Characteristics of Negative Corona Discharge in Single-Needle- and Multi- Needle-to-Plane Configurations

Transcription

1 Abdel-Salam et al. 2 Characteristics of Negative Corona Discharge in Single-Needle- and Multi- Needle-to-Plane Configurations M. Abdel-Salam, A. Hashem 2, and E. Sidique 3 Deartment of Electrical Engineering, Assiut University, Egyt 2 Deartment of Physics, Faculty of Science, Assiut University, Egyt 3 Deartment of Science and Math, Faculty of Education at New Valley, Assiut University, Egyt Abstract This aer investigates the characteristics of corona discharge in single-needle- and multi-needle-to-lane s including the onset voltage and the current-voltage relationshi and their deendency on the number of needles, the needles' height, the needles' ti radius, the needle-to-needle sacing and the sacing between needles and the ground late. The onset voltage is measured in the lab and calculated based on the criterion of self-recurrence of electron avalanches growing in the vicinity of the needles when stressed negatively. This calls for calculating the electric field in the vicinity of the needles using the charge simulation method. The calculated onset voltage values agree reasonably with those measured exerimentally. The corona current-voltage characteristics have been studied exerimentally to assess how the total corona current in multi-needle s is influenced by the number of needles, the needle-to-needle sacing and the sacing between needles and the ground late. Keywords Onset voltage, corona discharge, corona current, electric field, electron avalanche, single and multineedle s I. INTRODUCTION Electrical corona discharges in gases have many technical alications, for examle in lasma reactors, cold lasma chemistry, electro-hotograhy, electrostatic rinting, electrostatic searation, air ollution control, static electricity elimination, dielectric charging, flowinggas lasers, electrostatic reciitators, or ozonizers and also corona discharge reactors for air urification from noxious gases. In many of these cases, multioint discharge electrodes are utilized []. Most of the researches have mainly concerned on the corona discharge characteristics in a single oint to lane geometry. Although this has a fundamental hysical significance, its ractical alication is rather oor. It is worthwhile to understand the interaction of neighboring coronas to affect the discharge modes on rough surfaces which are characterized by discrete sots at which the discharge is localized [2]. To the authors knowledge, there are only a few aers which investigate electrical characteristics of corona discharge from multile interaction oints. Pioneering in this subject was the aer by Lama and Gallo [3]. It confirmed that adjacent localized discharges tend to reel each other, or simly to interact with each other. Abdel Salam et al. [4] have studied the ositive corona from two interacting needles, determining the corona current, corona onset voltage and ulse reetition rate. Thanh [5] has determined the current-voltage characteristics of multile oint electrode with needles arranged linearly or circularly. Yamamoto et al. [6] have determined theoretically Corresonding author: Mazen Abdel-Salam address: mazenas@yahoo.com the sace charge distribution in the multioint corona discharge assuming an infinite array of oints as the discharge electrode. The distribution of the corona current at the grounded lane against barbed multi oints rotruding from a late has been studied by McKinney et al. [7]. They have investigated the current distribution as influenced by the barb length, barb oint radius of curvature, barb attern, alied voltage, and late-tolane sacing on the current distribution. Through visualizing oxidation atterns of the current distributions on a coer ground lane, they discovered that the sace charges generated by adjacent oints (barbs) do not overla each other. They have showed that barb ti-tolane sacing and alied voltage control maximum current density, whereas barb length, barb sacing, and barb attern govern current density uniformity. The resent aer models the incetion of negative coronas develoed at five, nine and thirteen tis of sewing needles attached to a circular conducting late and ositioned oosite to a flat late. For comarison urose, the incetion of corona from a single needle attached to the center of the same circular late is investigated. Through this modeling, the onset voltage is obtained by formulating the conditions necessary for the discharge to be self sustained. The model takes into account all the individual rocesses and events, e.g. gas ionization, attachment, hoto-ionization, etc., which are thought to be effective in the discharge rocess. As these events are field deendent, the accurate charge simulation technique [8] and the method of images are used for field calculation. The onset voltage of corona in atmosheric air is calculated and measured in the laboratory. First, the method of calculating the alied field in the investigated ga with multile and single needles is exlained. Second, the mathematical modeling of the

2 22 International Journal of Plasma Environmental Science & Technology, Vol.7, No.2, JULY 203 (a) (b) (c) (d) (e) (f) (g) Fig.. Schematic diagrams. (a) Parallel lates saced distance L with hyerboloidal needles attached to the uer late. (b), (c), (d), (e), (f) and (g) Needles arrangement in the lane Z = L; in line, triangular, square, entagonal, hexagonal and square mesh resectively. discharge onset is resented. Third, the obtained onsetvoltage values are discussed and comared with the corresonding measured values for single and multineedle s. Fourth, the current-voltage characteristics of single- and multi-needle s are measured and discussed. Finally, the conclusions extracted from the resent work are resented. II. ELECTIC FIELD CALCULATION Fig. (a) shows two arallel horizontal lates saced distance L with hyerboloidal needles attached to the uer late. Each needle has ti radius r t and height h and the needles are arranged in different s as

