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Charging of metal probes by a flux of particles
Journal of Electrostatics 51}52 (2001) 124}130
Charging of metal probes by a #ux of particles Ryszard Kacprzyk , Juliusz B. Gajewski * Institute of Electrical Engineering Fundamentals, Wroc!aw University of Technology, WybrzezR e Wyspian& skiego 27, 50-370 Wroc!aw, Poland Institute of Heat Engineering and Fluid Mechanics, Wroc!aw University of Technology, WybrzezR e Wyspian& skiego 27, 50-370 Wroc!aw, Poland
Abstract The charging current of a metal bar probe as a function of the mass #ow rate of polyethylene, polypropylene and polystyrene particles that impact the probe while travelling through a pipe is presented in the paper. The probe is inserted into a PVC pipe through which the particles travel as carried by the #ux of air. The dependence of the probe charging current on the mass #ow rate is non-linear, mostly parabolic and quite di!erent from that presented by a simpli"ed mathematical model. 2001 Elsevier Science B.V. All rights reserved. Keywords: Bar probe; Probe charging; Mass #ow rate
1. Introduction An interest in the measurement of a level of the gas}solids #ow rate can be found in many monographs and regular papers [1}6]. To control di!erent technological processes, continuous indirect methods have the most widespread application because of a need for the continuous measurement of a controlled parameter. In a great deal of di!erent technologies including pneumatic transport one of the most important parameters is the mass #ow rate. One of the measurement methods of the mass #ow rate is that in which the triboelectri"cation e!ect is employed [5,6]. The e!ect appears during the mutual particle}particle, particle}duct wall, and particle}probe impacts, and especially these last impacts were utilized for designing and manufacturing commercial measuring devices [7]. The relationship between the mass #ow rate and the current of the bar type of probe was described in the paper. Polymer particles (PE,
* Corresponding author. Tel.: #48-71-320-3201; fax: #48-71-328-3818. E-mail address: [email protected] (J.B. Gajewski). 0304-3886/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 8 8 6 ( 0 1 ) 0 0 0 4 6 - 8
R. Kacprzyk, J.B. Gajewski / Journal of Electrostatics 51}52 (2001) 124}130
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PP, PS) transported by a #ux of air were used and constituted a solid phase. The particles hit a metal bar electrode of the probe and exchange the electric charge with it. A dc component of the probe current was measured as a result of collisions of the particles transported by an air stream with the probe inserted into a 50 mm diameter PVC duct. 2. Bar probe current The theoretical model in which the triboelectri"cation process was applied and which concerns a parallel-plate capacitor charged by a charge exchange between the surfaces of objects in contact expresses the following equation [4]:
;s !t q" 1!exp , (1) z where q is the charge exchanged during a collision, ; the potential di!erence that causes the charge to be transported during a contact, z the gap thickness between contacting objects during a collision, s the area of a contact, t the duration of a contact, the Maxwell's time constant for the particle material, and the permittivity of free space. The value ; depends on such parameters as the work functions of contacting objects, the particle diameter, the velocity and charge, the duct diameter, the space charge density in a duct, the gap thickness, and so on [6]. During the collisions of the particles with the bar probe and assuming that all the particles exchange the same charge with the probe, a dc component of the probe current can be expressed as
3 s;=hD !t I"nq" 1!exp , (2) 4z Ar where n is the number of particles colliding with the bar surface per unit time, = the mass #ow rate of a particle #ux, h the bar insertion depth, D the bar diameter, A the cross-section area of a duct, r the particle radius, and the density of particle material. In the above very simpli"ed expression, it was additionally assumed that E E E E E E
all the transported particles are spherical and have the same radius; distribution of the particles in the duct cross-section is uniform; particles are weakly conducting (t;); the bar probe does not disturb the #ow; the particles collide with the bar electrode in the area Dh, and the contact area for all the particles is identical, does not depend on the particle velocity, and equals s.
3. Measuring equipment The schematic diagram of a measuring circuit is shown in Fig. 1. The total length of a pneumatic transport installation (the length of a #ux of solid particles) was 4 m.
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Fig. 1. Schematic diagram of the experimental set-up. Description is given in the text.
