these insulations under voltage. As result, this can lead with the elongation of water drops to short-circuit of their dry leakage path and consequently their flashover by electrical discharges. The recurring heating of their surface by these electric arcs can lead to
their irreversible failure resulting in cracks and surface erosions [8–11]. Among the new solutions brought by some researchers to this problem, we can speak of the addition of some adjuvants to the composition of this polymer. As a first adjuvant, we mention aluminum trihydrate for the inhibition of the occurrence of superficial cracks in the insulation [12]. Moreover, The other elements added concern either silicon oxide for the growth of resistance to the deterioration of its surface [13], or the operation of the very good thermal conductivity of boron nitride for a fast dissipation of the heat released by the flashover arc of the insulation, and therefore contribute to the improvement of its resistance to heating [14]. Finally, the addition of melamine cyanurate to this polymer allows the extinction of the flashover arc in case of its appearance on the surface of the polymer [15]. Inspired by the effect of the lotus, several researchers have taken other tracks, including the development of superhydrophobic surfaces already exploited in some industrial fields [16–19]. Their design is mainly based on the absence of adhesion of any form of moisture coming into contact with their surface, which allows it to maintain its drought. Therefore, in case of their use as electrical insulators, they will keep their electrical insulation resistance and their dielectric strength constant regardless of the humidity’s degree of their environment use. Nowadays, there are few results of published works to inhibit the occurrence of electrical discharges on the superhydrophobic insulation’s surface by ejection outside it of any kind of humidity covering its surface under the
* Corresponding author. Laboratory of Electrical Engineering, Department of Electrical Engineering, University A. Mira of Bejaia, 06000, Bejaia, Algeria. E-mail address: [email protected] (F. Bouchelga). https://doi.org/10.1016/j.elstat.2019.103375 Received 22 April 2019; Received in revised form 25 September 2019; Accepted 27 September 2019 Available online 3 October 2019 0304-3886/© 2019 Elsevier B.V. All rights reserved.
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action of a weak direct electrical field [20–23]. For the reasons given, we opted, initially, for the making of a superhydrophobic insulation based on silicone. In a second step, we looked for a suitable electrode profile allowing the expulsion of all water drops outside the insulation in horizontal position, and consequently contributing to prevent the appearance of electrical discharge in order to optimize its longevity. Finally, this study is completed by the quantifi cation of the ratio of the evacuation voltages of all water drops outside the superhydrophobic insulation and its flashover without these drops according to some of its electro-geometrical parameters. These results will bring great contribution to the HDVC network in the world. 2. Experimental model and technique of measurement The main steps of a superhydrophobic coating of glass insulation are summarized in Fig. 1. The glass plate has the dimensions: 10 cm � 10 cm x 0.5 cm. Its upper surface is manually coated with two stacking layers which are composed of two different materials. The first layer of silicone gel is taken from a commercial product (Fig. 1a). The second layer is composed mainly of soot. This one is obtained by carbonization of some amount of silicone gel from the same product and sprayed with iso propanol alcohol (Fig. 1b). Its contribution on the fresh layer of silicone gel covering the glass (Fig. 1c) is possible by bringing it closer momentarily to the flame (Fig. 1b). The soot is applied on the fresh layer of silicone gel so that the carbon produced can adhere well on the sili cone coating. Fig. 1d reflects the image of the upper surface of the glass, blackened with soot and washed with tap water. A micropipette, equipped with an adjustable volume counter be tween 0 and 100 μl, is illustrated in Fig. 2. A well-defined quantity of water can be drawn from the solution contained in a beaker (Fig. 2a). This is deposited as a water drop on its surface (Fig. 2b). The measure ment of its contact angle on the insulation’s surface is determined using of a goniometer (Fig. 2d). The value of the static contact angle of a water drop, with 20 μl of volume, is in the order of 160 � (Fig. 2e). Its sliding angle on the same inclined surface compared to the horizontal is less than 2 � . These values are in accordance with those obtained by other researchers on a surface of a different nature [21,22]. Fig. 3 reflects the images of three geometries each of them repre senting a set of electrodes, respectively, full parallelepiped with rounded ends (Fig. 3a), cylindrical with five teeth in each electrode (Fig. 3b) and cylindrical in the shape of a bridge (Fig. 3c). The third profile is obtained from the second one after eliminating the internal teeth. The purpose of these configurations is to find a suitable profile facilitating the expulsion of water drops outside the insulation, without their attachment to the HV and ground electrodes. Their definitive disappearance from the insulation contributes very strongly in preventing the appearance of partial electrical discharges and/or the flashover of the material thus optimizing its longevity.
