Numerical Modeling of Conductive Particle Trajectories ... - IEEE Xplore

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 43, NO. 5, SEPTEMBER/OCTOBER 2007

Numerical Modeling of Conductive Particle Trajectories in Roll-Type Corona-Electrostatic Separators Mohamed Younes, Amar Tilmatine, Karim Medles, Mostefa Rahli, Member, IEEE, and Lucian Dascalescu, Senior Member, IEEE

Abstract—Several attempts have already been made to simulate particle trajectories in roll-type electrostatic separators. However, the predictive value of the results is limited by an excessive number of simplifying assumptions regarding the electric field distribution, as well as particle charging and discharging mechanisms. The present work is aimed at improving the existing models by taking into account: 1) the non-uniformity of the electric field in the active zone of the separator and 2) the effect of spark discharges occurring between the electrodes. Based on previous observations, the conductive particles were assumed to lift-off when no longer exposed to corona discharge. The numerical simulations were performed for particles of various sizes. The electric field was computed in each point of the trajectory using a finite element program. It was found that: 1) some of the smaller particles impact the static electrode and are deviated to the middling compartment of the collector and 2) field annealing which accompanies spark discharges significantly affects the trajectories of conductive particles. The results of this study could guide the design of new electrostatic separation applications. Index Terms—Charged particles, computational electrostatics, electrostatic separators.

Paper MSDAD-07-06, presented at the 2005 Industry Applications Society Annual Meeting, Hong Kong, October 2–6, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Electrostatic Processes Committee of the IEEE Industry Applications Society. Manuscript submitted for review October 31, 2005 and released for publication March 21, 2007. This work was supported in part by the European Commission under the Fond Européen de Développement Régional (FEDER) Program and within the framework of a Tassili project, which is jointly financed by the French and Algerian Governments. M. Younes and K. Medles were with the Electronics and Electrostatics Research Unit, Laboratory of Automatic and Industrial Data Processing (LAII), Higher Engineering School of Poitiers (ESIP), EA-1219, University Institute of Technology, 16021 Angoulême, France. They are now with the Electrostatics and High Voltage Research Unit, Department of Electrical Engineering, University Djilali Liabes, Sidi-bel-Abbes 22000, Algeria (e-mail: [email protected]; [email protected]). A. Tilmatine is with the Electrostatics and High Voltage Research Unit, Department of Electrical Engineering, University Djilali Liabes, Sidi-bel-Abbes 22000, Algeria (e-mail: [email protected]). M. Rahli is with the Optimization Power Systems Laboratory, Department of Electrical Engineering, University of Science and Technology, Oran 31000, Algeria (e-mail: [email protected]). L. Dascalescu was with the Electronics and Electrostatics Research Unit, Laboratory of Automatic and Industrial Data Processing (LAII), Higher Engineering School of Poitiers (ESIP), EA-1219, University Institute of Technology, 16021 Angoulême, France. He is now with the Electrostatics of Dispersed Media Research Unit, Electrohydrodynamic Group, Laboratory of Aerodynamic Studies, University of Poitiers, 16021 IUT Angoulême, France (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIA.2007.904363

I. I NTRODUCTION

T

HE ELECTROSTATIC separation of particles is an effective technology for recovering metallic and insulating materials from industrial wastes [1]–[3]. The particles to sort are deposited by a vibratory feeder on a grounded rotating roll electrode, which introduces them in a zone of an intense electric field created by one or several high-voltage electrodes. One of the electrodes creates a corona discharge, and thus charges all the particles by ion bombardment. The insulating particles adhere to the surface of the roll electrode under the effect of the electric image force, while the conducting ones are charged by electrostatic induction and projected towards the static electrode of opposite sign [4]–[8]. The trajectory of the metal particles in the electrostatic roletype separator is important because it influences in a significant way the outcome of the process, as well as the mass and the purity of the separated products [9], [10]. The aim of this paper is to simulate the conductive particle trajectories under various operating conditions, in order to derive some recommendations for the design of new industrial applications of electrostatic separation. II. N UMERICAL A NALYSIS OF THE E LECTRIC F IELD The complex configuration of the electrode system imposes the use of numerical methods for the calculation of the electric field in roll-type electrostatic separators [11], [12]. A software program (TRICOMP) based on the finite elements method [13] enabled the calculation of the electric field in the domain under study, as shown in Fig. 1. The equipotential lines determined by TRICOMP software are displayed in Fig. 2. The values of the electric field intensity in 30 000 points of the computational domain are recorded in a “.txt” file. They serve as input data of a program based on the finite differences method and that serves at the computation of the electric field strength in any point of the domain. The variation of the electric field as function of the angle α at the periphery of the rotating roll is shown in Fig. 3. III. D EPARTURE A NGLE The determination of departure angle of a conducting particle from the surface of the roll electrode is the first step of the trajectory simulation procedure. A particle on the rotating