The duct (D) was made of typical 50 mm diameter PVC pipes, and was equipped additionally with a conducting copper tape deposited on the inner surface of the pipes. A metal cyclone (C) was equipped in its lower part with a nozzle (E) and was fed with air from a turbine (T). The velocity of air was measured with an anemometer (A) and regulated by the angular speed of the turbine using a regulator (R). The #ux of air passed three electrodes (E1), (E2), and (E3) mounted on the lower part of the installation. The probe (P) was mounted in the upper part of the installation between an elbow and the cyclone. The bar probe current was measured with a picoammeter (pA) and registered by a recorder (X-T). The electrode (E1) was a needle electrode that produced dc corona discharges for charging solid particles travelling through the electrode zone. This electrode was energized by a dc high voltage supply (HV). Two remaining strip electrodes (E2) and (E3) were connected to the inputs of a two-channel storage oscilloscope (OSC) to enable measurement of the particle velocity. A measuring electrode of the probe was prepared as a spherically ended, 160 mm long metal bar with a diameter of 10 mm. The bar electrodes were made of aluminium (alu.), steel, or brass. The electrodes (E1)}(E3) were used in the measurements of particle velocity. The electrodes (E1) (a discharging system) contained the needle and semicylindrical electrodes, and were necessary to initially charge solid particles to permit the particle velocity measurement. The semicylindrical electrode was mounted on the outer surface of a PVC duct in the form of a 10 mm wide copper tape. The electrodes (E2) and (E3) were also mounted on the pipe surface in the form of cylinders whose length was 10 mm. Distances between electrodes (E1)}(E2) and (E2)}(E3) were kept constant and were equal to 100 mm. As a transported solid phase, commercially available the PE, PP, and PS particles were used. The particles were roughly spherical and their diameters ranged from 2.8 to 3.5 mm. 4. Experimental results and discussion The mass #ow rate = of the particle stream was determined from the relationship =" < M/l, L !
(3)
R. Kacprzyk, J.B. Gajewski / Journal of Electrostatics 51}52 (2001) 124}130
127
where M is the volume of circulating particles, < the most probable particle velocity, ! l the total particle distance (per one cycle), and the particle density. L The velocity < was determined by measuring the time of #ight of individual ! particles between electrodes (E2) and (E3). The particle time of #ight was measured with a storage oscilloscope whose two channels were controlled by signals from both electrodes. Measurements were carried out for the small number of circulating particles marked by a charge trapped in the ionized space of an electrode system (E1). The charged particle, passing by the electrodes (E2) and (E3), induced electric signals that were observed on the screen of the oscilloscope. A time delay between the signals observed was assumed to be equal to the time of #ight of the particle. It was experimentally proved that the most probable particle velocity < was linearly ! dependent on the air velocity < . The probe current was measured with a picoammeter. The time constant of the measuring circuit consisting of the probe and the picoammeter input was about 10 s. In all the experiments performed the bar probe was inserted into the PC pipe down to 40 mm. An example of the results obtained for the mass #ow rates that ranged from 0 to 5 kg/min for the PE particles (constant volume) is illustrated in Fig. 2. The strong non-linearities were generally observed in the case of di!erent particle and electrode materials for the mass #ow rates higher than 5 kg/min and sometimes I(=) dependencies were ambiguous. The results obtained for the PS and PP particles (for =(5 kg/min) are shown in Figs. 3 and 4, respectively. In both cases most of the I(=) characteristics can be approximated by parabolic functions of the form I"a=#b=. The computed values of the coe$cients a and b range, respectively, from !1.32 to 11.02 and from 0.61 to 3.14 for the constant velocity < of particles, and
Fig. 2. The current of the di!erent probes as a function of the mass #ow rate for the PE particles for a constant air velocity of 13.4 m/s.
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Fig. 3. The current of the di!erent probes as a function of the mass #ow rate for the PS particles for a constant air velocity of 13.4 m/s.
Fig. 4. The current of the di!erent probes as a function of the mass #ow rate for the PP particles for a constant air velocity of 13.4 m/s.
from !4.31 up to !24.4 (a) and from 0.99 to !6.7 (b) for the constant volume M of particles that was 100 cm. The current, as measured for the PS particles and the brass probe, was of negative polarity within the range of the mass #ow rates. In Fig. 3 it is shown as a modulus of
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129
Fig. 5. The probe current of the di!erent probes as a function of the mass #ow rate for the PE (a), PP (b) and PS (c) particles for a constant volume of 100 cm.
the value of the real probe current. Such an inversion of the current polarity was observed only in those experiments when these polymer particles and the brass probe were used. The results obtained for the constant particle volume are presented in Fig. 5. A linear dependence I(=) was observed for the PS particles only (Fig. 5c). For the PE and PP particles appropriate dependencies could be approximated by parabolic functions as earlier.