Fig. 2. Micropipette and goniometer for measuring the volume and the angle of contact of water drop on a superhydrophobic surface.
The number, volume, viscosity, arrangement and electrical conduc tivity of water drops were considered in this study. For reasons of simulation of condensation’s phenomena and natural rain, the number of water drops, deposited on the surface of the superhydrophobic insu lation, is varied between 1 and 25. The water drops are deposited in the form of several rows at the rate of 4 or 5 water drops per row and following the modes of zigzag (Fig. 4a) or straight line arrangements (Fig. 4b). Their choice maybe justified by the fact that the first type of arrangement is similar to that found during the condensation phenom enon [24] and the second because of the elevation of water drops’ evacuation voltage because of their mutual attraction during their expulsion outside the surface. The constellation of water drops is described by the following four parameters: Ldv, Ldd, Ldg and lrr (Fig. 4). In this study, their values are maintained equal to 0.8 cm for the first three sizes and 1 cm for the fourth. The device supporting the super hydrophobic insulation is illustrated in Fig. 4c. Its mobile upper arma ture is positioned horizontally during all tests. This arrangement is taken for reasons of reproduction of the most unfavorable situation, corre sponding to the lowest electrical performance of the superhydrophobic insulation. This is due precisely to the very low mobility of the water drops in this position and the high probability of the insulation’s flashover by electrical discharges, generated by these water drops, following their coalescence and their elongation under the action of an electrical field [21,22]. The size of the water drops formed during the phenomenon of condensation or natural rain is very different [24]. In order to consider this fact, the volume of water drops was varied be tween 20 and 100 μl. According to the environmental conditions, the purity and the conductivity of water formed on the insulating surface differ from one place to another, so the solution used is a mixture of distilled water, and neutral kaolin with a mass varied between 0 and 100 g for thickening the polluting layer and sodium chloride so as to modify its electrical conductivity. The electrical conductivity’s interval of the polluting solution is varied between 10 μS/cm and 20 mS/cm in order to simulate the pollution levels of the sites between a very low level of contamination and a very heavily contaminated one. The con ductivity of each prepared polluting solution is measured using an electrical conductivity meter with moving probe. The measuring station, illustrated in Fig. 5, consists of a step-up transformer delivering at its secondary a maximum AC voltage of 135 kV and a current of 80 mA. This voltage is rectified by diode (D) in direct (positive polarity: 1) or indirect (negative polarity: 2). The Vcr displays the real voltage applied to the superhydrophobic insulation. The applied insulation voltage is raised manually in steps of 0.5 kV
Fig. 1. Main steps in the manufacture of a silicone superhydrophobic insu lating surface. 2
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Fig. 3. Geometries and characteristics of the electrodes delimiting the superhydrophobic insulating surface.
Fig. 4. Arrangements’ modes for water drops on the surface of the insulation and its support.
Uiem is the applied voltage obtained from the test in the time of i (kV); N is the total times of the valid test, N ¼ 20; RSD is the relative standard deviation of the test result. Since the evacuation voltage of the water drops is related to the ambient temperature, the pressure and the humidity of the air prevailing in the laboratory and that the various tests were not carried out during the same period, in order to compare the direct voltage of water drops’ ejection for the two polarities, all the results obtained were brought back to the normal conditions of temperature θ0, pressure P0 and humidity H0 (θ0 ¼ 20 � C, P0 ¼ 100 kPa and H0 ¼ 11 g/m3) using the following re lationships [25]:
Fig. 5. Diagram for measuring the direct voltage of water drops’ ejection and visualization of their expulsion outside the insulation.
until the last water drop is ejected from the insulation surface. This voltage creates an electric field between the electrodes that generates forces on the drops. Because this voltage is not applied directly to the drops, it is considered an ‘‘indirect voltage of expulsion (Uie)’’, which we will simply call the ‘‘expulsion voltage’’ (Ue) in this document. The display device for the expulsion of water drops outside the material and partial discharges and/or of flashover is shown in Fig. 5. It consists of a camera (Cam) at 1000 photos/s for the recording of the various steps of water drops’ evacuation and a PC for image processing using video studio software 11. For each parameter of influence investigated in this paper, a series of 20 tests were carried out and the retained value of the expulsion voltage of each of water drops, is the arithmetic average of all those obtained on the same series of measurement. The average value and standard devi ation formulas of the ejection voltage of water drops are shown in Formula 1 and 2: N 1 X Uem ¼ Uiem N i¼1
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uN uP u ðUiem Uem Þ2 t1 100% RSD ¼ : Uem N 1
Ue ¼
KH Uem Kd
(3)
With: Uem: Expulsion voltage of the water drops, measured at the tem perature θ and the pressure P and the humidity H; Ue: Ejection voltage of the water drops under normal conditions (θ0, P0 and Hr0); Kd: Correction factor relating to the temperature and the pressure whose expression has the form: Kd ¼
2:93P ð273 þ θÞ
(4)
Where:
(1)
P (pressure) is in kPa and θ (temperature) in � C; KH: Correction factor relating to humidity. Its value is deduced from the charts given in Ref. [25]. The good repetition of the measurement techniques allowed us to have maximum relative RSD equal to 5%.