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YOUNES et al.: NUMERICAL MODELING OF CONDUCTIVE PARTICLE TRAJECTORIES IN ROLL-TYPE CORONA-ELECTROSTATIC SEPARATORS

Fig. 1. Two-dimensional domain of calculation representing a cross-section of the electrostatic separator (all the data are in mm).

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Fig. 3. Variation of the electric field as a function of the angle α at the periphery of the roll electrode. Computations carried out with TRICOMP software.

Fig. 4. Forces acting on a particle in contact with the roll electrode.

Using (2), and replacing Fg and Fc by their expressions given as Fig. 2.

Equipotential lines computed with TRICOMP software.

electrode is subjected to mechanical and electrical forces (Fig. 4) [14]–[16]: Fi electric image force; Fq electric field force; Fg gravitational force; Fc centrifugal force. The departure condition of the conducting particle is expressed by the following equation [10]: Fi + Fg cos(αd ) − Fq − Fc = 0

(1)

where αd is the departure angle. For a cylindrical particle of radius r and length L that reaches horizontally the electrode, the resulting force Fel = Fq − Fi is [17] Fel = 4.49 εo r LE 2 .

(4)

Fc = mv 2 /R

(5)

where m is the mass of the particle and v is the tangential speed of the rotating roll, (3) becomes 4.49 εo rE 2 + ρπr2 v 2 /R − ρπr2 g cos(αd ) = 0.

(6)

The departure angle αd depends then on the speed, the radius of the particle, and the applied voltage. Fig. 5 displays the variation of αd with respect to the speed for different values of the radius and for an applied voltage U = 30 kV. IV. C OMPUTATIONAL M ETHOD

(2)

After taking off from the cylinder surface, the particle is subjected to only two forces: Fq and Fg . The movement is then governed by the following expression [10]:

(3)

QE + mg = mγ

The departure condition given by (1) becomes Fel + Fc − Fg cos(αd ) = 0.

Fg = mg

(7)

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Fig. 6. Fig. 5. Departure angle as function of the rotation speed for different particle radii r.

For determining the point (i + 1), having the coordinates (xi+1 , yi+1 ), we use the following equations:

where E = E(xi , yi ) is the electric field in any point (xi , yi ) on the trajectory and Q is the charge acquired by electrostatic induction [17] Q = 6.283 rLεo E0

(8)

E0 being the electric field in the point where the particle takes off from the cylinder. The force QE can be decomposed into two forces, Fqx along the horizontal axis and Fqy along the vertical axis so that Fqx = kLEx

(9)

Fqy = kLEy

(10)

where k = 6.283 rεo E. The force Fg is constant, while Fq changes because of the field variation in the domain. A precise simulation must take into account that fact; then a program based on the finite differences method is employed in order to determine the electric field values in any point of the domain. Let the first point of the trajectory be the departure point (x0 , y0 ), where the acceleration and the initial speed take the following values: γx (x0 , y0 ) = kLEx (x0 , y0 )/Lρπr2

(11)

γy (x0 , y0 ) = (kLEy (x0 , y0 )) /Lρπr2 ) − g

(12)

vx (x0 , y0 ) = v0 cos(αd )

(13)

vy (x0 , y0 ) = v0 sin(αd )

(14)

x0 = R sin(αd ) + 15

(15)

y0 = R cos(αd ) + 30

(16)

where v0 represents the tangential speed of the roll electrode. The next point of the trajectory, of coordinates (x1 , y1 ), is calculated from the following equations: x1 = 0.5γx (x0 , y0 )dt2 + vx (x0 , y0 )dt + x0

(17)

2

(18)

y1 = 0.5γy (x0 , y0 )dt + vy (x0 , y0 )dt + y0 .

