Dielectric behaviour of particle-contaminated air-gaps in the presence of corona

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Dielectric behaviour of particle-contaminated air-gaps in the presence of corona
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  Journal of ELECTROST TICS ELSEVIER Journal of Electrostatics 36 (1996) 253-275 Dielectric behaviour of particle contaminated air gaps in the presence of corona Lucian Dascalescu , Adrian Samuila, Robert Tobaz6on Laboratoire d Eleetrostatique et de Matbriaux Diblectriques, C.N.R.S., B.P. 166, 38042 Grenoble Cedex 9, France Received 3March 1995; accepted 31 July 1995 Abstract The operating conditions of corona-electrostatic separators, of various electroprecipitators, and of other similar high-voltage devices are influenced by the size and shape of the particles which pass through the inter-electrode air-gap. The presence of corona discharge affects the movements and the charge of the particles, and hence modifies the breakdown threshold. The numerical analysis of the electric field, using a charge simulation program, enabled the evaluation of the effects. Two other computer programs were written in order to analyse the conditions in which micro-discharges can occur between charged particles and electrodes of opposite polarities, and to estimate the consequences of such an event on the global dielectric strength of an ionized air-gap. Nevertheless, a systematical experimental study was necessary to fully-understand the phenomena. The basic electrode arrangement consisted in a matrix of corona-emitting points situated above a plate electrode. In some experiments, a grounded metallic grid was interposed between the two electrodes connected to high-voltage supplies of opposite polarities, so that the ionic current density and the intensity of the electric field be independently controlled. Both the computational results and the experimental data demon- strated that the presence of particles in air-gaps affected by corona discharges has a more important influence on the dielectric strength than in the case of a charge-free electric field. Keywords: Corona; Particle contamination; Electrostatic separation; Electrical breakdown; Air gaps; Pauthenier's formula; Spark discharge 1 Introduction The presence of particles in compressed gas insulated systems has been demon- strated to reduce dramatically the breakdown voltage. In some cases, the rigidity of the gases was found to be as low as 10% of the uncontaminated value [1]. Numerous * Corresponding author. 0304-3886/96/ 15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0304-3886(95)00050-X  254 L. Dascalescu et al./Journal of Electrostatics 36 1996) 253-275 Fig 1. Spark discharge due to the presence of an mm-size metallic particle between the electrodes of a roll-type corona-electrostatic separator. 1: corona electrode; 2: grounded rotating roll electrode; 3: granular material; 4: vibratory feeder. papers [2-7] have been published on this topic since 1968, when Dakin and Hughes [8] showed that: i) a quite low uniform electric field was able to lift and move heavy metallic spheres in air or in transformer oil; ii) breakdown could be initiated by the microdischarge produced by these particles when approaching the electrodes. Most of the reported experiments were carried out with a.c. high-voltages. They involved different gases air, SF6, N2), in a wide range of pressures, and were made in plane- parallel or coaxial electric fields, with either conducting or insulating particles, of various shapes and specific weights. The recent progresses in the electrostatic technologies such as gas cleaning, xerocopying, painting, separation of granular materials) have expanded the spectrum of high-voltage installations the dielectric strength of which might be affected by the presence of particles. For instance, recent studies of Morar et al. [9], Iuga et al. [10], and Dascalescu et al. [11] revealed that the d.c. high-voltage operating conditions of corona-electrostatic separators are influenced by the size and shape of the particulates which pass through the inter-electrode gap. Most of the above-cited electrotechnolo- gies make use of corona as the charging mechanism for the processed particles dust collected in the precipitators, mm-size granules selectively sorted in the elec- troseparators). This justifies the interest for studying the behaviour of conducting particles in d.c. corona fields Fig. l), which is inherently different than in charge-free electric fields, as demonstrated by the experimental results communicated by  L. Dascalescu et al./Journal of Electrostatics 36 1996) 253-275 255 corona electrode IIIII III >0 F*> mg E n ) t o corona electrode IIllllll I q>0 Q(t3)>0 corona electrode corona electrode I I I I I I I I I I I I I I I q>0 I Q tl) l< Eo < I QI q>0 Q t2) ~ xlrl t 1 t2 corona electrode corona electrode I I I I I I I I I I I I_11 I I q>0 0<Q t4)<Q q>0 ~1 Q ts)[ > <ta) Eo t3 t4 t 5 Fig. 2. Physical mechanism of particle-initiated breakdown between parallel plate electrodes in the pres- ence of d.c. corona; to: contact charging; tl: lift-off; tz: maximum amplitude of particle movement Xm: extreme position of the particle above the electrode); t3: descent; t4: micro-discharge between the positively-charged particle and the bottom electrode of opposite polarity Xd: distance at which the micro-discharge occurs); ts: breakdown of the main air-gap between the upper electrode and the particle shorted to the bottom electrode. Dascalescu et al. [12], and explained by the mathematical model published by Dascalescu and Mihailescu [13]. The aim of this paper is to give a better understanding of the basic mechanism which reduces the breakdown threshold of cm-size air-gaps, simultaneously affected by the presence of mm-size particles and of d,c. corona, at atmospheric pressure. The study will focus on conducting spheres, as the insulating particles have been found to influence less the dielectric behaviour of gases. 