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Non-intrusive solids charge and mass flow measurements with an electrostatic flow probe
Journal of Electrostatics 46 (1999) 271}284
Non-intrusive solids charge and mass #ow measurements with an electrostatic #ow probe Juliusz B. Gajewski* Institute of Heat Engineering and Fluid Mechanics, Technical University of Wroc!aw, WybrzezR e S. Wyspian& skiego 27, 50-370 Wroc!aw, Poland Received 18 August 1998; received in revised form 8 December 1998; accepted 9 December 1998
Abstract An electrostatic #ow probe for measurement of the electric charge, mass #ow rate, volume loading, or concentration of solid particles travelling along a pneumatic transport pipe is mounted on a dielectric pipe section. The particles contact the inner wall surface of the dielectric pipe and cause it to be charged. The charging of this wall can be a serious metrological problem because of its in#uence on any non-contact measuring system based upon the electrostatic (inductive) #ow probe which is a non-contact, non-intrusive device. The objective of this paper is to prove mathematically that there does not exist a problem of the dielectric pipe wall tribocharging from the metrological point of view when certain conditions are ful"lled. For the sake of illustration a sample measurement result obtained in a series of experiments performed with di!erent powdered and granulated materials is shown to retain the validity of the mathematical and physical models. Also there have been carried out computer simulation and numerical analyses of an equivalent circuit of the probe and preampli"er to show the time response of the system to the charging of the dielectric pipe inner wall and its in#uence on the readings. 1999 Elsevier Science B.V. All rights reserved. Keywords: Electrostatic #ow probe; Tribocharging; Charged powder; Mass #ow rate; Pneumatic transport of powder; ESD hazard
1. Introduction An electrostatic (inductive) #ow probe and measuring system intended for the continuous, real-time, indirect, non-intrusive measurement of the electric charge, mass
* Tel.: #48-71-320-3821; fax: #48-71-328-3818. 0304-3886/99/$ } see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 8 8 6 ( 9 8 ) 0 0 0 6 4 - 3
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#ow rate, volume loading, or concentration of solid particles, that are transported pneumatically in pipes, are based upon electrostatic induction. This phenomenon is used to enable the electric signals generated by the #ow of charged particles, that is the so-called electrostatic yow noise, to be traced and monitored continuously over a long time by any measuring system, whose "rst and principal part is the non-contact electrostatic #ow probe. The pipe #ow of charged solid particles is a complex stochastic (stationary and ergodic) process. Unfortunately, such inductive probes should be separated from the #ow for many reasons, for example, in order not to disturb the particle #ow. To guarantee the undisturbed #ow noise detection the probe must be mounted or placed on a dielectric pipe, which is transparent with respect to an electric "eld, as produced by the charged particles. The inner surface of a dielectric pipe section, whose cross-section is the same as that of a main pipeline as for its diameter and shape, is in the direct contact with the #ux of solid particles that charge it during many intense impacts. The highly charged surface of the pipe wall can be a cause of disturbances to the measurements being performed, as well as of the "re and explosion ESD hazard. The dielectric pipe section, which is coaxial with and has the same diameter (or the internal cross-sectional area) as the metal grounded pipe, through which solid particles travel, and the probe mounted on this section along with the connecting wire and the preampli"er are placed in the inside of a measuring head (chamber). The head is a solid metal construction that provides mechanical support, thermal protection, and electromagnetic screening. It has two #anges to enable it to be installed between two other #anges of the normal, actual pipe sections of a pipeline. The propagating brush discharges sometimes were observed while they were being developed along the wall surface to the grounded pipe. They occurred only for a few di!erent kinds of powdered materials and without harmful, devastating consequences. They were seen visually and metrologically in the form of impulses of an extremely short, in"nitesimal duration and relatively not too high a peak value. Those impulses overlapped the normal time-varying probe signal induced by the #ow of charged particles. The frequency of the impulse occurrence was very low; there were two, three impulses during one sampling cycle (record length). It has no signi"cant in#uence on the measurements, and moreover the impulse peaks can be removed by a special program when a microprocessor-based measuring system is used. Even if they would be included in the process of calculation of di!erent random signal characteristics, for example, the e!ective values or mean values of probe signals, the "nal outcome would be good, likely, and similar to that obtained by not taking the impulse values into calculations. It will be shown below that there are no serious metrological problems brought about by the dielectric wall charging itself and any electrostatic discharge from and along the wall surface to the nearest grounded metal parts of a transporting pipe. A thorough analysis of the physical object: the dielectric pipe, the probe, and the preampli"er, and its equivalent electric circuit will provide the proof of this thesis. The electric circuit was analyzed theoretically using electric circuit theory. Also computer simulation and numerical analyses of the circuit were made and their results are revealed to give plausible grounds for the above thesis. An example of the experimental results is presented as well.
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2. Real system electric circuit considerations The electrostatic #ow probe and measuring system, whose part (a preampli"er) is enclosed in the measuring head, is illustrated in Fig. 1. The whole measuring system consists of the head with one probe (or two when it is used for measuring the mean #ow velocity by the cross-correlation method) and of a microprocessor-based system, which was described in detail in Ref. [1]. The head has a strong, solid housing (1) for protecting its inside against the external mechanical stresses and forces, the in#uence of ambient conditions (temperature and humidity), and the external, detrimental electromagnetic signals. The probe (2) is mounted tightly on the dielectric pipe section (3) and is connected with a preampli"er (4) with a short wire to lower the total capacitance of the probe, connecting wire, and preampli"er input. The head used in the laboratory experiments, whose results are presented here, has a housing of 2 mm stainless steel sheet. The dimensions of the head's outer walls are 510;510;660 mm. In the inside of the head there is a dielectric pipe section, whose internal diameter is 130 mm. The dielectric pipe is made of a polymethyl methacrylate (PMMA) cylinder 10 mm thick. The PMMA mean resistivity and relative permittivity are about 10 ) m and 4, respectively. The metal ring probe is mounted tightly on the dielectric pipe section. The dielectric pipe has the same inner and outer diameters as those of the pneumatic, usually metal pipeline. The probe has the shape of the circular, full ring made of a thin, copper strip 0.5 mm thick and 20 mm wide. The total probe potential is a sum of two potentials. First potential is induced in the probe by the charged particles #owing in a sensing zone of the probe. The intense charging of the inner wall surface of the dielectric pipe section causes the charges to be generated, which in turn induce also the potential in the probe. The induction action of the charges of pipe-travelling particles on the probe was depicted elsewhere [2]. Only an impact of the surface charges on the probe potential is discussed here. In the further considerations subscripts are used for denoting all the electrical quantities which are taken into account. The digits 1, 2, and 3 in the subscripts correspond with the relevant four-terminal network elements, and they refer to the
Fig. 1. Experimental measuring head and system. Description in the text.