3 Abdel-Salam et al. 23 (a) (b) Fig. 2. Schematic diagrams. (a) Arrangement of simulation charges and boundary oints at a given z j -z j level for needles in the square (b) Arrangement of simulation charges and boundary oints on the stressed late. shown in Figs. (b)-(g) in the lane Z = L. The uer late is stressed by voltage V with resect to the grounded lower late. A. Charge Simulation Technique The charge simulation method [8] is used to calculate the otential and the electric field in the sace surrounding the needles between the two arallel lates. The surface charge on the uer late and needles is simulated by oint charges. Image charges with resect to the ground lower late are considered. This ensures that the ground late is ket at zero otential. Each needle is divided into N horizontal levels saced unequally with increasing distance from ti toward the needle base according to a geometry series. The z(j) coordinate for that levels is given by:

4 24 International Journal of Plasma Environmental Science & Technology, Vol.7, No.2, JULY 203 j j L h A B z, j =, 2, 3,, N N h B, A C rt A where B is the base of the geometry series, A is the first term of the geometry series, C is a fraction in the resent work. At each z-level for each needle, a number N r of simulation oint charges are uniformly distributed on a circle centered on the axis of needle with a radius r(j), j =, 2, 3,, N equals to a fraction β of the needle radius at the same z-level as shown in Fig. 2(a) Thus, the total number of the simulated oint charges for each needle is (N N r ). The surface charge on the stressed late is simulated by N 2 horizontal ring charges centered on the axis of the stressed late with a radius r (j) and saced at gradually increasing distances along the z-direction. At each z-level, the ring is simulated by N oint charges uniformly distributed on its erihery. Each ring has a coordinate z (j) related to its radius r (j) as exressed by: z (j) = L + r (j), j =, 2,, N 2 The total number of the oint charges simulating the stressed late is (N 2 N ). Therefore the total number of the simulation oint charges is N (= N n N N r +N 2 N ) where, N n is the total number of needles. Symmetry of needles could be utilized to reduce the number of unknown simulation charges. For the case of square Figs. (d) and 2(a), for examle, the number of unknown charges N is reduced to n 8 A.. Electric Potential Nn N Nr N2 N The otential i at an ith oint of coordinates (x i, y i, z i ) is the algebraic sum of the otential contributions due to all simulation charges Q j, j =, 2, 3,, N. i N ij j where, P ij is the otential coefficient exressed as: Q j () (2) ij 4 o 2 j =, 2, 3, 4,, N i =, 2, 3, 4,, N x i x j yi y j zi z x x 2 y y 2 z z 2 j 2 i j i j i j where, is the distance between the ith oint and the jth simulation oint, 2 is the distance between the ith oint and the image of the jth simulation oint and (x j, y j, z j ) are the coordinates of the jth simulation charge. 0 is ermittivity of free sace. A.2. Boundary Conditions The boundary condition is that the otential at any boundary oint (x i, y i, z i ) chosen on both the stressed late and the attached needles is equal to the known alied voltage V. The otential at any oint on the ground late electrode is equal to zero and this is automatically satisfied by considering the image charges, which are symmetrically located with resect to that late. A.3. Boundary Points To evaluate the unknown simulation charges Q j, j =, 2, 3,, n, a set of boundary oints equal in number to that of the unknown simulation charges is chosen on the surface of the needles and the stressed late as shown in Fig. 2 to satisfy the boundary conditions: = V at the stressed late and needles, = 0 at ground late. First, corresonding to each unknown simulation ring charge of stressed late, boundary oints are chosen at the late itself at a radial distance equal to the ring radius. Thus, the z-coordinate of the boundary oints is equal to the sacing L between the arallel lates. Second, corresonding to each unknown simulation charge of each needle, a boundary oint is chosen on the surface of the needles at the same z-level and along the same radial direction. A.4. Determination of the Unknowns Satisfaction of the boundary conditions at the boundary oints formulates a set of equations relating the values of simulation charges to the otential values at the boundary oints. This is exressed in a matrix form as: Q V P (3) where [P] is the otential coefficient matrix (with dimension n n), [Q] are unknown simulation charges matrix (with dimension n ), and [V] are the otential values of the boundary oints matrix (with dimension n ). Solution of the set of Eq. (3) using the Gauss eliminations method [3] determines the unknown simulation charges Q j. A.5. Accuracy of Solution and Check Points To check the accuracy of the solution, a set of check oints is chosen, each check oint is located between two successive boundary oints. The calculated otential value is to be checked against the alied value for check