2. Theoretical aspects A plane-parallel electric field Eo (Fig. 2) between two horizontal plate electrodes can represent an acceptable model for most of the situations which have a practical interest. Following Thomson s reasoning [14], the distribution of Eo and of the unipolar space-charge density q in the air-gap of permittivity ~ can be evaluated with: Eo(3) = [2J(s -- ~)/ ~k) + E 2 (s)] 1/2, (1) _ E2~sxq - 1/2 q ~) = -- J/k) [2J(s -- ~)/ ek) + o~ p3 , (2) where k represents the ion mobility and J is the density of the current between the two electrodes situated at a distance s, ~ being the vertical coordinate of the system, such that ~ = 0 at the bottom (grounded) electrode and ~ = s at the upper (charge- injecting) electrode, of potential V.  256 L. Dascalescu et al./Journal of Electrostatics 36 1996) 253-275 In the hypothesis of a very strong charge injection (i.e., q s) ~ - oo), the electric field at the upper electrode is Eo s) = 0. In that case, the intensity of the electric field at the surface of the bottom electrode becomes: Eo(O) = (3) Eu., (3) where E. = V/s 4) is the field in a charge-free gap stressed by a d.c. voltage V. The variation of Eo in the proximity of the bottom electrode is of only about 5 for 1-~ of the inter-electrode gap: Eo(0.1s) = [2J O.9s)/ ek)] :/2 = 0.91/2 Eo(0) ~ 0.95 Eo(0). (5) In gases, the ratio Eo/E,n is significantly inferior to 3, i.e., Eo O)=2E,n, 1 <2<1.5, (6) and the field in the proximity of the non-injecting electrode is quasi-uniform. The above formula shows that the space charge intensifies the electric field on the surface of the bottom (non-ionizing) electrode. This fact should be borne in mind when examining the peculiarities of physical phenomena in the ionized air-gap between two high-voltage electrodes. The presence of a conducting particle in such a device represents an important perturbation. Before a voltage was applied between the electrodes, the particle is found on the bottom plane, by virtue of the gravitational force. As soon as the electrodes are connected to a d.c. high-voltage supply, the particle acquires an electric charge Qm, by contact with the electrode (instant to in Fig. 2). Frlici calculated Qm for particles of various shapes, in the hypothesis that the electrode is affected by a charge-free uniform electric field [15]; for instance, a sphere of radius R acquires a charge: Q~ = 27z3/3)eR2 Eo . (7) In a first approximation, for particles which are small relative to the air-gap between the electrodes, the same formula can be also used in the presence of a space charge, but E0 has to be substituted with Eo(0) given by (6). The particle in contact with an electrode is subjected to an electrostatic detachment force F* which is proportional to the amount of charge that it has acquired (Qm). Due to the attraction between the image charges, this detachment force is inferior to the force F~ = QmEo exerted by the electric field on the same particle, at some distance from the electrode. For a sphere, F* can be analytically evaluated as [15]: F* = 0.832QmEo. (8) The condition for detachment can be calculated by equating the electrostatic force F* to the gravitational force Fg. If F* < gg the particle remains at rest on the bottom electrode, but it represents a protrusion which affects the rigidity of the air-gap.  L. Dascalescu et al./Journal of Electrostatics 36 1996) 253-275 57 In F* > Fg, the particle detaches from the bottom plane. The lift-off field can be evaluated with the following formula [3]: Elo = 0.494 Rps 9/e) 1/2. (9) Since the contact with the electrode has ceased (instant tl in Fig. 2) and the particle evolves in a space charge q of opposite polarity, the charge Q of a sphere diminishes [16]: dO/dr = Q - Q~)E/ zQ), 10) where Qs represents the maximum (saturation) charge acquired in an ionized electric field: Qs = 12~eR2Eo, (11) and z is a time constant: z = 4~flqk). (12) In accordance with Pauthenier s formula, which was confirmed by experiments carried out with steel balls of 3 mm diameter [17], the saturation charge Qs acquired in a mono-ionised field is 1.825 times the maximum charge Qm of the same particle in contact with an electrode in a uniform charge-free electric field. As a consequence of charge diminution in the mono-ionised field, the electrostatic force F decreases quite fast and eventually changes its sign, making the particle return to the electrode. At the instant t2 (Fig. 2), the particle reaches the highest position Xm above the bottom electrode. As the distance x between the positively-charged particle and the electrode of negative polarity reduces (instant t3 in Fig. 2), the local intensity of the electric field in the particle-electrode gap increases. An electron avalanche can develop along the axis of this gap and a micro-discharge occurs between the particle and the electrode (instant t4 in Fig. 2). The conditions for such a local breakdown can be evaluated analytically, for uncharged spheres, using the method of Hara and Akazaki [18], or numerically, as demonstrated in [193. Through the channel of the micro-discharge, the particle acquires practically the same potential as the bottom electrode, with which it can be assumed to be shorted. Such a particle determines a significant intensification of the electric field in the air-gap between the particle and the upper electrode, of opposite polarity. Under these circumstances, a critical electron avalanche may develop at the top of the particle (instant ts in Fig. 2). Parekh and Srivastava [19] were able to evaluate the breakdown voltage Vb for a charge-free gap between plate electrodes in the presence of a mobile spherical particle. As the space charge modifies the behaviour of conductive particles, it is expected that the value of the breakdown voltage will be different in a corona discharge. The results presented in the following sections of the paper confirm this expectation.
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