(2)
Where: Uem is the average of the measured expelling voltage of each of the water drops (kV);
3
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3. Results and discussion
evacuation is one by one expulsion of all the water drops. Finally, the groupo-individual mode of ejection is the combination of the two pre ceding types and consists of successive evacuation of a set of small water drops, sometimes; each of them is accompanied by an individual water drop. With regard to the direction of the drops’ movement, their moving is either only done in one direction (towards the high voltage or the grounded electrode), or bidirectional (towards the high voltage or the grounded electrode), regardless of their location on the leakage path of the insulation. It results from the visualization of the electro hydrodynamic behavior of the water drops more frequent appearance of the groupo-individual and bidirectional expulsion mode of these water drops despite the nature of their arrangement and the polarity of the applied voltage. Regarding the hydrodynamic and electrical forces governing the expulsion of water drops outside the insulation’s surface, we relied on the Navier - Stockes equation, based on the conservation of motion forces and modeling the motion of an incompressible water drop ac cording to relation 5:
3.1. Electrical performance of superhydrophobic insulation without water drops Fig. 6 gives the flashover voltage histogram of the superhydrophobic insulation without water drops as a function of the profile (Pf) of the electrodes delimiting the same surface between electrodes having a total leakage path Lf equal to 4 cm. The value of the mentioned magnitude will serve as a reference to the expulsion voltage of water drops outside the insulation’s surface after they have been deposited on it while it is switched off. As a result, the flashover voltage of the dry insulation under bridge electrodes is greater than that obtained under electrodes with teeth or full electrodes. The maximum relative difference between the insulation’s flashover voltages under bridge and full electrode is about 13%. This can be explained by the decreasing of the contact surface of each of the electrodes with the insulation’s superhydrophobic surface going from full electrodes to those with bridge. Indeed, the flashover path of the insulation, under full or toothed electrodes, is performed at the base of the HV and ground electrodes in contact with the surface of the insulation. This explains the imprint left by the elec trical flashover discharge on this surface. On the other hand, in the case of bridge electrodes, the path of the electrical flashover discharge of the insulation is practically in the air at the height of the bridges, which explains the absence of the discharge’s trace on its surface. For that reason, the place of birth and the length of flashover discharge of the insulation differ from the bridge electrodes compared to the full ones. The maximum relative difference between the negative and the positive DC voltage is about 3%. This difference is negligible, since it is less than the maximum RSD find in this study (ffi 5%). Therefore, the polarity has no effect on the insulation’s flashover voltage, since this is always governed by two negative and positive discharges regardless of the po larity of the DC voltage applied to the dry insulation.
� ! � ∂V ! ! ! ! rPΔ þ μr2 V þ F ¼ d þ V :r V ∂t
(5)
Where: - d, V and μ respectively represent fluid density, velocity and viscosity; ! ! - The three terms: rPΔ , μr2 V and F respectively represent the ef fects of forces due to the pressure, the viscosity and the electrostatic force exerted on the water drop; - The right member of the equality 5 designates the acceleration of the water drop under the three forces’ action. Assuming that the drop retains its spherical shape during its motion and that the surface is superhydrophobic (θ¼ 160� ), the electrostatic ! force F plays a predominant role in the movement of the drop on the superhydrophobic insulation’s surface [26–28]. For an individual water drop, placed on a superhydrophobic surface and put under the action of an electric field, the expression of this electric force is of the form [29]: � � 1 2 1 2 dε F ¼ ρt E (6) ρm jEj rε þ r jEj 2 2 d ρm