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electric charge on the dielectric wall surface, probe, and grounded electromagnetic screen, respectively. To consider the e!ect of the surface charges on the probe potential, the very similar circuit diagram is proposed though it is more developed. As before, it is assumed that the source of a useful signal is here an alternating current generator. The generator in all the electric circuit analyses represents the time-varying charge of the wall surface; this charge is an actual signal source. The whole diagram includes also the preampli"er, as shown in Fig. 2. There are three following important branches shown in the diagram: 1}3 means the source of an electrostatic #ow noise signal represented by an alternating current generator; 1}2 is the capacitive}resistive coupling of the inner charged wall surface with the electrostatic #ow probe; 2}3 represents the whole probe circuit including the input of any preampli"er. The circuit is equivalent to the three-electrode system, as presented in Ref. [2], and a set of capacitance matrix equations applies also here. By keeping in mind that
(t)"0 and C "C "0, the equations are as follows: q "(C #C ) !C ,
(1a)
q "!C #(C #C ) ,
(1b)
q "!C !C ,
(1c)
where q is the charge of the inner wall surface, q is the total charge of the probe, q "!(q #q ) is the charge induced on the inner surface of the grounded housing of the head, C is the mutual capacitance between the charged wall surface and the probe, C is the mutual capacitance between the charged wall and the grounded head housing, C is the total capacitance including the probe self-capacitance C with respect to the head housing, the connecting wire capacitance C , and the preampli "er's input capacitance C . The potentials , , and concern the wall surface, probe, and head housing, respectively. Both all the charges and potentials are time-dependent functions: q"q(t) and " (t), but for simplicity they will be written temporarily as q and . The resistances of the system are de"ned similarly as are the capacitances.
Fig. 2. Circuit diagram of the active four-terminal network made up of the alternating current generator, probe, and preampli"er.
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In the previous considerations [1] the resistances R and R were neglected as being of very little importance to the relationship between the potential ("u ) of the probe and the total, net charge q carried on the #owing particles. The both resistances are much higher than R . Now the resistance R is taken into account in calculations, and has a "nite value. It is at present assumed that there exist only charges on the wall surface, as said above; the dynamic e!ect of #owing charged particles on probe potential was discussed in detail in the previous paper [2]. During the process of the wall charging, the wall surface charge increases with time exponentially from zero up to its maximum value Q (the saturation charge), as can be deduced by analyzing many known reports [3}8]. The variation with time of this charge can be revealed using the following equation: q (t)"Q [1!exp(!t/q )], (2) where q is the time constant of the charging of the wall surface. The total potential of the probe can be expressed in the following form:
"a q #a q #a q " # # . (3) To "nd the relationship of the probe potential with the charge q of the dielectric pipe wall, one must determine the electric current #owing in the branch 1}2 according to Kirchhow's current law. For the active four-terminal network, as drawn in Fig. 2, the following circuit equation applies: d
!
d
"C # . C [ ! ]# (4) dt dt R R After the substantial rearrangement of Eq. (4) and the insertion of Eq. (1b) into Eq. (4) have been made, the following equation is obtained: q R C !R C
dq # "0. # (5) dt R C R C R Let the total capacitance C be a sum of the capacitances of the probe itself (self-capacitance) C and of the connecting wire and preampli"er input together C : C "C #C . The charge q "q #q and is a sum of those related to the probe itself q and to all the physical capacitances q existing when the probe is loaded by any measuring instrument. Since the following relations hold true q "C ( # )"C ( ! ), q "C , Eq. (4) can be rewritten in the form d
d
C
# "C # . C dt R dt C R
(6) (7)
(8)
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Now for the sake of simplicity of further considerations let us assume that the Coulomb potential (t) of the probe produced by the charge q (t) of the dielectric wall can be expressed as a certain linear function of this charge
"a q "a Q [1!exp(!t/q )] (9) This assumption about the linear relationship between and q is well-founded, because the charged wall surface can be treated as a stationary `electrodea which is immovable in relation to the probe, to a "rst approximation. Such an electrode is not equipotential. The distribution of the surface charge is neither known nor wellde"ned, and it is certainly nonuniform. This should not be any theoretical or metrological problem considering that non-contact probes, sensors, or transducers of that type tend to average spatially all random variables over a certain volume (sensing or viewing zone) and produce as output a time varying function: f"f (t) if a given physical quantity is a space- and time-dependent variable [9]. If the variable is only a function of space (x, y, z) in the steady state, then the probe output is a constant value or zero depending on the total output resistance, as will be shown later. By inserting Eq. (9) into Eq. (8) one obtains d
1 1 # "a C Q C exp(!t/q )#a C Q [1!exp(!t/q )], (10) dt R q ¹ where ¹"R C is the time constant of the capacitive}resistive coupling of the inner wall surface with the probe. The Laplace transform of Eq. (10) is of the form U (s) ¹!q 1 11 sC U (s)# !C (0)"a C Q #a C Q , (11) ¹ sq #1 ¹ s R where the initial condition is being obtained from Eq. (1a) and Eq. (1b) by bearing in mind that q (0)"q (0)"0, and hence for the initial instant t"0, the initial condition is C
(0)" q (0)"k q (0)"0. (12) ! C C #C C #C C In the end, the equation for U (s) is as follows: ¹!q 1 1 1 U (s)"a C R Q #a C R Q , (13) ¹ (sq #1)(sq#1) ¹ s(sq#1) where q"R C is the time constant of the probe circuit. In the time domain, Eq. (13) is given by
¹!q R exp(!z/q ) exp[!(t!z)/q] dz
(t)"A ¹qq 1 R #A 1(z) exp[!(t!z)/q] dz, ¹q where A"a C R Q is the factor of proportionality.
(14)
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The "nal time form of the solution of Eq. (14) is expressed by 1 ¹!q [exp(!t/q )!exp(!t/q)]#A [1!exp(!t/q)], (15)
(t)"A ¹(q !q) ¹ whose analysis shows that the time course of this function of potential (or voltage) has three signi"cant and important parts from the mathematical and physical point of view. They are the following: E The function starts from zero for t"0: (0)"0; E The probe potential tends to its maximum or minimum depending on the sign of a net charge Q
(t )"
¹!q ¹#q!2q q \O O\O "A ¹(q !q) ¹!q q ¹!q ¹#q!2q q \O O\O 1 (16) !A #A , ¹(q !q) ¹!q q ¹ qq ¹#q!2q q ln ; for t"t " q !q ¹!q q E The limit of the function, to which it tends asymptotically, is
1 1
(R)"A "a C R Q , ¹ ¹
(17)
when time approaches in"nity: tPR. One can show that the function (15) tends to zero when time approaches in"nity for the extremely high value of the resistance R (R PR), and then the time constant ¹ is also very high (¹PR), as results from Eq. (17). At the same time, one must state that the probe co-operating with the preampli"er di!erentiates almost ideally a signal produced by the charged inner wall of the dielectric pipe and induced in the probe when the resistance R is very high and the total resistance R is as low as possible, as shown in Ref. [2]. An analysis of the mathematical model (15) of the real physical circuit and phenomenon, and of the e!ect of a highly charged dielectric pipe wall on the measurements of the electric charges or mass #ow rate, or volume loading (concentration) of particulates in pneumatic transport pipelines shows that there does not exist any disturbance that would be harmful from the metrological point of view, as believed. Even in the worst case, when the resistance R is "nite and lower than a certain critical value which is about 10 ), the charged wall signal is also di!erentiated but potential or voltage maximum is shifted to the higher values of time. The critical value results from a computer simulation of the probe}preampli"er circuit and its numerical analysis, which will be shown in the next chapter. In this case, the "nal value of the probe potential (voltage) is constant for the high values of time and this seems not to be
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a problem, since any microprocessor-based measuring system, device, instrument, as widely used nowadays, can monitor this constant potential value and take it into account as a constant background when displaying the proper, accurate value of a measurand.