5 Abdel-Salam et al. 25 oints at the surface of the needles and the stressed late. The deviation of the calculated otential at these check oints from the alied voltage is a measure of the accuracy of roosed simulation method. The rms value of the otential deviation V averaged over the stressed late and the needles should not exceed a rescribed value; ± % in the resent work. B. Electric Field Once the accuracy is checked and the simulation charges are determined, the electric field intensity at any oint (x, y, z ) can be determined: E E x y E z 4 o 4 o 4 o N j N j N j x x j Q j 3 y y j Q j 3 z z j Q j 3 x x j 3 2 y y j 3 2 z z j 3 2 (4) (5) (6) The magnitude of the electric field intensity at oint is calculated as: E 2 x 2 y 2 z E E E [V/m] (7) III. CORONA ONSET VOLTAGE CALCULATION When the electrode is stressed negatively, the electric field near a needle ti reaches the threshold value for ionization of gas molecules by electron collision. A rimary electron avalanche starts to develo along the direction of maximum field away from the needle ti as shown in Fig. 3. With the growth of the avalanche through the so-called ionization zone of thickness li, more electrons are develoed at its head, more hotons are emitted in all directions and more ositive ions are left in the avalanche wake. The number of electrons N e (l) at a distance l from the starting oint (l = 0) along the direction of maximum stress is given by: l N e ( l) ex (8) l l dl 0 where is the ionization coefficient and is the coefficient of electron attachment. The ionization and attachment coefficients deend on the electric field [9]. For a successor avalanche to be started, the receding avalanche should somehow rovide an initiating electron at the needle surface, ossibly by hotoemission, ositive-ion imact, metastable action, or field emission, Fig. 3. Field emission is ossible only at field strengths exceeding V/m [2]. Electron emission by ositive-ion imact is more than two orders of magnitude less robable than hotoemission [2]. Metastables have been reorted to have an effect aroximately equal to that of ositive-ion imact [9]. Therefore, only the first mechanism (electron emission by hotons) was considered in determining the incetion voltage V 0 [0]. The number of electrons hoto-emitted from the needle surface is e l i h 0 l N l g l ex l N ( h) dl (9) e where l i, the ionization-zone thickness, is the limiting value of z at which =. h is Townsend s second coefficient due to the action of hotons, is the absortion coefficient at atmosheric ressure and g (l) is a geometry factor to account for the fact that some hotons are not received by the needle []. The condition for a new (successor) avalanche to develo is N e (h) (0) The corona onset voltage V 0 does not aear exlicitly in the relation (0). However, the alied voltage affects the values of (l), (l), and hence, N e (l). The onset voltage V 0 is the critical value which fulfills the equality (0). IV. DISCHARGE PARAMETERS In order to calculate the onset voltage of corona at atmosheric ressure, the equality (9) was solved using the values available in [9,, 2], for,, h and. The equations relating [cm - ] and [cm - ] at atmosheric ressure P [torr] to the electric field E [V/cm] were exressed as: P Fig. 3. The develoment of an avalanche. 2 3 E 5 E P E ex 22 P P P for E P

6 26 International Journal of Plasma Environmental Science & Technology, Vol.7, No.2, JULY 203 Fig. 4. Schematic diagram of exerimental setu. E 9.682ex 2642 P P E 5ex 365 P P E for P E for P The coefficient of hoton absortion was taken 5 cm - []. The coefficient of electron emission by hotons h was taken []. V. EXPERIMENTAL SETUP AND TECHNIQUE A. Exerimental Setu The two arallel lates were brass discs of 75 mmdiameter with rounded edges to avoid edge discharge, Fig. 4. The needles are the tis of stainless steel sewing needles with ti radius r t = 0.03 mm. The needles have height h = 2.34 mm. The needle-to-needle sacing m is varying from 2.5 to 5 mm. The ga sacing (L-h) is varying in the range from 5 to 2.5 mm. The alied voltage is a negative DC voltage obtained from a DC high voltage ower suly (manufactured by Gamma High Voltage Research, Inc., USA) of variable outut voltage 0-50 kv, outut current 0-6 ma and regulation 0.005%. The voltage was alied to the uer late through a 2 MΩ limiting resistance to revent any damage of the measuring instruments when flashover occurs between the lates. The lower late was grounded through a sensitive digital multi-meter to record DC corona current down to 0.0 A with accuracy ±0.8% and resolution 0 na, Fig. 4. B. Exerimental Technique The ground late was connecter to ground through a digital micro-ammeter used for measuring the corona current from stressed needles. The onset voltage is the alied voltage when the micro ammeter starts to record a reading just above the zero value. The onset voltage in air was measured for single-needle and multi-needle s with different needle-to-needle sacings and ga sacings. VI. RESULTS AND DISCUSSION A. Accuracy of Proosed Charge Simulation Technique The accuracy of charge simulation technique is checked by investigating how the boundary conditions are satisfied for all s with single- and multineedle (square, triangular, entagonal, hexagonal, square mesh and line s), Figs. (b)-(g). It is satisfactory that the maximum ercentage error of the calculated surface otential of the needles and the stressed late did not exceed 0.49%, which confirms the accuracy of the roosed simulation of surface charges on the needles and the stressed late. The integral of the calculated electric field along the ga axis excluding the sace occuied by the needles is equal to the alied voltage with a deviation less than 0.3% cases of single- and multi-needle. This is another measure of the accuracy of the roosed charge simulation technique. For a unit alied voltage, Figs. 5-8 show the calculated otential distribution for a unit alied voltage over the surfaces of the stressed late and needles of single needle and square s with 5, 9 and 3 needles (r t = 0.03 mm, h = 2.34 mm, (L-h) = 0 mm and m = 5 mm), Fig. (d). For N = 23, N 2 = 50, N r = 40 and N = 40, such that, the simulation charges of the stressed late and each needle in each case were, 920, resectively. The otential-deviation of the calculated otential from the alied voltage value over the surface of the stressed late and needles did not exceed 0.3%,