Minimal departure angle.

xi+1 = 0.5γx (xi , yi )dt2 + vx (xi , yi )dt + xi

(19)

yi+1 = 0.5γy (xi , yi )dt2 + vy (xi , yi )dt + yi

(20)

where γx (xi , yi ) = kLEx (xi−1 , yi−1 )/Lρπr2

(21)

γy (xi , yi ) = (kLEy (xi−1 , yi−1 )) /Lρπr2 ) − g

(22)

vx (xi , yi ) = γx (xi−1 , yi−1 )dt + vx (xi−1 , yi−1 )

(23)

vy (xi , yi ) = γy (xi−1 , yi−1 )dt + vy (xi−1 , yi−1 ).

(24)

It is clear from (21) and (22) that the trajectory of the granule of an assumed cylindrical form does not depend on its length L. V. C ALCULATION OF THE T RAJECTORY The calculation of the trajectory is performed under the hypothesis that all the particles take off from the surface of the roll as soon as they exit the space charge zone. In fact, before leaving this zone the conducting particles undergo multiple bounces at the surface of the roll [10]. Since the extension of the space charge zone √ at the periphery of the roll does not exceed the value s = d 3 [18], the minimal departure angle is calculated as follows (Fig. 6): αdmin = α + ∆α/2

[in radians]

αdmin = (α + ∆α/2).360/2π

or

[in degrees]

(25)

with ∆α = s/R. Using (11)–(24) and considering the simplifying assumption given by (25), the program determines the coordinates of about 2500 points on particle trajectory, the time step being set at 0.1 ms. The trajectories of four particles of different radii are represented in Fig. 7. The computed values of the departure angle αd , the abscissa xc (xc coordinate of the impact point on the y = 0 plan), and the time interval from lift-off to the final position


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Fig. 8. Reestablishment of the 30 kV rated high-voltage voltage after a spark between the corona and roll electrodes of a laboratory electrostatic separator.

Fig. 7.

Computed trajectories for different particule radii r.

TABLE I HORIZONTAL ABCISSA xc AND FALL DURATION ∆tc FOR DIFFERENT VALUES OF GRANULE RADIUS, DEPARTURE ANGLE αd = 39◦

∆tc are given in Table I. It is to note that some particles make impact with the sidewall of the separator. The attraction produced by the high voltage static electrode is more effective for the particles of small radius, which is justified by (21) and (22) showing that the reduction in the radius increases γx and decreases γy . VI. E FFECT OF S PARK D ISCHARGES During the electrostatic separation of the granular mixtures, sparks occur between the corona electrode and the roll. After each spark, the high voltage supply needs a certain time to reestablish the stable operation conditions. The curve in Fig. 8 represents the oscilograph of the high voltage between the electrodes of a laboratory separator, when a spark discharge occurred due to the passage of an elongated copper particle through the corona field zone. The high voltage supply was a model M583, GAMMA, Ormond Beach, FL, and it needed about 450 ms to reestablish the rated voltage level after the spark [19]. Since the transit time of a particle from the departure point to the collector plan (y = 0) is nearly 250 ms (see Table I), some particles will not be subjected to the action of the electric field and will fall with a projectile motion. The spark can occur at any time (ta ), measured from the moment of particle lift off. The computed trajectories of a 0.2 mm radius particle for different values of ta are displayed in Fig. 9 (see also Table II). The computed results show that if the spark occurs at a time ta > 120 ms, it does not significantly modify the trajectory of the particle. However, the difference

Fig. 9. Computed trajectories of a particle (radius 0.2 mm), for various time intervals between particle lift-off and the occurrence of a spark discharge between the electrodes.

TABLE II ABSCISSA xc AND FALL DURATION ∆tc AS A FUNCTION OF THE APPEARANCE TIME OF THE SPARK

is very clear between the trajectory ta1 = 0 (the spark occurs at the very moment of particle lift off) and the trajectory without spark ta5 . Therefore, the electrostatic process should be designed so that spark discharges be avoided during normal operation.