3. Computer simulation and numerical analysis of the active four-terminal network The results are presented below of the computer simulation and numerical analysis of the four-terminal network, in which the source of a signal is an alternating current generator (see Fig. 3) that is a model for the surface charge generated on the inner dielectric pipe wall. All the values of the circuit parts and elements were accepted on the basis of many experiments and evaluations. The current produced during the charging of the inner wall surface has a value of 10 nA and rises up to its maximum value with a time constant of 5 s; this was evaluated on the basis of experimental results yielded using granulated polypropylene. The current is then of the following form: i (t)"10\[1!exp(!t/5)]. The internal generator resistance is assumed to be 1 T). Since the charged solid particles #ow through the whole cross-section of a pipe during the fully developed turbulent #ow, as assumed, especially the network resistances and capacitances are evaluated as sensibly constant on the basis of many years' experience. Their rather real values are given in the equivalent circuit diagram in Fig. 3. The calculated time constant q of the network is about 80 ls. The computer simulation has been done for the real circuit consisting of the probe and preampli"er, whose "rst stage is built on the basis of an operational ampli"er AD 549 and which operates as an inverting one. This ampli"er was synthesized within a specially written subroutine that has been used throughout all the simulations and numerical analyses of the active four-terminal network. The results of the simulations were obtained for two speci"c cases to "nd a certain critical, boundary value of the resistance R , below which the circuit transmits the signal proportionally, and above which the signal is di!erentiated and attenuated strongly down to a value of a C R Q /¹ or zero, when ¹ tends to in"nity. This boundary value was determined empirically during several computer simulations and
Fig. 3. Equivalent circuit diagram of the active four-terminal network made up of the alternating current generator, electrostatic #ow probe, and preampli"er.
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analyses made with a trial-and-error method and is about 10 ). The results obtained for the values of the resistance R around this boundary one are presented here in Fig. 4 for the coupling resistance R equal (1) 10 and (2) 10 ). The curves (1) and (2) concern the voltage u (t) at the output of a "rst stage of the measuring preampli"er. The rough estimation of the expression a C R Q /¹ gives an extremely low value of the order of single microvolts for a resistance R of 10 ). One can expect that this value is rather sensibly constant for a given circuit con"guration throughout even lengthy experiments and observations. Such a value can be assumed as insigni"cant for the metrological outcome, the more so as it can be computed and taken into account in the determination of di!erent probe signal parameters by the microprocessor-based measuring system. The same conclusion can be drawn when analyzing the plot of the output preampli"er voltage u (t) for low values of the resistance R , namely below 10 ). The voltage approaches asymptotically the other value of the expression a C R Q /¹, which is now higher because of the lower time constant ¹. The results presented of the computer simulation and numerical analysis of the real probe and preampli"er circuit con"rm those of the theoretical analysis. The both approaches to solution to the problem seem to provide substantial evidence that there
Fig. 4. Plots of the time variations of the generator current i (t) and output preampli"er voltage u (t) for the following values of the resistance R : (1) 10 and (2) 10 ).
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does not exist any metrological disturbance when the dielectric pipe section is used to separate the probe from the two-phase gas}solids pipe #ow. The only problem is still an ESD hazard that can potentially bring about "re and even explosion in a pipeline. This is a problem of somewhat di!erent and more complex nature than only metrological one, and must be assessed and considered independently.
4. Practical aspects of wall surface discharges Fig. 5 shows a sample computer printout of a copy of the monitor screen that displays functions of the microprocessor-based measuring system, as used in the laboratory experiments during thorough veri"cation and calibration tests. The measuring system was employed, amongst other things, to the dual-channel measurements of a mean #ow velocity of solid particles by means of the cross-correlation method, as described in detail in Ref. [1]. The signals were sampled using 8-bit procedures to enable further computation of the characteristic stochastic signal parameters as, for example, the e!ective (RMS) values, the mean values, the mean values of recti"ed signals, as well as the auto- and cross-correlation functions, and so forth. The physically occurring discharges from the highly charged surface of any dielectric contacting solid particles travelling along this surface at relatively high velocities produce impulses that induce the potential impulses in the probe. The impulses were observed rather rarely and only for some powdered materials and speci"c transport conditions. Also they occurred not too frequently. For example, during one of the laboratory experiments the probe signal was sampled by the microprocessor-based
Fig. 5. Sample computer printout (the copy of a monitor screen) of the plot of a digitally processed analog probe signal in the "rst measuring channel and of the processed data. The arrows (1) and (2) show the discharge impulses superimposed on the main probe signal curve. Description in the text.
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measuring system at a sampling frequency f of 3943 Hz providing 4000 samples. Hence, the record length ¹ was about 1.014 s. As shown in Fig. 5, two impulses occurred within the whole period of sampling, and interval between them was approximately 0.56 s. The diagram in Fig. 5 has two axes. The axis of ordinates is scaled in quanta; for the 8-bit A/D converter used 1 quantum is equal to 40 mV, since the full range of voltages, that is their peak-to-peak values, is 10 V (from !5 to #5 V). The axis of abscissa is the number of samples, whose full range is from 1 to 4000 for each signal sample set. The image of the plot analyzed on the screen can be optionally magni"ed in the directions of both axes or in only one direction, or reduced. Below the plot of a probe signal in one of the measuring channels there is a set of processed data concerning both the signal curve displayed and other parameters of the particle #ow in a pipe of pneumatic transport. There is a legend in which the abbreviations of di!erent names of data, parameters, quantities, functions, etc. are used, and explanations of those abbreviations are as follows: NAME NPNTS SFREQ DPROB START
SAMPD
NUSAC INDEL MDEL AMPL MVAL MVR RMS COCOR DEL TRANT VELOC
the name entered of a given data set the number of the samples collected of the signals X and > in a set of sequences the sampling frequency the probe spacing (a distance between probes) the starting point, i.e. the number of a "rst sample in the set X, from which the calculation of the autocorrelation and cross-correlation functions starts the step, with which the samples of each sequence are taken for correlation, e.g. 1 means that every one sample is taken, 2 } that every second, 3 } that every third, etc. the total number of samples of the both sequences X and > taken for calculations of the cross-correlation function the initial delay in samples } a shift of the beginning of the sequence of the signal > samples in relation to the sequence of the signal X samples. the maximum delay in samples the maximum amplitude (value) of a signal within a whole analyzed range of samples the mean value of a signal the mean value of a recti"ed signal the e!ective value of a signal the correlation coe$cient the delay in samples of a signal > in relation to X for the maximum value of the correlation coe$cient the delay in time, i.e. time delay or transit time the mean value of the solids #ow velocity
In general, the digits 1 and 2 in the legend mean the numbers of the probes used or of measuring channels. The cross-correlation functions were obtained with the use of the 8-bit correlation procedure.