7 Abdel-Salam et al. 27 Calculated otential, V Calculated otential on central needle surface Calculated otential on stressed late surface Alied voltage Distance measured from the ga axis along the stressed late, mm Fig. 5. Calculated otential versus distance measured from the ga axis along the central needle and stressed late in single needle comared with the unit alied voltage. Calculated otential, V Calculated otential on central needle surface Calculated otential on R needle surface Calculated otential on R2 needle surface Calculated otential on stressed late surface Alied voltage Distance measured from the ga axis along the stressed late, mm Fig. 7. Calculated otential versus distance measured from the ga axis along the needles and stressed late in a square with 9-needles comared with the unit alied voltage. Calculated otential, V Calculated otential on central needle surface Calculated otential on R needle surface Calculated otential on stressed late surface Alied voltage Calculated otential, V Calculated otential on central needle surface Calculated otential on R needle surface Calculated otential on R2 needle surface Calculated otential on R3 needle surface Calculated otential on stressed late surface Alied voltage Distance measured from the ga axis along the stressed late, mm Fig. 6. Calculated otential versus distance measured from the ga axis along the needles and stressed late in a square with 5-needles comared with the unit alied voltage. which confirms the accuracy of the roosed simulation of surface charges on the stressed late and the needles. B. Electrostatic Field along the Needles' Axes The electrostatic field intensity along the needles' axes (arallel to z-axis) starting from the surface of the needle down to grounded late is shown in Figs. 9-2 for single-, five-, nine- and thirteen-needles attached with the stressed late. The needles in multi-needle are arranged in two erendicular rows (square, Fig. (d)) equidistant from the grounded late, (Lh) = 0 mm and saced equally from each other in each direction, m = 5 mm. The needles have the same ti radius r t = 0.03 mm and the same height h = 2.34 mm. The uer late with the needle are stressed by kv. In the case of multi-needle s it is clear that the field near the outer needles is higher than that for the central needle. This is simly exlained by the shielding effect imosed on the central needle due to the other needles, Figs. 3-5 (magnification of Figs. 0-2). On the other hand, the field near the grounded late for the outer needles is smaller than that for the central needle, Distance measured from the ga axis along the stressed late, mm Fig. 8. Calculated otential versus distance measured from the ga axis along the needles and stressed late in a square with 3-needles comared with the unit alied voltage. Figs. 6-8 (magnification of Figs. 0-2). This conforms to the fact that the voltage alied to the needles is the same, so the line integral of the field value from needles surfaces down to the grounded late should be the same. C. Electrostatic Field along Ga Axis or Z-Axis The electrostatic field intensity along the ga axis (Zaxis) starting from the surface of the central needle down to grounded late is shown in Fig. 9 for single-needle case and multi-needle cases (square with five-, nine- and thirteen- needles). It is clear that the field near the central needle in case of single needle is higher than that for multi-needle s. This is simly exlained by the shielding effect imosed on the central needle due to other needles as mentioned before, Fig. 20 (magnification of Fig. 9). On the other hand, the field near the grounded late for single-needle is smaller than that for multi-needle, Fig. 2 (magnification of Fig. 9). This conforms to the fact that the voltage alied to the needles is the same, so the line integral of the field value