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Fig. 10. Trajectories of fine particles that collide with the high-voltage static electrode.

Fig. 11. Trajectory of a fine particle colliding with the static electrode and then the roll electrode.

VII. I MPACT OF THE G RANULES W ITH THE S TATIC E LECTRODE Small-radius particles that can impact the high voltage static electrode acquire a charge of opposite sign, and are then attracted towards the grounded roll electrode. The effect of the impact between the particle and the high voltage electrode was considered in the simulation program. The calculation is based on the assumption that an elastic shock occurs between the conducting particle and the electrode (conservation of the momentum). • The speed value after the shock (reflected speed) is equal to that before the shock (incidental speed); • The incidence angle is equal to the reflection angle. The computed results show that after the impact with the high voltage electrode, such particles can be collected in the middling product compartment. Represented in Fig. 10 are the trajectories of two granules of radius 0.11 mm and 0.15 mm that experienced an impact with the high voltage electrode. For finer particles (smaller radius), this impact can be followed by a second impact with the roll electrode. This situation is illustrated by the simulation results obtained with a 0.1 mm radius granule (Fig. 11). These kinds of results can indicate the optimum position of the splitter between the middling and non-conductor compartments of the collector. In the case where all the conductive particles are very fine and the impact with the static electrode cannot be avoided, a splitter a few centimeters of width could be placed as shown in Fig. 12. The utility of such a splitter, which must be of insulating material in order not to influence too much the distribution of the electric field, shall be confirmed by a thorough experimental study.

Fig. 12. Trajectories of fine particles colliding with the static electrode and an additional splitter.

fects of three factors which can influence the quality of the electrostatic separation role-type process: 1) the diversity of size and shape of the particles present in the materials to be treated; 2) the spark discharges that occur between the electrodes, accompanied by of the diminution of the applied high voltage and thus of the electric field; and 3) the impact between the particles and the high voltage static electrode. From a practical point of view, the simulation results point out the importance of particle sizing prior to the electrostatic separation. This is the only way to reduce the dispersion of particle trajectories and improve the overall efficiency of the process. ACKNOWLEDGMENT

VIII. C ONCLUSION The numerical simulation of the conducting particles trajectories allows us to refine the comprehension of the ef-

The authors would like to thank Prof. A. Samuila, Dr. A. Mihalcioiu, and Dr. T. Nassreddine for pertinent comments and suggestions.