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The two impulses, as seen in Fig. 5, and others, as observed further, were not detrimental to the measurements made during that and other sessions. They occurred only in the case of this material, that is granulated polypropylene, as shown here. When others were used, for example, aluminosilicate powder, polyethylene granules, etc., the discharges and impulses superimposed on the useful probe signals were not detected and consequently recorded at all. Also it is important to notice that during the many measurement sessions the maximum values of impulses did not exceed a value of 5 V too often, that is the peak value of voltage at the input of both the preampli"er and an A/D converter AD 587. It is worth noticing that both impulses have negative polarity, as have also the mean values of both probes' output potentials (voltages). This is directly tied to the results of the former theoretical analysis and of the numerical analysis, as believed, namely the very low negative value of the probe voltage mean value can be strictly related with the value of the potential function limit a C R Q /¹ for su$ciently long times t. A mean value of !49 mV (or !30 mV in the second channel), and, of course, each such a value, can easily be taken into account in every computation made by the microprocessor system to obtain a real value of a parameter, quantity, function, etc., as determined by the measuring system. As mentioned above, the microprocessor-based measuring system is capable of "ltering and/or smoothing digitally the probe's output signal after it has been converted into a digital one. Such an example of the measuring system possibility is revealed in the successive diagram in Fig. 6. The description of the whole diagram is the same as that in Fig. 5. One can see that the values of all the characteristics of the probe signals, as processed after they had been "ltered, are slightly lower than those of the signals with the impulses superimposed on them. This means that there is a certain contribution of the impulse value to the total value of each characteristic computed. This addition and the resulting di!erences between all the characteristics' values are so small that the e!ect of discharge impulses on the measurement results can be neglected even if the impulses are not "ltered from the probe signals. For instance, the relative errors for the values of all the characteristics calculated, when the values of the "ltered characteristics are assumed to be real, and can be reference ones, are the following: p +2.1%, p +0.1%, p +0.3%. +4 * +40 0+1 Another problem can emerge when the discharges develop, if at all, from the charged wall surface to the nearest grounded element of a transporting installation, namely the input circuits of any measuring devices can be damaged. But as a general rule, all measuring systems, especially their input circuits, are well protected against overload (excessive current or voltage). Moreover, the discharges do not occur continuously but from time to time, and their impulses observed in the probe potential (voltage) do not have too great an impact on the measured or rather determined value, for example, of the e!ective voltage, as is in practice. The number of such impulses within one cycle of sampling is very low and is not more than three, as shown here. The microprocessor-based measuring system, as used in laboratory experiments, "lters all undesired impulses superimposed on a useful probe signal, after digital conversion (sampling) of the analog probe signal has been done.
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Fig. 6. Sample computer printout of the same digitally processed analog probe signal, as shown in Fig. 5, in the "rst measuring channel and of the processed data after the discharge impulses were "ltered.
Concluding, there is no problem with the intense charging of the dielectric wall surface nor with the discharges from that surface from the metrological point of view. The only ESD hazard occurs in this situation, namely the initiation of "re and/or explosion if an air-powdered material mixture is su$ciently sensitive to any electric discharge, whose energy is higher than the minimum ignition energy (MIE) of the mixture.
5. Conclusions The results of the thorough theoretical and numerical analyses, as well as those obtained during di!erent many years' experiments permit one to state again that there are no signi"cant disturbances of non-intrusive #ow parameter measurements with any non-contact electrostatic #ow probe, as created by the electrostatic discharges under such metrological conditions, as presented here. The microprocessor-based measuring system, as used in the laboratory experiments, makes it possible to eliminate any impact of the discharge impulses on the system readings. Even if a measuring system is incapable of "ltering the impulses from the useful probe signals, there exists a possibility of avoiding any inconvenience coming from the intense charging of a wall surface of any dielectric pipe section. In such a case it seems to be a good solution to this problem that the calibration of any system based upon the induction #ow probes and intended for indirect measurements of the #ow physical quantities and parameters should be done. If the measuring system has no such possibility to store adequate, relevant calibration data, it should be calibrated only
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under and for well-de"ned #ow conditions as those encountered in industry, for example. Also the system calibration should be repeated periodically for the system inspection, even if the pneumatic transport conditions are sensibly constant over a long time. In general, the charging of the dielectric pipe wall and resulting discharge impulses can be treated as a certain type of background to di!erent non-intrusive measurements performed with the electrostatic #ow probe for a given material pneumatically transported, a dielectric material, of which the pipe section is made, and given transport conditions.
References [1] J.B. Gajewski, Monitoring electrostatic #ow noise for mass #ow and mean velocity measurement in pneumatic transport, J. Electrostat. 37 (1996) 261. [2] J.B. Gajewski, Dynamic e!ect of charged particles on the measuring probe potential, in: Proc. 8th Int. Conf. on Electrostatics ELECTROSTATICS '97, Poitiers-Futuroscope, France, 1997, J. Electrostat. 40 & 41 (1997) 437. [3] B.N. Cole, M.R. Baum, F.R. Mobbs, An investigation of electrostatic charging e!ects in high-speed gas}solids pipe #ows, Proc. Instn. Mech. Engrs. 184 (Part 3C) (1969}70), paper 10, 77. [4] A. Chowdry, C.R. Westgate, The role of bulk traps in metal}insulator contact charging, J. Phys. D 7 (1974) 713. [5] J. Fuhrmann, Contact electri"cation of dielectric solids, J. Electrostat. 4 (1978) 109. [6] A.G. Bailey, Electrostatic hazards in powder silos, Proc. 7th Conf. on Electrostatic Phenomena ELECTROSTATICS '87, Oxford, England, 1987, Inst. Phys. Ser. 85 (1987) 1. [7] J.A. Cross, Electrostatics: Principles, Problems and Applications, Hilger, Bristol, 1987. [8] D.M. Taylor, P.E. Secker, Industrial Electrostatics: Fundamentals and Measurements, Research Studies Press, Taunton, 1994. [9] J.B. Gajewski, Electrostatic, inductive ring probe bandwidth, Meas. Sci. Technol. 7 (1996) 1766.