8 28 International Journal of Plasma Environmental Science & Technology, Vol.7, No.2, JULY R needle R2 needle u to grounded late, mm Fig. 9. Electrostatic field distribution along axis below central needle for single-needle at an alied voltage of kv u to grounded late, mm from the central needle surface down to the grounded late should be the same whatever the number of needles. D. Corona Onset Voltage Calculation R needle Fig. 0. Electrostatic field distribution along axis below the needles for multi-needle case (square with 5-needle) at an alied voltage of kv. The roosed criterion (0) is alied for different s such as triangular with 4, 7 and 0 needles, square with 5, 9 and 3 needles, entagonal with 6, and 6 needles, hexagonal with 7, 3 and 9 needles, line with 3, 5 and 7 needles and square mesh with 9 and 25 needles (r t = 0.03 mm, (L-h) = 0 mm, h = 2.34 mm and m = 3 mm in all cases). The calculated corona onset voltage values are reorted in Tables I and II and are comared with that of single-needle. D.. Onset Voltage as Influenced by Needle-to-needle Sacing The onset voltage values of corona on the needles of the multi-needle cases such as in the square u to grounded late, mm Fig.. Electrostatic field distribution along axis below the needles for multi-needle case (square with 9-needle) at an alied voltage of kv R needle R2 needle R3 needle u to grounded late, mm Fig. 2. Electrostatic field distribution along axis below the needles for multi-needle case (square with 3-needle) at an alied voltage of kv. deend on the needle-to-needle sacing for the same needle radius, needle height and ga sacing. The onset voltage is higher for corona on the central needle when comared with other needles, Figs. 22 and 23. This is attributed to the decrease of the field in the vicinity of the central needle due to the above mentioned shielding effect by the other needles. With the increase of the needle-to-needle sacing, the onset voltage decreases because of the less shielding effect which makes the field in the vicinity of needles increases. With further increase of the needle-to-needle sacing, the onset voltage aroaches the same value for all needles where each needle behaves searately with no interaction (shielding) among needles, Figs. 22 and 23. It is quite clear that the difference between the corona onset voltage of the outer needle and that of the central needle decreases with the increase of the needle-to-needle sacing, Figs. 22 and 23. D.2. Onset Voltage as Influenced by Number of Needles In any case of multi-needle s, it is quite clear that the onset voltage V 0 is the highest for the

9 Abdel-Salam et al R needle R needle u to grounded late, mm Fig. 3. Electrostatic field distribution along axis below the needles for multi-needle case (square with 5-needle) near the needles at an alied voltage of kv R needle R2 needle u to grounded late, mm Fig. 4. Electrostatic field distribution along axis below the needles for multi-needle case (square with 9-needle) near the needles at an alied voltage of kv u to grounded late, mm Fig. 6. Electrostatic field distribution along axis below the needles for multi-needle case (square with 5-needle) near the grounded late at an alied voltage of kv R needle R2 needle u to grounded late, mm Fig. 7. Electrostatic field distribution along axis below the needles for multi-needle case (square with 9-needle) near the grounded late at an alied voltage of kv R needle R2 needle R3 needle R needle R2 needle R3 needle u to grounded late, mm Fig. 5. Electrostatic field distribution along axis below the needles for multi-needle case (square with 3- needle) near the needles at an alied voltage of kv. central needle and decreases for needles in the direction away from the central one. This is because the central needle in multi-needle s is fully shielded by the other needles as stated above with a subsequent decrease of the field at its surface. At the central needle, the onset voltage increases with the increase of the number of needles, Tables I and II as the shielding effect u to grounded late, mm Fig. 8. Electrostatic field distribution along axis below the needles for multi-needle case (square with 3-needle) near the grounded late at an alied voltage of kv. becomes more ronounced with the increase of the number of needles. It is quite clear that, the onset voltage of the outer needles decreases with the increase of the number of needles for the triangular, square, entagonal and hexagonal s, Table I. On the contrary, the onset voltage increases with the increase of the number of needles for the line and square mesh s,

10 30 International Journal of Plasma Environmental Science & Technology, Vol.7, No.2, JULY 203 Table II in agreement with revious findings [4] for line. This is evident from the calculated values of the electric field at the needles' tis for all s, Tables III and IV, where the field value of the outer needles increases with the increase of the Single needle Five needles Nine needles Thirteen needles Distance along ga axis(z-axis), mm Fig. 9. Electrostatic field distribution along the ga axis (z-axis) for single-case and multi- needle cases (square with 5, 9 and 3 needles) at an alied voltage of kv. number of needles for the triangular, square, entagonal and hexagonal s, Table III. On the contrary, the field value decreases with the increase of the number of needles for the line and square mesh s, Table IV. Also, it is quite clear that the onset voltage values of any multi-needle s are higher than that from single-needle, Tables I and II, and this is attributed to the decrease of the field in the vicinity of the outer needles due to the above mentioned shielding effect by the other needle. D.3. Onset Voltage as Influenced by Needle Ti Radius The onset voltage V 0 values of corona for singleneedle and multi-needle s are influenced by the needle ti radius for the same the needle-to-needle sacing, needle height and ga sacing, Fig. 24. With the increase of the needle ti radius of needles, the onset voltage increases because of the exected decrease of the alied field. It is quite clear that the difference between Single needle Five needles Nine needles Thirteen needles Single needle Five needles Nine needles Thirteen needles Distance along ga axis(z-axis), mm Distance along ga axis(z-axis), mm Fig. 20. Electrostatic field distribution along the ga axis (z-axis) near the central needle for single-case and multi- needle cases (square with 5, 9 and 3 needles) at an alied voltage of kv. Fig. 2. Electrostatic field distribution along the ga axis (z-axis) near the grounded late for single-case and multi-needle cases (square with 5, 9 and 3 needles) at an alied voltage of kv. TABLE I CALCULATED CORONA ONSET VOLTAGE VALUES FOR SINGLE- AND MULTI-NEEDLE CONFIGURATIONS (TRIANGULAR, SQUARE, PENTAGONAL AND HEXAGONAL CONFIGURATION) Triangular Square Pentagonal Hexagonal Corona onset voltage, kv Central-needle R-needle R2-needle R3-needle -Needle Needles Needles Needles Needle Needles Needles Needles Needle Needles Needles Needles Needle Needles Needles Needles