5. Conclusions Obtained results permit one to draw the following conclusions: E for the weakly conducting particles, the probe charging current I depends generally non-linearly on the mass #ow rate =; E the value of current and its direction depend on the material of the probe electrode and particles, as shown in Eq. (2); E for the higher mass #ow rates ('5 kg/min) I(=) characteristics can be ambiguous; E in the range of monotonic changes of the I(=) characteristics (W(5 kg/min) the shape of an approximating function and their constant coe$cients depend on the material of the electrode and the particles used; E the observed non-linearities suggest that assumptions used in the simpli"cation of the relationship (2) were not ful"lled (e.g. in reality the contact area s depends on the particle velocity and its elasticity coe$cient).
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Acknowledgements This work was carried out as the statutory research at Wroc"aw University of Technology and was "nanced by the State Committee for Scienti"c Research, Warsaw, Poland.
References [1] P.P. Kremlevskij, Raschodomery i sc\ etciki kolic\ estva, Izd. Masinostroenie, Leningrad, 1975. [2] F.C. Kinghorn, Flow measurement methods } past, present and future, Transducer Technol. 10 (1983) 12. [3] R.A. Furness, J.E. Heritage, Commercially available #owmeters and future trends, Meas. Control 19 (1986) 25. [4] H. Masuda, S. Matsusaka, S. Nagatani, Measurements of powder #ow rate in gas}solids pipe #ow based on the static electri"cation of particles, Adv. Powder Technol. 5 (1994) 241. [5] J.B. Gajewski, Monitoring electrostatic #ow noise for mass #ow and mean velocity measurement in pneumatic transport, J. Electrostat. 37 (1996) 261}276. [6] H. Masuda, S. Matsusaka, H. Shimomura, Measurement of mass #ow rate of polymer powder based on static electri"cation of particles, Adv. Powder Technol. 9 (1998) 169. [7] Tribo#ow, Catalogue (Continuous Dry Solid Flow Monitor 2601). Auburn International, Inc., Danvers, MA.
Charging of metal probes by a #ux of particles Ryszard Kacprzyk , Juliusz B. Gajewski * Institute of Electrical Engineering Fundamentals, Wroc!aw University of Technology, WybrzezR e Wyspian& skiego 27, 50-370 Wroc!aw, Poland Institute of Heat Engineering and Fluid Mechanics, Wroc!aw University of Technology, WybrzezR e Wyspian& skiego 27, 50-370 Wroc!aw, Poland
Abstract The charging current of a metal bar probe as a function of the mass #ow rate of polyethylene, polypropylene and polystyrene particles that impact the probe while travelling through a pipe is presented in the paper. The probe is inserted into a PVC pipe through which the particles travel as carried by the #ux of air. The dependence of the probe charging current on the mass #ow rate is non-linear, mostly parabolic and quite di!erent from that presented by a simpli"ed mathematical model. 2001 Elsevier Science B.V. All rights reserved. Keywords: Bar probe; Probe charging; Mass #ow rate
1. Introduction An interest in the measurement of a level of the gas}solids #ow rate can be found in many monographs and regular papers [1}6]. To control di!erent technological processes, continuous indirect methods have the most widespread application because of a need for the continuous measurement of a controlled parameter. In a great deal of di!erent technologies including pneumatic transport one of the most important parameters is the mass #ow rate. One of the measurement methods of the mass #ow rate is that in which the triboelectri"cation e!ect is employed [5,6]. The e!ect appears during the mutual particle}particle, particle}duct wall, and particle}probe impacts, and especially these last impacts were utilized for designing and manufacturing commercial measuring devices [7]. The relationship between the mass #ow rate and the current of the bar type of probe was described in the paper. Polymer particles (PE,
* Corresponding author. Tel.: #48-71-320-3201; fax: #48-71-328-3818. E-mail address: [email protected] (J.B. Gajewski). 0304-3886/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 8 8 6 ( 0 1 ) 0 0 0 4 6 - 8
R. Kacprzyk, J.B. Gajewski / Journal of Electrostatics 51}52 (2001) 124}130
125