Non-intrusive solids charge and mass #ow measurements with an electrostatic #ow probe Juliusz B. Gajewski* Institute of Heat Engineering and Fluid Mechanics, Technical University of Wroc!aw, WybrzezR e S. Wyspian& skiego 27, 50-370 Wroc!aw, Poland Received 18 August 1998; received in revised form 8 December 1998; accepted 9 December 1998
Abstract An electrostatic #ow probe for measurement of the electric charge, mass #ow rate, volume loading, or concentration of solid particles travelling along a pneumatic transport pipe is mounted on a dielectric pipe section. The particles contact the inner wall surface of the dielectric pipe and cause it to be charged. The charging of this wall can be a serious metrological problem because of its in#uence on any non-contact measuring system based upon the electrostatic (inductive) #ow probe which is a non-contact, non-intrusive device. The objective of this paper is to prove mathematically that there does not exist a problem of the dielectric pipe wall tribocharging from the metrological point of view when certain conditions are ful"lled. For the sake of illustration a sample measurement result obtained in a series of experiments performed with di!erent powdered and granulated materials is shown to retain the validity of the mathematical and physical models. Also there have been carried out computer simulation and numerical analyses of an equivalent circuit of the probe and preampli"er to show the time response of the system to the charging of the dielectric pipe inner wall and its in#uence on the readings. 1999 Elsevier Science B.V. All rights reserved. Keywords: Electrostatic #ow probe; Tribocharging; Charged powder; Mass #ow rate; Pneumatic transport of powder; ESD hazard
1. Introduction An electrostatic (inductive) #ow probe and measuring system intended for the continuous, real-time, indirect, non-intrusive measurement of the electric charge, mass
* Tel.: #48-71-320-3821; fax: #48-71-328-3818. 0304-3886/99/$ } see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 8 8 6 ( 9 8 ) 0 0 0 6 4 - 3
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#ow rate, volume loading, or concentration of solid particles, that are transported pneumatically in pipes, are based upon electrostatic induction. This phenomenon is used to enable the electric signals generated by the #ow of charged particles, that is the so-called electrostatic yow noise, to be traced and monitored continuously over a long time by any measuring system, whose "rst and principal part is the non-contact electrostatic #ow probe. The pipe #ow of charged solid particles is a complex stochastic (stationary and ergodic) process. Unfortunately, such inductive probes should be separated from the #ow for many reasons, for example, in order not to disturb the particle #ow. To guarantee the undisturbed #ow noise detection the probe must be mounted or placed on a dielectric pipe, which is transparent with respect to an electric "eld, as produced by the charged particles. The inner surface of a dielectric pipe section, whose cross-section is the same as that of a main pipeline as for its diameter and shape, is in the direct contact with the #ux of solid particles that charge it during many intense impacts. The highly charged surface of the pipe wall can be a cause of disturbances to the measurements being performed, as well as of the "re and explosion ESD hazard. The dielectric pipe section, which is coaxial with and has the same diameter (or the internal cross-sectional area) as the metal grounded pipe, through which solid particles travel, and the probe mounted on this section along with the connecting wire and the preampli"er are placed in the inside of a measuring head (chamber). The head is a solid metal construction that provides mechanical support, thermal protection, and electromagnetic screening. It has two #anges to enable it to be installed between two other #anges of the normal, actual pipe sections of a pipeline. The propagating brush discharges sometimes were observed while they were being developed along the wall surface to the grounded pipe. They occurred only for a few di!erent kinds of powdered materials and without harmful, devastating consequences. They were seen visually and metrologically in the form of impulses of an extremely short, in"nitesimal duration and relatively not too high a peak value. Those impulses overlapped the normal time-varying probe signal induced by the #ow of charged particles. The frequency of the impulse occurrence was very low; there were two, three impulses during one sampling cycle (record length). It has no signi"cant in#uence on the measurements, and moreover the impulse peaks can be removed by a special program when a microprocessor-based measuring system is used. Even if they would be included in the process of calculation of di!erent random signal characteristics, for example, the e!ective values or mean values of probe signals, the "nal outcome would be good, likely, and similar to that obtained by not taking the impulse values into calculations. It will be shown below that there are no serious metrological problems brought about by the dielectric wall charging itself and any electrostatic discharge from and along the wall surface to the nearest grounded metal parts of a transporting pipe. A thorough analysis of the physical object: the dielectric pipe, the probe, and the preampli"er, and its equivalent electric circuit will provide the proof of this thesis. The electric circuit was analyzed theoretically using electric circuit theory. Also computer simulation and numerical analyses of the circuit were made and their results are revealed to give plausible grounds for the above thesis. An example of the experimental results is presented as well.
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2. Real system electric circuit considerations The electrostatic #ow probe and measuring system, whose part (a preampli"er) is enclosed in the measuring head, is illustrated in Fig. 1. The whole measuring system consists of the head with one probe (or two when it is used for measuring the mean #ow velocity by the cross-correlation method) and of a microprocessor-based system, which was described in detail in Ref. [1]. The head has a strong, solid housing (1) for protecting its inside against the external mechanical stresses and forces, the in#uence of ambient conditions (temperature and humidity), and the external, detrimental electromagnetic signals. The probe (2) is mounted tightly on the dielectric pipe section (3) and is connected with a preampli"er (4) with a short wire to lower the total capacitance of the probe, connecting wire, and preampli"er input. The head used in the laboratory experiments, whose results are presented here, has a housing of 2 mm stainless steel sheet. The dimensions of the head's outer walls are 510;510;660 mm. In the inside of the head there is a dielectric pipe section, whose internal diameter is 130 mm. The dielectric pipe is made of a polymethyl methacrylate (PMMA) cylinder 10 mm thick. The PMMA mean resistivity and relative permittivity are about 10 ) m and 4, respectively. The metal ring probe is mounted tightly on the dielectric pipe section. The dielectric pipe has the same inner and outer diameters as those of the pneumatic, usually metal pipeline. The probe has the shape of the circular, full ring made of a thin, copper strip 0.5 mm thick and 20 mm wide. The total probe potential is a sum of two potentials. First potential is induced in the probe by the charged particles #owing in a sensing zone of the probe. The intense charging of the inner wall surface of the dielectric pipe section causes the charges to be generated, which in turn induce also the potential in the probe. The induction action of the charges of pipe-travelling particles on the probe was depicted elsewhere [2]. Only an impact of the surface charges on the probe potential is discussed here. In the further considerations subscripts are used for denoting all the electrical quantities which are taken into account. The digits 1, 2, and 3 in the subscripts correspond with the relevant four-terminal network elements, and they refer to the
Fig. 1. Experimental measuring head and system. Description in the text.