11 Abdel-Salam et al. 3 TABLE II CALCULATED CORONA ONSET VOLTAGE VALUES FOR SINGLE- AND MULTI-NEEDLE CONFIGURATIONS (LINE AND SQUARE MESH CONFIGURATION) Square mesh Corona onset voltage, kv Central-needle R-needle R2-needle R3-needle -Needle Needles Needles Needles Central-needle R-needle Rc-needle R2-needle Rs-needle Rc2-needle -Needle Needles Needles Line TABLE III CALCULATED ELECTRIC FIELD VALUES FOR SINGLE- AND MULTI-NEEDLE CONFIGURATIONS (TRIANGULAR, SQUARE, PENTAGONAL AND HEXAGONAL CONFIGURATION) Triangular Square Pentagonal Hexagonal Electric field, kv/mm Central-needle R-needle R2-needle R3-needle -Needle Needles Needles Needles Needle Needles Needles Needles Needle Needles Needles Needles Needle Needles Needles Needles TABLE IV CALCULATED ELECTRIC FIELD VALUES FOR SINGLE- AND MULTI-NEEDLE CONFIGURATIONS (LINE AND SQUARE MESH CONFIGURATION) Square mesh Electric field, kv/mm Central-needle R-needle R2-needle R3-needle -Needle Needles Needles Needles Central-needle R-needle Rc-needle R2-needle Rs-needle Rc2-needle -Needle Needles Needles Line the corona onset voltage of the single needle case and that of the multi-needle s increases with the increase of the needle ti radius. Fig. 24 Shows the calculated onset voltage versus needle ti radius, at constant needle-to-needle sacing m = 5 mm, needle height h = 2.34 mm and ga sacing (L-h) = 5 mm for single-needle case and multi-needle square. D.4. Onset Voltage as Influenced by Needle Height The onset voltage V 0 values for single-needle and multi-needle s is influenced by the needle height for the same the needle-to-needle sacing, needle ti radius and ga sacing, Fig. 25. With the increase of the needle height of needles, the onset voltage decreases because of the exected decrease of the alied field. It is quite clear that the difference between the corona onset voltage of the single-needle case and the multi-needle s increases with the increase of the needle height. Fig. 25 shows that calculated onset voltage versus needle height, at constant needle-to-needle sacing m = 5 mm, needle ti radius r t = 30 m and ga sacing (L-h) = 0 mm for single-needle case and multi-needle square.

12 32 International Journal of Plasma Environmental Science & Technology, Vol.7, No.2, JULY 203 Corona Onset voltage, kv R needle Corona Onset Voltage, kv Single-needle Five-needles Nine-needles Needle-to-Needle sacing, mm Needle height, mm Fig. 22. Variation of corona onset voltage with needle-to-needle sacing of multi-needle case (square with five-needle at r t = 0.03 mm, (L-h) = 5 mm and h = 2.34 mm). Fig. 25. Calculated onset voltage versus needle height. Corona Onset voltage, kv R needle R2 needle Needle-to-Needle sacing, mm Fig. 26. Effect of ga sacing on current-voltage characteristics of single-needle case (r t = 0.03 mm and h = 2.34 mm). Fig. 23. Variation of corona onset voltage with needle-to-needle sacing of multi-needle case (square with nine-needle at r t = 0.03 mm, (L-h) = 5 mm and h = 2.34 mm). Corona Onset Voltage, kv Single-needle Five-needles Nine-needles ti radius, m Fig. 24. Calculated onset voltage versus needle ti radius. E. Calculated Onset Voltages against Those Measured Exerimentally Table V gives the calculated and measured values of the corona onset voltage V 0 for single needle of radius r t = 0.03 mm and height h = 2.34 mm as influenced by Fig. 27. Effect of ga sacing on current-voltage characteristics of square with 5 needles (r t = 0.03 mm, h = 2.34 mm and m = 2.5, 5 mm). the ga sacing (L-h) = 5, 7.5, 0 and 2.5 mm. It is quite clear that the calculated values agreed reasonably with those measured exerimentally with a deviation not exceeding 0.98%. Table VI gives the calculated and measured values of the corona onset voltage V 0 for square with five needles (r t = 0.03 mm and height h = 2.34 mm) as influenced by the ga sacing (L-h) and by the needle-to-