PP, PS) transported by a #ux of air were used and constituted a solid phase. The particles hit a metal bar electrode of the probe and exchange the electric charge with it. A dc component of the probe current was measured as a result of collisions of the particles transported by an air stream with the probe inserted into a 50 mm diameter PVC duct. 2. Bar probe current The theoretical model in which the triboelectri"cation process was applied and which concerns a parallel-plate capacitor charged by a charge exchange between the surfaces of objects in contact expresses the following equation [4]:
;s !t q" 1!exp , (1) z where q is the charge exchanged during a collision, ; the potential di!erence that causes the charge to be transported during a contact, z the gap thickness between contacting objects during a collision, s the area of a contact, t the duration of a contact, the Maxwell's time constant for the particle material, and the permittivity of free space. The value ; depends on such parameters as the work functions of contacting objects, the particle diameter, the velocity and charge, the duct diameter, the space charge density in a duct, the gap thickness, and so on [6]. During the collisions of the particles with the bar probe and assuming that all the particles exchange the same charge with the probe, a dc component of the probe current can be expressed as
3 s;=hD !t I"nq" 1!exp , (2) 4z Ar where n is the number of particles colliding with the bar surface per unit time, = the mass #ow rate of a particle #ux, h the bar insertion depth, D the bar diameter, A the cross-section area of a duct, r the particle radius, and the density of particle material. In the above very simpli"ed expression, it was additionally assumed that E E E E E E
all the transported particles are spherical and have the same radius; distribution of the particles in the duct cross-section is uniform; particles are weakly conducting (t;); the bar probe does not disturb the #ow; the particles collide with the bar electrode in the area Dh, and the contact area for all the particles is identical, does not depend on the particle velocity, and equals s.
3. Measuring equipment The schematic diagram of a measuring circuit is shown in Fig. 1. The total length of a pneumatic transport installation (the length of a #ux of solid particles) was 4 m.
126
R. Kacprzyk, J.B. Gajewski / Journal of Electrostatics 51}52 (2001) 124}130
Fig. 1. Schematic diagram of the experimental set-up. Description is given in the text.
The duct (D) was made of typical 50 mm diameter PVC pipes, and was equipped additionally with a conducting copper tape deposited on the inner surface of the pipes. A metal cyclone (C) was equipped in its lower part with a nozzle (E) and was fed with air from a turbine (T). The velocity of air was measured with an anemometer (A) and regulated by the angular speed of the turbine using a regulator (R). The #ux of air passed three electrodes (E1), (E2), and (E3) mounted on the lower part of the installation. The probe (P) was mounted in the upper part of the installation between an elbow and the cyclone. The bar probe current was measured with a picoammeter (pA) and registered by a recorder (X-T). The electrode (E1) was a needle electrode that produced dc corona discharges for charging solid particles travelling through the electrode zone. This electrode was energized by a dc high voltage supply (HV). Two remaining strip electrodes (E2) and (E3) were connected to the inputs of a two-channel storage oscilloscope (OSC) to enable measurement of the particle velocity. A measuring electrode of the probe was prepared as a spherically ended, 160 mm long metal bar with a diameter of 10 mm. The bar electrodes were made of aluminium (alu.), steel, or brass. The electrodes (E1)}(E3) were used in the measurements of particle velocity. The electrodes (E1) (a discharging system) contained the needle and semicylindrical electrodes, and were necessary to initially charge solid particles to permit the particle velocity measurement. The semicylindrical electrode was mounted on the outer surface of a PVC duct in the form of a 10 mm wide copper tape. The electrodes (E2) and (E3) were also mounted on the pipe surface in the form of cylinders whose length was 10 mm. Distances between electrodes (E1)}(E2) and (E2)}(E3) were kept constant and were equal to 100 mm. As a transported solid phase, commercially available the PE, PP, and PS particles were used. The particles were roughly spherical and their diameters ranged from 2.8 to 3.5 mm. 4. Experimental results and discussion The mass #ow rate = of the particle stream was determined from the relationship =" < M/l, L !