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electric charge on the dielectric wall surface, probe, and grounded electromagnetic screen, respectively. To consider the e!ect of the surface charges on the probe potential, the very similar circuit diagram is proposed though it is more developed. As before, it is assumed that the source of a useful signal is here an alternating current generator. The generator in all the electric circuit analyses represents the time-varying charge of the wall surface; this charge is an actual signal source. The whole diagram includes also the preampli"er, as shown in Fig. 2. There are three following important branches shown in the diagram: 1}3 means the source of an electrostatic #ow noise signal represented by an alternating current generator; 1}2 is the capacitive}resistive coupling of the inner charged wall surface with the electrostatic #ow probe; 2}3 represents the whole probe circuit including the input of any preampli"er. The circuit is equivalent to the three-electrode system, as presented in Ref. [2], and a set of capacitance matrix equations applies also here. By keeping in mind that
(t)"0 and C "C "0, the equations are as follows: q "(C #C ) !C ,
(1a)
q "!C #(C #C ) ,
(1b)
q "!C !C ,
(1c)
where q is the charge of the inner wall surface, q is the total charge of the probe, q "!(q #q ) is the charge induced on the inner surface of the grounded housing of the head, C is the mutual capacitance between the charged wall surface and the probe, C is the mutual capacitance between the charged wall and the grounded head housing, C is the total capacitance including the probe self-capacitance C with respect to the head housing, the connecting wire capacitance C , and the preampli "er's input capacitance C . The potentials , , and concern the wall surface, probe, and head housing, respectively. Both all the charges and potentials are time-dependent functions: q"q(t) and " (t), but for simplicity they will be written temporarily as q and . The resistances of the system are de"ned similarly as are the capacitances.
Fig. 2. Circuit diagram of the active four-terminal network made up of the alternating current generator, probe, and preampli"er.
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In the previous considerations [1] the resistances R and R were neglected as being of very little importance to the relationship between the potential ("u ) of the probe and the total, net charge q carried on the #owing particles. The both resistances are much higher than R . Now the resistance R is taken into account in calculations, and has a "nite value. It is at present assumed that there exist only charges on the wall surface, as said above; the dynamic e!ect of #owing charged particles on probe potential was discussed in detail in the previous paper [2]. During the process of the wall charging, the wall surface charge increases with time exponentially from zero up to its maximum value Q (the saturation charge), as can be deduced by analyzing many known reports [3}8]. The variation with time of this charge can be revealed using the following equation: q (t)"Q [1!exp(!t/q )], (2) where q is the time constant of the charging of the wall surface. The total potential of the probe can be expressed in the following form:
"a q #a q #a q " # # . (3) To "nd the relationship of the probe potential with the charge q of the dielectric pipe wall, one must determine the electric current #owing in the branch 1}2 according to Kirchhow's current law. For the active four-terminal network, as drawn in Fig. 2, the following circuit equation applies: d
!
d
"C # . C [ ! ]# (4) dt dt R R After the substantial rearrangement of Eq. (4) and the insertion of Eq. (1b) into Eq. (4) have been made, the following equation is obtained: q R C !R C
dq # "0. # (5) dt R C R C R Let the total capacitance C be a sum of the capacitances of the probe itself (self-capacitance) C and of the connecting wire and preampli"er input together C : C "C #C . The charge q "q #q and is a sum of those related to the probe itself q and to all the physical capacitances q existing when the probe is loaded by any measuring instrument. Since the following relations hold true q "C ( # )"C ( ! ), q "C , Eq. (4) can be rewritten in the form d
d
C
# "C # . C dt R dt C R
(6) (7)
(8)
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Now for the sake of simplicity of further considerations let us assume that the Coulomb potential (t) of the probe produced by the charge q (t) of the dielectric wall can be expressed as a certain linear function of this charge
"a q "a Q [1!exp(!t/q )] (9) This assumption about the linear relationship between and q is well-founded, because the charged wall surface can be treated as a stationary `electrodea which is immovable in relation to the probe, to a "rst approximation. Such an electrode is not equipotential. The distribution of the surface charge is neither known nor wellde"ned, and it is certainly nonuniform. This should not be any theoretical or metrological problem considering that non-contact probes, sensors, or transducers of that type tend to average spatially all random variables over a certain volume (sensing or viewing zone) and produce as output a time varying function: f"f (t) if a given physical quantity is a space- and time-dependent variable [9]. If the variable is only a function of space (x, y, z) in the steady state, then the probe output is a constant value or zero depending on the total output resistance, as will be shown later. By inserting Eq. (9) into Eq. (8) one obtains d
1 1 # "a C Q C exp(!t/q )#a C Q [1!exp(!t/q )], (10) dt R q ¹ where ¹"R C is the time constant of the capacitive}resistive coupling of the inner wall surface with the probe. The Laplace transform of Eq. (10) is of the form U (s) ¹!q 1 11 sC U (s)# !C (0)"a C Q #a C Q , (11) ¹ sq #1 ¹ s R where the initial condition is being obtained from Eq. (1a) and Eq. (1b) by bearing in mind that q (0)"q (0)"0, and hence for the initial instant t"0, the initial condition is C
(0)" q (0)"k q (0)"0. (12) ! C C #C C #C C In the end, the equation for U (s) is as follows: ¹!q 1 1 1 U (s)"a C R Q #a C R Q , (13) ¹ (sq #1)(sq#1) ¹ s(sq#1) where q"R C is the time constant of the probe circuit. In the time domain, Eq. (13) is given by
¹!q R exp(!z/q ) exp[!(t!z)/q] dz
(t)"A ¹qq 1 R #A 1(z) exp[!(t!z)/q] dz, ¹q where A"a C R Q is the factor of proportionality.
(14)
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The "nal time form of the solution of Eq. (14) is expressed by 1 ¹!q [exp(!t/q )!exp(!t/q)]#A [1!exp(!t/q)], (15)
(t)"A ¹(q !q) ¹ whose analysis shows that the time course of this function of potential (or voltage) has three signi"cant and important parts from the mathematical and physical point of view. They are the following: E The function starts from zero for t"0: (0)"0; E The probe potential tends to its maximum or minimum depending on the sign of a net charge Q
(t )"
¹!q ¹#q!2q q \O O\O "A ¹(q !q) ¹!q q ¹!q ¹#q!2q q \O O\O 1 (16) !A #A , ¹(q !q) ¹!q q ¹ qq ¹#q!2q q ln ; for t"t " q !q ¹!q q E The limit of the function, to which it tends asymptotically, is
1 1
(R)"A "a C R Q , ¹ ¹
(17)
when time approaches in"nity: tPR. One can show that the function (15) tends to zero when time approaches in"nity for the extremely high value of the resistance R (R PR), and then the time constant ¹ is also very high (¹PR), as results from Eq. (17). At the same time, one must state that the probe co-operating with the preampli"er di!erentiates almost ideally a signal produced by the charged inner wall of the dielectric pipe and induced in the probe when the resistance R is very high and the total resistance R is as low as possible, as shown in Ref. [2]. An analysis of the mathematical model (15) of the real physical circuit and phenomenon, and of the e!ect of a highly charged dielectric pipe wall on the measurements of the electric charges or mass #ow rate, or volume loading (concentration) of particulates in pneumatic transport pipelines shows that there does not exist any disturbance that would be harmful from the metrological point of view, as believed. Even in the worst case, when the resistance R is "nite and lower than a certain critical value which is about 10 ), the charged wall signal is also di!erentiated but potential or voltage maximum is shifted to the higher values of time. The critical value results from a computer simulation of the probe}preampli"er circuit and its numerical analysis, which will be shown in the next chapter. In this case, the "nal value of the probe potential (voltage) is constant for the high values of time and this seems not to be
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a problem, since any microprocessor-based measuring system, device, instrument, as widely used nowadays, can monitor this constant potential value and take it into account as a constant background when displaying the proper, accurate value of a measurand.