3.2. Electrical performance of superhydrophobic insulation covered with water drops 3.2.1. Expulsion mode of water drops from the insulation Regarding the number of expelled water drops and the linking of their evacuation from the surface of the insulation to the electrodes or their ejection bluntly outside the surface, 3 distinct modes were iden tified regardless of the arrangement mode of water drops and the po larity of the applied voltage: individual, with group, or groupoindividual ejection of water drops. The group mode of expulsion means that it takes the form of a set of small water drops leaving sepa rately and successively the surface of the insulation. The individual
Where: E, ρt, ε and ρm respectively represent the electric field, the total charge, the dielectric permittivity of water and the voluminal density. The three terms of the right member of equation (6) represent respectively the Coulomb force, the dielectrophoretic force, and the electrostriction pressure. In this study, the last two terms are neglected because of the uni formity of the electric field prevailing in the planar electrode system and the keep of the spherical shape of the water drop during its expulsion from the insulation. Therefore, the ejection of a single water drop outside the insulation is practically caused by the Coulomb force. In the case of several water drops, the expulsion of water drop from a row which is parallel to the electrodes and very close to them is gov erned by the resultant Coulomb forces and mutual forces of drops’ attraction along the creepage distance of the insulation and of repulsion, perpendicular to the creepage distance in the plane of the insulation [30, 31]. As the water drops in a row move in parallel to the direction of the applied field, so the repulsive forces are considered negligible in this case. In summary, the ejection outside the insulation of the water drops of each row is governed mainly by the resultant Coulomb force directed to the nearest electrode (HV or ground) and the force of mutual attraction directed towards the row of adjacent drops and the force of Coulomb is the most dominant in this case. Fig. 7 summarize some important phases of the group and
Fig. 6. Flashover voltage of superhydrophobic insulation without drops as a function of electrodes’ profile (Lc ¼ 4 cm, Ef: Full electrodes, Et: Tooth elec trodes, Eb: Bridge electrodes, Pf: profile of high voltage electrodes and ground). 4
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Fig. 7. Groups and bidirectional evacuation stages of 25 zigzag water drops of the insulation surface with full electrodes (Ua: Applied voltage, Vd ¼ 60 μl, σv ¼ 10 μS/cm).
bidirectional expulsion mode of a multitude of water drops, arranged in zigzag under negative DC voltage (Fig. 7). Their evacuation from the insulation surface under full electrodes is established completely in 3 steps in the case of their arrangement in zigzag (Fig. 7). Fig. 7a illustrates the zigzag arrangement of 25 water drops covering the surface of the superhydrophobic insulation without voltage (Ua ¼ 0 kV). The image of Fig. 7b corresponds to a phase where small group of water drops is attracted by the HV electrode after coalescence of some of the other persistent drops (Ua ¼ 5 kV). Fig. 7c shows the presence of 4 drops on the surface of the insulation (Ua ¼ 10 kV). Some of the missing drops were attracted to the grounded electrode and the others were ejected squarely outside the insulation. Fig. 7d shows the image of a surface clear of all its drops (Ua ¼ 13.5 kV); their distribution is almost equitable on the high voltage and grounded electrodes. Finally, it appears from Fig. 7 a taper of some drops held by the HV and ground electrodes especially those at their ends. Such deformation of these water drops generally results short-circuit of the leakage path of the insulation, which can lead to partial electrical discharges that can evolve to flashover of the material’s surface. This constitutes a defect characterizing the profile of the full parallelepiped electrodes. The evolution of the expulsion voltage outside the insulation of a set of water drops as a function of their rank is illustrated by Fig. 8. The latter gives histogram characterizing the ratio
water drops from the surface of the insulation to the HV electrode in a ratio
Fig. 8.
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Fig. 9. Partial expulsion of the water drops from the insulation’s surface with full electrodes and the flashover of it (Vd ¼ 40 μl, mk ¼ 0 g/l, σv ¼ 10 μS/cm).
Fig. 10. Partial evacuation of water drops from the surface of the insulation with tooth electrodes and the flashover of it (Vd ¼ 40 μl, Ck ¼ 40 g/l, σv ¼ 10 μS/cm).
Fig. 11. Complete ejection of water drops outside the insulation with bridge electrodes (Vd ¼ 40 μl, Ck ¼ 40 g/l, σv ¼ 10 μS/cm).