R EFERENCES [1] L. Dascalescu, A. Iuga, and R. Morar, “Electrostatic technologies for the recycling of non-ferrous metals and plastics from wastes,” in The Modern Problems of Electrostatics With Applications in Environmental Protection, I. I. Inculet, F. T. Tanasescu, and R. Cramariuc, Eds. Dordrecht, The Netherlands: Kluwer, 1999, pp. 77–87. [2] A. Iuga, R. Morar, A. Samuila, and L. Dascalescu, “Electrostatic separation of metals and plastics from granular industrial wastes,” Proc. Inst. Electr. Eng.—Sci. Meas. Technol., vol. 148, pp. 47–54, 1999. [3] E. Lawver and W. P. Dyrenforth, “Electrostatic separation,” in Electrostatics and Its Applications, A. D. Moore, Ed. New York: Wiley, 1973, pp. 221–249. [4] R. Morar, A. Iuga, L. Dascalescu, and A. Samuila, “Factors which influence the insulation-metal electroseparation,” J. Electrostat., vol. 30, pp. 403–412, 1993. [5] I. I. Inculet, G. S. P. Castle, and J. D. Brown, “Electrostatic separation of plastics for recycling,” Particulate Sci. Technol., vol. 16, pp. 91–100, 1998. [6] L. Dascalescu, A. Iuga, and R. Morar, “Corona-electrostatic separation: An efficient technology for recovery of metals and plastics from industrial wastes,” Magn. Electr. Separation, vol. 4, pp. 241–255, 1993. [7] L. Dascalescu, R. Morar, A. Iuga, A. Samuila, and V. Neamtu, “Electrostatic separation of insulating and conductive particles from granular mixes,” Particulate Sci. Technol., vol. 16, pp. 25–42, 1998. [8] Y. Higashiyama and K. Asano, “Recent progress in electrostatic separation technology,” Particulate Sci. Technol., vol. 16, pp. 77–90, 1998. [9] K. B. Tennal, D. Lindquist, M. K. Mazumder, R. Rajan, and W. Guo, “Efficiency of electrostatic separation of minerals from coal as function of size and charge distributions of coal particles,” in Conf. Rec. 1999 IEEE IAS Annu. Meeting, St. Louis, MI, vol. 4, pp. 2137–2142. [10] L. Dascalescu, “Mouvements des particules conductrices dans un séparateur à haute tension pour matériaux granulaires,” J. Electrostat., vol. 32, pp. 305–316, 1994. [11] L. Dascalescu, “Numerical analysis of the electric field of roll-type electrostatic separators,” J. Electrostat., vol. 29, pp. 255–267, 1993. [12] S. Vlad, M. Mihailescu, D. Rafiroiu, A. Iuga, and L. Dascalescu, “Numerical analysis of the electric field in plate-type electrostatic separators,” J. Electrostat, vol. 48, pp. 217–229, 2000. [13] [Online]. Available: www.tricomp.com [14] N. J. Felici, “Forces et charges de petits objets en contact avec une électrode affectée d’un champ électrique,” Rev. Gen. Electr., vol. 75, pp. 1145–1160, 1966. [15] J. F. Delon, “Théorie de la séparation électrostatique à l’aide de l’effet corona,” Ann. Mines, vol. 3, pp. 37–50, 1966. [16] L. Dascalescu, A. Mizuno, R. Tobazeon, P. Atten, R. Morar, A. Iuga, M. Mihailescu, and A. Samuila, “Charges and forces on conductive particles in roll-type corona-electrostatic separators,” IEEE Trans. Ind. Appl., vol. 31, no. 5, pp. 947–956, Sep./Oct. 1995. [17] L. Dascalescu, A. Samuila, and R. Tobazéon, “Cylindrical conductive particles in the proximity of an electrode affected by a high-intensity electric field,” J. Electrostat., vol. 37, pp. 173–196, 1996. [18] L. Dascalescu, A. Iuga, R. Morar, V. Neamtu, I. Suarasan, A. Samuila, and D. Rafiroiu, “Corona and electrostatic electrodes for high-tension separators,” J. Electrostat., vol. 29, pp. 211–225, 1993. [19] A. Mihalcioiu, V. Neamtu, A. Stochita, and L. Dascalescu, “High-voltage monitoring in electrostatic separators,” IEEE Trans. Ind. Appl, vol. 43, no. 5, pp. 224–231, Jan./Feb. 2007.

Mohamed Younes was born in Mostagnem, Algeria, in 1965. He received the degree in electrical engineering from the University of Sciences and Technology, Oran, Algeria, in 1989 and the Magister (Dr. Eng.) degree from the University Djilali Liabes, Sidi-bel-Abbes, Algeria, in 1998. He is currently working toward the Ph.D. degree at the University Djilali Liabes, and he spent 12 months at the University Institute of Technology, Angoulême, France, under a research scholarship, in order to prepare a part of his Ph.D. thesis. He is currently a Senior Lecturer of electrical engineering and a member of the Electrostatics and High Voltage Engineering Research Unit, Department of Electrical Engineering, University Djilali Liabes. His current research interests include high-voltage engineering, computational electrostatics, and fuzzy logic, topics on which he has published several scientific papers in international and national journals, as well as in conference proceedings.

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Amar Tilmatine received the M.S. degree in electrical engineering and the Magister (Dr. Eng.) degree from the University of Science and Technology, Oran, Algeria, in 1988 and 1991, respectively. Since 1991, he has been teaching electric field theory and high-voltage techniques with the Department of Electrical Engineering, University Djilali Liabes, Sidi-bel-Abbes, Algeria. He was the Chairman of the Scientific Committee of this institute from November 2002 to November 2005. He is currently an Associate Professor and the Head of the Electrostatics and High Voltage Research Unit, Department of Electrical Engineering, University Djilali Liabes. From 2001 to 2006, he visited the Electronics and Electrostatics Research Unit, University Institute of Technology, Angoulême, France, at least once a year, as an Invited Scientist, where he worked on a joint research project on new electrostatic separation technologies. His other fields of interest are high-voltage insulation and gas discharges.