13 Abdel-Salam et al. 33 Fig. 28. Effect of ga sacing on current-voltage characteristics of square with 9 needles (r t = 0.03 mm, h = 2.34 mm and m = 2.5, 5 mm). Fig. 3. I-V Characteristics of different number of needles at (Lh) = 5 mm and 0 mm (h = 2.34 mm, r t = 0.03 mm and m = 2.5 mm). Fig. 29. I-V Characteristics of different number of needles at (Lh) = 5 mm and 0 mm (h = 2.34 mm, r t = 0.03 mm and m = 5 mm). Fig. 30. I-V Characteristics of different number of needles at (Lh) = 7.5 mm and 2.5 mm (h = 2.34 mm, r t = 0.03 mm and m = 5 mm). needle sacing m. It is quite clear that the calculated values agreed reasonably with those measured exerimentally with a deviation not exceeding 0.4%. Table VII gives the calculated and measured values of the corona onset voltage V 0 for square with nine needles (r t = 0.03 mm and height h = 2.34 mm) Fig. 32. I-V Characteristics of different number of needles at (L-h) = 7.5 mm and 2.5 mm (h = 2.34 mm, r t = 0.03 mm and m = 2.5 mm). as influenced by the ga sacing (L-h) and by the needleto-needle sacing m. It is quite clear that the calculated values agreed reasonably with those measured exerimentally with a deviation not exceeding 0.62%. It is quite clear from Tables VI and VII that the corona onset voltage values of the multi-needle deend on the needle-to-needle sacing for the same needle radius, needle height and ga late sacing. With the increase of the needle-to-needle sacing, the onset voltage decreases because of the less shielding effect which makes the field in the vicinity of needles increases. Also, it is quite clear from the Tables VI and VII that the onset voltage values for multi-needle square s decreases with the increase of the number of needles. This is evident from the calculated values of the electric field at the needles' ti for square, Table III, as the field value of the outer needles increases with the increase of the number of needles. Tables V, VI and VII indicate that the corona onset voltage for multi-needle square is higher than that for single-needle. This attributed to the interaction between the needles in multi-needle

14 34 International Journal of Plasma Environmental Science & Technology, Vol.7, No.2, JULY 203 Ga sacing (L-h), mm TABLE V CALCULATED AND MEASURED CORONA ONSET VOLTAGE FOR SINGLE-NEEDLE CONFIGURATION Ga sacing (L-h), mm Calculated onset voltage Measured onset voltage (Vo-c), kv (Vo-m), kv Deviation (%) TABLE VI CALCULATED AND MEASURED CORONA ONSET VOLTAGE FOR FIVE-NEEDLE SQUARE CONFIGURATION Needle-to-needle sacing, m = 2.5 mm Calculated Measured onset voltage onset voltage Deviation (%) (Vo-c), kv (Vo-m), kv Needle-to-needle sacing, m = 5 mm Calculated Measured onset voltage onset voltage Deviation (%) (Vo-c), kv (Vo-m), kv Ga sacing (L-h), mm TABLE VII CALCULATED AND MEASURED CORONA ONSET VOLTAGE FOR NINE-NEEDLE SQUARE CONFIGURATION Needle-to-needle sacing, m = 2.5 mm Measured onset voltage (Vo-m), kv Calculated onset voltage (Vo-c), kv Deviation (%) Needle-to-needle sacing, m = 5 mm Measured onset voltage (Vo-m), kv Calculated onset voltage (Vo-c), kv Deviation (%) , which results in a decrease of the field in the vicinity of needles with a subsequent increase of the onset voltage in multi-needle. F. Corona Current-Voltage Characteristics Corona current-voltage characteristics were studied exerimentally for single- needle and multi-needle square s with 5 and 9 needles at varying ga sacing (L-h) and needle-to-needle sacing m as shown in Figs. 26 through 32. The needles height h and the needle ti radius r t were ket constant at 2.34 mm and mm, resectively. F.. Effect of Ga Sacing (L-h) For single-needle, the larger the ga sacing, the higher the onset voltage and the smaller is the corona current at the same alied voltage, needle radius and height, Fig. 26. For multi-needle square s, the larger the ga sacing, the higher the onset voltage and the smaller is the total corona current at the same alied voltage, needle-to-needle sacing, needle radius and height for five-needle, Fig. 27 and nine-needle, Fig. 28, s. It is quite clear that the corona current decreases with the increase of ga sacing, Figs , for the same alied voltage. This is simly exlained by the resulting decrease of the electric field along the flux lines, where the corona ions are convicting between the needles and the grounded late. The more the ga sacing, the more is the decrease of the electric field along the flux lines with subsequent decease of the corona current for the same alied voltage in agreement with Figs F.2. Effect of needle-to-needle sacing (m) The total corona current in case of multi-needle s deends on the needle-to-needle sacing as shown in Figs. 27 and 28. When the needles are close to each other, the corona current is significantly small. The smaller the needle-to-needle sacing, the higher the onset voltage and the smaller is the total corona current at the same alied voltage, number of needles, needle radius and height. This is because the decrease of the needle-to-needle sacing reflects itself on the increase of the shielding effect between needles and the resulting decrease of the electric field in the vicinity of needles and increase of the onset voltage. F.3. Effect of number of needles (N n ) Figs show the corona current versus the alied voltage for both single needle case and multineedle square with 5 and 9 needles at different ga sacings. The corona onset voltage V 0 of multi-needle s is slightly higher than that of a single needle as mentioned above. The current-voltage characteristics of the multi-needle lie all below those for single needle from the onset until a critical value of an alied voltage is reached. From this oint onward, the sloe of the characteristics for multi-