visualization of the electrohydrodynamic behavior of the water drops show that the frequency of occurrence of the partial electrical discharges and the insulation’s flashover with tooth electrodes (Fig. 9) is weaker than under full electrodes (Fig. 10). This is almost zero under bridge electrodes (Fig. 11). This is justified by the fact that the full and rounded electrodes retain all the water drops. Because of their small radius of curvature, they taper it and the two partial nets, formed in the vicinity of the two electrodes, meet and short-circuit the leakage distance of the insulation and cause the flashover of the material. The problem of tooth electrodes is explained by their sharp geometry, that favors the attrac tion and trapping of a number of water drops very reduced compared to that collected by the full electrodes. On the other hand, the bridge electrodes with high radius of curvature eject practically all the water drops from the surface of the insulation and rarely one or two drops hang
on their ends, but without causing any electric discharges. Whatever the mode of water drops’ arrangement (Fig. 9a1–b1) and the polarity of the voltage applied to the insulation, leaving the surface of the material under the effect of an electrical field, the first water drops are hooked onto the HV and grounded electrodes respectively (Fig. 9a1–b2). Following their accumulation and their taper with the growth of the electrical field, they succeed with the other drops not yet evacuated or those pushed back by the electrodes, to short-circuit most of the insulation’s dry leakage path, which generates, the formation of partial electrical discharges between the partial water nets (Fig. 9a3–b3), that develop with the increase of the applied voltage, then eventually cause the material’s flashover (Fig. 9a4–b4). In the case of toothed electrodes (Fig. 10a1–b1), some drops are able to escape by passing between the teeth, but others hitched up on the 6
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teeth while attracting others (Fig. 10a2–b2). Their accumulation at the vicinity of the electrodes and the coalescence of some drops not yet expelled from the surface, cause the reduction of the dry leakage path of the insulation (Fig. 10a3–b3). This results an incomplete evacuation of the water drops and the birth of partial electrical discharges between the drops. This discharges progress with the increase of the applied voltage and can lead to the flashover of the material with a lower probability than previously (Fig. 10a4–b4), regardless of the type of water drops’ arrangement with or without kaolin and the polarity of the applied voltage. Fig. 11 gives the essential steps of a complete expulsion, according to groupo-individual and bidirectional mode, of a multitude of water drops with kaolin, deposited on the surface of a superhydrophobic insulation with bridge electrodes (Fig. 11a1–b1). In a ratio
3.2.3. Number of water drops’ rows and their arrangement mode on the insulation In this section, we are particularly interested in the effect of the number of water drops’ rows (Nr) and the mode of their arrangement (Ar) on the electrical performance of the superhydrophobic insulation. The results obtained are illustrated in Fig. 13, giving the characteristic
Fig. 12.
Fig. 13.
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Fig. 14.
Fig. 16.
insulation, this causes the elevation of its expulsion voltage, which in volves the growth of the
In order to study the electrohydrodynamic behavior of water drops on a superhydrophobic insulation under DC voltage, a super hydrophobic insulating surface, based on silicone, was made. The static contact angle of a water drop, placed in a horizontal position on this surface, is of the order of 160� . The sliding angle on this surface, inclined compared to the horizontal, is less than 2� . The visualization of the electrohydrodynamic phenomenon of water drops has highlighted the most frequent apparition of a groupoindividual and bidirectional expulsion mode of these water drops outside the insulation’s surface, regardless of the geometrical and electrical parameters of water drops and the polarity of the applied voltage. Among the three selected electrode geometries, the bridge electrode set has a better profile, allowing easy and fast ejection of all water drops squarely outside the insulation under the application of a voltage which can, in the most unfavorable case, exceed slightly half of that causing its flashover without these water drops, which pass under the bridges constituting the two electrodes without any clinging to their feet. Thus, the formation of any partial electrical discharge and/or of the material’s flashover is inhibited by such a profile and therefore, the super hydrophobicity of the insulation is preserved and its longevity is optimized. Deposition of water drops in straight lines requires a greater evacu ation voltage than under a zigzag arrangement regardless of their vol ume, viscosity and electrical conductivity. The variation of the electrical conductivity of water drops covering the insulation does not in any way affect its electrical performance, on the other hand, the effects exerted by their volume and the amount of kaolin added to the polluting solution on the superhydrophobicity of this material are respectively positive and negative. Finally, the polarity has no influence on the direct expulsion voltage
polarization time constant τ ¼ εσa decreases from 708 μs (εa ¼ 80 � 8.8 e 12 F/m and σ 1 ¼ 10 7 S/m) to 0.35 μs (εa ¼ 80 � 8.8 e 12 F/m and σ 2 ¼ 2.10 2 S/m) is very small in front of the time application of the electric field or of expulsion of the last drop from the insulation (te ffi 10 s) that the water drops’ ejection voltage is not influenced by their electrical conductivity. This result is in very good agreement with those obtained under DC with a superhydrophobic surface delimited by non-uniform electric field electrodes and on which a water drop of electrical conductivity varying between 20 μS/cm and 3 mS/cm [20,33] or between 1 and 107 μS/cm [27]. In addition, the curves of the expul sion voltage of water drops as a function of their electrical conductivity are almost identical for the two polarities of the applied voltage stress. 3.2.6. Kaolin concentration of the water solution Fig. 16 shows the appearance of the characteristic of the ratio
K. Hamour et al.
Journal of Electrostatics 102 (2019) 103375
of the water drops as a function of their electro-geometrical parameters investigated in this study.
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