Karim Medles was born in Tipaza, Algeria, in 1972. He received the M.S. and Magister (Dr. Eng.) degrees in electrical engineering and the Ph.D. degree from the University Djilali Liabes, Sidi-bel-Abbes, Algeria, in 1994, 1999, and 2006, respectively. His thesis was partly prepared at the University Institute of Technology, Angoulême, France, with an 18-month research scholarship awarded by the French Government. In 1999, he joined the Department of Electrical Engineering, University Djilali Liabes, as a Senior Lecturer, where he is currently an Assistant Professor. He is a member of the Electrostatics and High Voltage Engineering Research Unit, Department of Electrical Engineering, University Djilali Liabes. He has published several scientific papers in international and national journals, as well as in conference proceedings. He was invited as a Visiting Scientist in France. His current research interest includes power systems, high-voltage engineering, and electrostatics.

Mostefa Rahli (M’96) was born in Mascara, Algeria, on October 24, 1949. He received the B.S., Magister (Dr. Eng.), and Ph.D. degrees in electrical engineering from the University of Sciences and Technology, Oran, Algeria, in 1979, 1985, and 1996, respectively. From 1987 to 1991, he was a Visiting Professor with the Montefiore Electrical Institute, University of Liège, Liège, Belgium, where he worked on power systems analysis. He is currently a Professor of electrical engineering with the University of Sciences and Technology, Oran, Algeria. His research interests include operation and planning of electric energy systems, as well as optimization theory and its applications.

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Lucian Dascalescu (M’93–SM’95) received the degree (with first class honors) from the Technical University of Cluj-Napoca, Cluj-Napoca, Romania, in 1978, the Dr. Eng. degree in electrotechnical materials from the Polytechnic Institute of Bucharest, Bucharest, Romania, and the Dr. Sci. degree and the “Habilitation à Diriger de Recherches” Diploma in physics from the Joseph Fourier University, Grenoble, France. His professional career began at the Combinatul de Utilaj Greu S.A. (Heavy Equipment Works), ClujNapoca. In 1983, he joined the Technical University of Cluj-Napoca, as an Assistant Professor, later becoming an Associate Professor of electrical engineering. From October 1991 to June 1992, he was a Research Fellow with the Laboratory of Electrostatics and Dielectric Materials, Grenoble, France, where he returned in January 1994, after one year as an Invited Research Associate and Lecturer with Toyohashi University of Technology, Toyohashi, Japan, and three months as a Visiting Scientist with the University of Poitiers, Poitiers, France. For four years, he taught a course in electromechanical conversion of energy at the University Institute of Technology, Grenoble. In September 1997, he was appointed as a Professor of electrical engineering and automated systems and the Head of the Electronics and Electrostatics Research Unit, University Institute of Technology, Angoulême, France. Since 1999, he has also been the Head of the Department of Management and Engineering of Manufacturing Systems. He is currently the Head of the Electrostatics of Dispersed Media Research Unit, which is part of the Electrohydrodynamic Group, Laboratory of Aerodynamic Studies, University of Poitiers. He is the author of several textbooks in the field of electrical engineering and ionized gases. He is the holder of 14 patents, has written more than 70 papers, and was invited to lecture on the electrostatics of granular materials at various universities and international conferences in China (1988), Poland (1990), USA (1990, 1997, 1999), Japan (1993), France (1993), U.K. (1998), Romania (1999, 2004, 2006), Canada (2001), Belgium (2002), and Algeria (2005, 2006). Prof. Dascalescu is a Senior Member of the IEEE Industry Applications Society and the Chair of its Electrostatic Processes Committee. He is a member of the French Society of Electrostatics, Electrostatics Society of Romania, Société des Electriciens et Electroniciens, and Club Electrotechnique, Electronique, Automatique, France.