3. Computer simulation and numerical analysis of the active four-terminal network The results are presented below of the computer simulation and numerical analysis of the four-terminal network, in which the source of a signal is an alternating current generator (see Fig. 3) that is a model for the surface charge generated on the inner dielectric pipe wall. All the values of the circuit parts and elements were accepted on the basis of many experiments and evaluations. The current produced during the charging of the inner wall surface has a value of 10 nA and rises up to its maximum value with a time constant of 5 s; this was evaluated on the basis of experimental results yielded using granulated polypropylene. The current is then of the following form: i (t)"10\[1!exp(!t/5)]. The internal generator resistance is assumed to be 1 T). Since the charged solid particles #ow through the whole cross-section of a pipe during the fully developed turbulent #ow, as assumed, especially the network resistances and capacitances are evaluated as sensibly constant on the basis of many years' experience. Their rather real values are given in the equivalent circuit diagram in Fig. 3. The calculated time constant q of the network is about 80 ls. The computer simulation has been done for the real circuit consisting of the probe and preampli"er, whose "rst stage is built on the basis of an operational ampli"er AD 549 and which operates as an inverting one. This ampli"er was synthesized within a specially written subroutine that has been used throughout all the simulations and numerical analyses of the active four-terminal network. The results of the simulations were obtained for two speci"c cases to "nd a certain critical, boundary value of the resistance R , below which the circuit transmits the signal proportionally, and above which the signal is di!erentiated and attenuated strongly down to a value of a C R Q /¹ or zero, when ¹ tends to in"nity. This boundary value was determined empirically during several computer simulations and
Fig. 3. Equivalent circuit diagram of the active four-terminal network made up of the alternating current generator, electrostatic #ow probe, and preampli"er.
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analyses made with a trial-and-error method and is about 10 ). The results obtained for the values of the resistance R around this boundary one are presented here in Fig. 4 for the coupling resistance R equal (1) 10 and (2) 10 ). The curves (1) and (2) concern the voltage u (t) at the output of a "rst stage of the measuring preampli"er. The rough estimation of the expression a C R Q /¹ gives an extremely low value of the order of single microvolts for a resistance R of 10 ). One can expect that this value is rather sensibly constant for a given circuit con"guration throughout even lengthy experiments and observations. Such a value can be assumed as insigni"cant for the metrological outcome, the more so as it can be computed and taken into account in the determination of di!erent probe signal parameters by the microprocessor-based measuring system. The same conclusion can be drawn when analyzing the plot of the output preampli"er voltage u (t) for low values of the resistance R , namely below 10 ). The voltage approaches asymptotically the other value of the expression a C R Q /¹, which is now higher because of the lower time constant ¹. The results presented of the computer simulation and numerical analysis of the real probe and preampli"er circuit con"rm those of the theoretical analysis. The both approaches to solution to the problem seem to provide substantial evidence that there
Fig. 4. Plots of the time variations of the generator current i (t) and output preampli"er voltage u (t) for the following values of the resistance R : (1) 10 and (2) 10 ).
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does not exist any metrological disturbance when the dielectric pipe section is used to separate the probe from the two-phase gas}solids pipe #ow. The only problem is still an ESD hazard that can potentially bring about "re and even explosion in a pipeline. This is a problem of somewhat di!erent and more complex nature than only metrological one, and must be assessed and considered independently.
4. Practical aspects of wall surface discharges Fig. 5 shows a sample computer printout of a copy of the monitor screen that displays functions of the microprocessor-based measuring system, as used in the laboratory experiments during thorough veri"cation and calibration tests. The measuring system was employed, amongst other things, to the dual-channel measurements of a mean #ow velocity of solid particles by means of the cross-correlation method, as described in detail in Ref. [1]. The signals were sampled using 8-bit procedures to enable further computation of the characteristic stochastic signal parameters as, for example, the e!ective (RMS) values, the mean values, the mean values of recti"ed signals, as well as the auto- and cross-correlation functions, and so forth. The physically occurring discharges from the highly charged surface of any dielectric contacting solid particles travelling along this surface at relatively high velocities produce impulses that induce the potential impulses in the probe. The impulses were observed rather rarely and only for some powdered materials and speci"c transport conditions. Also they occurred not too frequently. For example, during one of the laboratory experiments the probe signal was sampled by the microprocessor-based
Fig. 5. Sample computer printout (the copy of a monitor screen) of the plot of a digitally processed analog probe signal in the "rst measuring channel and of the processed data. The arrows (1) and (2) show the discharge impulses superimposed on the main probe signal curve. Description in the text.
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measuring system at a sampling frequency f of 3943 Hz providing 4000 samples. Hence, the record length ¹ was about 1.014 s. As shown in Fig. 5, two impulses occurred within the whole period of sampling, and interval between them was approximately 0.56 s. The diagram in Fig. 5 has two axes. The axis of ordinates is scaled in quanta; for the 8-bit A/D converter used 1 quantum is equal to 40 mV, since the full range of voltages, that is their peak-to-peak values, is 10 V (from !5 to #5 V). The axis of abscissa is the number of samples, whose full range is from 1 to 4000 for each signal sample set. The image of the plot analyzed on the screen can be optionally magni"ed in the directions of both axes or in only one direction, or reduced. Below the plot of a probe signal in one of the measuring channels there is a set of processed data concerning both the signal curve displayed and other parameters of the particle #ow in a pipe of pneumatic transport. There is a legend in which the abbreviations of di!erent names of data, parameters, quantities, functions, etc. are used, and explanations of those abbreviations are as follows: NAME NPNTS SFREQ DPROB START
SAMPD
NUSAC INDEL MDEL AMPL MVAL MVR RMS COCOR DEL TRANT VELOC
the name entered of a given data set the number of the samples collected of the signals X and > in a set of sequences the sampling frequency the probe spacing (a distance between probes) the starting point, i.e. the number of a "rst sample in the set X, from which the calculation of the autocorrelation and cross-correlation functions starts the step, with which the samples of each sequence are taken for correlation, e.g. 1 means that every one sample is taken, 2 } that every second, 3 } that every third, etc. the total number of samples of the both sequences X and > taken for calculations of the cross-correlation function the initial delay in samples } a shift of the beginning of the sequence of the signal > samples in relation to the sequence of the signal X samples. the maximum delay in samples the maximum amplitude (value) of a signal within a whole analyzed range of samples the mean value of a signal the mean value of a recti"ed signal the e!ective value of a signal the correlation coe$cient the delay in samples of a signal > in relation to X for the maximum value of the correlation coe$cient the delay in time, i.e. time delay or transit time the mean value of the solids #ow velocity
In general, the digits 1 and 2 in the legend mean the numbers of the probes used or of measuring channels. The cross-correlation functions were obtained with the use of the 8-bit correlation procedure.