15 Abdel-Salam et al. 35 needle is steeer than that of single needle characteristics in agreement with revious findings [5, 4]. This is because, the corona aears in single needle case before the multi-needle s as the corona onset voltage V 0 for multi-needle s is higher than that from single needle case. This is why the corona current is higher for the single needle case when comared with that from multi-needle of the same alied voltage. In the multi-needle, the corona aears first on the outer needles. With the increase of the alied voltage, corona inwards starts to aear on the inner needles. VII. CONCLUSION On the basis of the analysis resented in this aer, the following conclusions may be drawn: ) In multi-needle s, the field is minimum near the central needle and increases near the needles in the direction outwards due to the shielding effect imosed on the central needle by the other needles. 2) The field near the central needle in case of single needle is higher than that for multi-needle s due to the shielding effect imosed on the central needle by the other needles. 3) In multi-needle s, the calculated onset voltage decreases gradually in the direction away from the central needle reaching its minimum value at the outer needles where the maximum value at the central needle. 4) The calculated onset voltage increases with the increase of the radius of needles for the same needle height, needle-to-needle sacing and ga sacing for single- and multi-needle s. 5) In single- and multi-needle s, the calculated onset voltage decreases with the increase of the needle height for the same needle radius, needle-to-needle sacing and ga sacing. 6) The calculated onset voltage decreases with the increase of the number of needles for triangular, square, entagonal and hexagonal s, whereas it increases with the increase of the number of needles for the line and square mesh s. 7) The onset voltage of corona in single-needle and multi-needle square s with 5 and 9 needles is calculated and measured in the laboratory. The calculated values agreed reasonably with those measured exerimentally. 8) The onset voltage of corona for multi-needle s is higher than that of single-needle in agreement with revious findings [5, 4]. 9) The larger the ga sacing, the higher the onset voltage and the smaller is the total corona current for the same alied voltage, needle-to-needle sacing, needle radius and height for single- and multi-needle s. 0) For multi-needle s the larger the needle-to-needle sacing, the smaller the corona onset voltage and the higher is the total corona current. REFERENCES [] A. Jaworek and A. Krua, "Electrical Characteristics of a Corona Discharge Reactor of Multioint-to-Plane Geometry," Czechoslovak Journal of Physics, vol. 45, , 995. [2] L. B. Loeb, Electrical Coronas: Their Basic Physical Mechanisms, University of California Press, Berkeley, USA, 965. [3] W. L. Lama and C. F. Gallo, "Interaction of the 'Trichel' current ulses of a air of negative coronas," Journal of Physics D: Alied Physics, vol. 6, , 973. [4] M. Abdel-Salam, A. A. Fattah, M. M. Saied, and M. Tharwat-El- Mohandes, "Positive Corona Pulse Characteristics from Two Interacting Needles in Air," IEEE Transactions on Industry Alications, vol. IA-2, , 985. [5] L. C. Thanh, "Negative Corona in a Multile Interacting Point-to- Plane Ga in Air," IEEE Transactions on Industry Alications, vol. IA-2, , 985. [6] T. Yamamoto, P. A. Lawless, and L. E. Sarks, "Narrow-ga oint-to-lane corona with high velocity flows," IEEE Transactions on Industry Alications, vol. 24, , 988. [7] P. J. McKinney, J. H. Davidson, and D. M. Leone, "Current distributions for barbed late-to-lane coronas," IEEE Transactions on Industry Alications, vol. 28, , 992. [8] H. Singer, H. Steinbigler, and P. Weiss, "A Charge Simulation Method for the Calculation of High Voltage Fields," IEEE Transactions on Power Aaratus and Systems, vol. PAS-93, , 974. [9] E. Nasser, Fundamentals of Gaseous Ionization and Plasma Electronics, J. Wiley and Sons, N.Y., USA, 97. [0] M. Khalifa, M. Abdel-Salam, and M. Abou-Seada, "Calculation of Negative Corona Onset Voltage," IEEE-PES aer No. C , 973. [] M. P. Sarma and W. Janischewskyj, "D.C. corona on smooth conductors in air. Steady-state analysis of the ionisation layer," Proceedings of the Institution of Electrical Engineers, vol. 6,. 6-66, 969. [2] A. von Engel, Handbuch der Physik, Sringer Verlag, Berlin, 956, vol. 2, [3] M. L. James, G. M. Simth, and J. C. Wolford, Alied Numerical Methods for Digital Comutation 3rd ed., New York, Harer and Row, 985. [4] J. Koller and L. Aubrecht, "Pulse roerties of negative corona discharge," Acta Physica Slovaca, vol. 53, , 2003.