(3)
R. Kacprzyk, J.B. Gajewski / Journal of Electrostatics 51}52 (2001) 124}130
127
where M is the volume of circulating particles, < the most probable particle velocity, ! l the total particle distance (per one cycle), and the particle density. L The velocity < was determined by measuring the time of #ight of individual ! particles between electrodes (E2) and (E3). The particle time of #ight was measured with a storage oscilloscope whose two channels were controlled by signals from both electrodes. Measurements were carried out for the small number of circulating particles marked by a charge trapped in the ionized space of an electrode system (E1). The charged particle, passing by the electrodes (E2) and (E3), induced electric signals that were observed on the screen of the oscilloscope. A time delay between the signals observed was assumed to be equal to the time of #ight of the particle. It was experimentally proved that the most probable particle velocity < was linearly ! dependent on the air velocity < . The probe current was measured with a picoammeter. The time constant of the measuring circuit consisting of the probe and the picoammeter input was about 10 s. In all the experiments performed the bar probe was inserted into the PC pipe down to 40 mm. An example of the results obtained for the mass #ow rates that ranged from 0 to 5 kg/min for the PE particles (constant volume) is illustrated in Fig. 2. The strong non-linearities were generally observed in the case of di!erent particle and electrode materials for the mass #ow rates higher than 5 kg/min and sometimes I(=) dependencies were ambiguous. The results obtained for the PS and PP particles (for =(5 kg/min) are shown in Figs. 3 and 4, respectively. In both cases most of the I(=) characteristics can be approximated by parabolic functions of the form I"a=#b=. The computed values of the coe$cients a and b range, respectively, from !1.32 to 11.02 and from 0.61 to 3.14 for the constant velocity < of particles, and
Fig. 2. The current of the di!erent probes as a function of the mass #ow rate for the PE particles for a constant air velocity of 13.4 m/s.
128
R. Kacprzyk, J.B. Gajewski / Journal of Electrostatics 51}52 (2001) 124}130
Fig. 3. The current of the di!erent probes as a function of the mass #ow rate for the PS particles for a constant air velocity of 13.4 m/s.
Fig. 4. The current of the di!erent probes as a function of the mass #ow rate for the PP particles for a constant air velocity of 13.4 m/s.
from !4.31 up to !24.4 (a) and from 0.99 to !6.7 (b) for the constant volume M of particles that was 100 cm. The current, as measured for the PS particles and the brass probe, was of negative polarity within the range of the mass #ow rates. In Fig. 3 it is shown as a modulus of
R. Kacprzyk, J.B. Gajewski / Journal of Electrostatics 51}52 (2001) 124}130
129
Fig. 5. The probe current of the di!erent probes as a function of the mass #ow rate for the PE (a), PP (b) and PS (c) particles for a constant volume of 100 cm.
the value of the real probe current. Such an inversion of the current polarity was observed only in those experiments when these polymer particles and the brass probe were used. The results obtained for the constant particle volume are presented in Fig. 5. A linear dependence I(=) was observed for the PS particles only (Fig. 5c). For the PE and PP particles appropriate dependencies could be approximated by parabolic functions as earlier.
5. Conclusions Obtained results permit one to draw the following conclusions: E for the weakly conducting particles, the probe charging current I depends generally non-linearly on the mass #ow rate =; E the value of current and its direction depend on the material of the probe electrode and particles, as shown in Eq. (2); E for the higher mass #ow rates ('5 kg/min) I(=) characteristics can be ambiguous; E in the range of monotonic changes of the I(=) characteristics (W(5 kg/min) the shape of an approximating function and their constant coe$cients depend on the material of the electrode and the particles used; E the observed non-linearities suggest that assumptions used in the simpli"cation of the relationship (2) were not ful"lled (e.g. in reality the contact area s depends on the particle velocity and its elasticity coe$cient).
130
R. Kacprzyk, J.B. Gajewski / Journal of Electrostatics 51}52 (2001) 124}130
Acknowledgements This work was carried out as the statutory research at Wroc"aw University of Technology and was "nanced by the State Committee for Scienti"c Research, Warsaw, Poland.
References [1] P.P. Kremlevskij, Raschodomery i sc\ etciki kolic\ estva, Izd. Masinostroenie, Leningrad, 1975. [2] F.C. Kinghorn, Flow measurement methods } past, present and future, Transducer Technol. 10 (1983) 12. [3] R.A. Furness, J.E. Heritage, Commercially available #owmeters and future trends, Meas. Control 19 (1986) 25. [4] H. Masuda, S. Matsusaka, S. Nagatani, Measurements of powder #ow rate in gas}solids pipe #ow based on the static electri"cation of particles, Adv. Powder Technol. 5 (1994) 241. [5] J.B. Gajewski, Monitoring electrostatic #ow noise for mass #ow and mean velocity measurement in pneumatic transport, J. Electrostat. 37 (1996) 261}276. [6] H. Masuda, S. Matsusaka, H. Shimomura, Measurement of mass #ow rate of polymer powder based on static electri"cation of particles, Adv. Powder Technol. 9 (1998) 169. [7] Tribo#ow, Catalogue (Continuous Dry Solid Flow Monitor 2601). Auburn International, Inc., Danvers, MA.