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The two impulses, as seen in Fig. 5, and others, as observed further, were not detrimental to the measurements made during that and other sessions. They occurred only in the case of this material, that is granulated polypropylene, as shown here. When others were used, for example, aluminosilicate powder, polyethylene granules, etc., the discharges and impulses superimposed on the useful probe signals were not detected and consequently recorded at all. Also it is important to notice that during the many measurement sessions the maximum values of impulses did not exceed a value of 5 V too often, that is the peak value of voltage at the input of both the preampli"er and an A/D converter AD 587. It is worth noticing that both impulses have negative polarity, as have also the mean values of both probes' output potentials (voltages). This is directly tied to the results of the former theoretical analysis and of the numerical analysis, as believed, namely the very low negative value of the probe voltage mean value can be strictly related with the value of the potential function limit a C R Q /¹ for su$ciently long times t. A mean value of !49 mV (or !30 mV in the second channel), and, of course, each such a value, can easily be taken into account in every computation made by the microprocessor system to obtain a real value of a parameter, quantity, function, etc., as determined by the measuring system. As mentioned above, the microprocessor-based measuring system is capable of "ltering and/or smoothing digitally the probe's output signal after it has been converted into a digital one. Such an example of the measuring system possibility is revealed in the successive diagram in Fig. 6. The description of the whole diagram is the same as that in Fig. 5. One can see that the values of all the characteristics of the probe signals, as processed after they had been "ltered, are slightly lower than those of the signals with the impulses superimposed on them. This means that there is a certain contribution of the impulse value to the total value of each characteristic computed. This addition and the resulting di!erences between all the characteristics' values are so small that the e!ect of discharge impulses on the measurement results can be neglected even if the impulses are not "ltered from the probe signals. For instance, the relative errors for the values of all the characteristics calculated, when the values of the "ltered characteristics are assumed to be real, and can be reference ones, are the following: p +2.1%, p +0.1%, p +0.3%. +4 * +40 0+1 Another problem can emerge when the discharges develop, if at all, from the charged wall surface to the nearest grounded element of a transporting installation, namely the input circuits of any measuring devices can be damaged. But as a general rule, all measuring systems, especially their input circuits, are well protected against overload (excessive current or voltage). Moreover, the discharges do not occur continuously but from time to time, and their impulses observed in the probe potential (voltage) do not have too great an impact on the measured or rather determined value, for example, of the e!ective voltage, as is in practice. The number of such impulses within one cycle of sampling is very low and is not more than three, as shown here. The microprocessor-based measuring system, as used in laboratory experiments, "lters all undesired impulses superimposed on a useful probe signal, after digital conversion (sampling) of the analog probe signal has been done.
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Fig. 6. Sample computer printout of the same digitally processed analog probe signal, as shown in Fig. 5, in the "rst measuring channel and of the processed data after the discharge impulses were "ltered.
Concluding, there is no problem with the intense charging of the dielectric wall surface nor with the discharges from that surface from the metrological point of view. The only ESD hazard occurs in this situation, namely the initiation of "re and/or explosion if an air-powdered material mixture is su$ciently sensitive to any electric discharge, whose energy is higher than the minimum ignition energy (MIE) of the mixture.
5. Conclusions The results of the thorough theoretical and numerical analyses, as well as those obtained during di!erent many years' experiments permit one to state again that there are no signi"cant disturbances of non-intrusive #ow parameter measurements with any non-contact electrostatic #ow probe, as created by the electrostatic discharges under such metrological conditions, as presented here. The microprocessor-based measuring system, as used in the laboratory experiments, makes it possible to eliminate any impact of the discharge impulses on the system readings. Even if a measuring system is incapable of "ltering the impulses from the useful probe signals, there exists a possibility of avoiding any inconvenience coming from the intense charging of a wall surface of any dielectric pipe section. In such a case it seems to be a good solution to this problem that the calibration of any system based upon the induction #ow probes and intended for indirect measurements of the #ow physical quantities and parameters should be done. If the measuring system has no such possibility to store adequate, relevant calibration data, it should be calibrated only
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under and for well-de"ned #ow conditions as those encountered in industry, for example. Also the system calibration should be repeated periodically for the system inspection, even if the pneumatic transport conditions are sensibly constant over a long time. In general, the charging of the dielectric pipe wall and resulting discharge impulses can be treated as a certain type of background to di!erent non-intrusive measurements performed with the electrostatic #ow probe for a given material pneumatically transported, a dielectric material, of which the pipe section is made, and given transport conditions.
References [1] J.B. Gajewski, Monitoring electrostatic #ow noise for mass #ow and mean velocity measurement in pneumatic transport, J. Electrostat. 37 (1996) 261. [2] J.B. Gajewski, Dynamic e!ect of charged particles on the measuring probe potential, in: Proc. 8th Int. Conf. on Electrostatics ELECTROSTATICS '97, Poitiers-Futuroscope, France, 1997, J. Electrostat. 40 & 41 (1997) 437. [3] B.N. Cole, M.R. Baum, F.R. Mobbs, An investigation of electrostatic charging e!ects in high-speed gas}solids pipe #ows, Proc. Instn. Mech. Engrs. 184 (Part 3C) (1969}70), paper 10, 77. [4] A. Chowdry, C.R. Westgate, The role of bulk traps in metal}insulator contact charging, J. Phys. D 7 (1974) 713. [5] J. Fuhrmann, Contact electri"cation of dielectric solids, J. Electrostat. 4 (1978) 109. [6] A.G. Bailey, Electrostatic hazards in powder silos, Proc. 7th Conf. on Electrostatic Phenomena ELECTROSTATICS '87, Oxford, England, 1987, Inst. Phys. Ser. 85 (1987) 1. [7] J.A. Cross, Electrostatics: Principles, Problems and Applications, Hilger, Bristol, 1987. [8] D.M. Taylor, P.E. Secker, Industrial Electrostatics: Fundamentals and Measurements, Research Studies Press, Taunton, 1994. [9] J.B. Gajewski, Electrostatic, inductive ring probe bandwidth, Meas. Sci. Technol. 7 (1996) 1766.