Journal of
ELECTROSTATICS ELSEVIER
Journal of Electrostatics 37 (1996) 261276
Monitoring electrostatic flow noise for mass flow and mean velocity measurement in pneumatic transport J u l i u s z B. G a j e w s k i Institute of Heat Engineering and Fluid Mechanics, Technical UniversiO' of Wroclaw. Wybrze~e S. Wyspiahskiego 27, 50370 Wroctaw, Poland
Received 12 November 1995; accepted after revision 29 April 1996
Abstract This paper presents experimental results of research on the electrostatic, noncontact measurement of the mass flow rate and mean flow velocity of solids in pneumatic transport lines. We also describe a microprocessorbased system, based on the measurement method, that had been built to be installed in industrial installations. The system permits rapid mass flow rate and mean flow velocity measurements in quasireal time. The method is based on the phenomenon of electrostatic induction  the effect of the flux of charged solid particles flowing in a pipe on measuring ring probes (inductive transducers). The research, described in this paper, provides experimental verification of the measuring system. Results obtained for two different materials (aluminosilicate and granulated polypropylene) show the relationships between the effective values (RMS) and mean values of rectified electric signals induced in the measuring probes by the flow of charged solid particles and the mass flow rate of those particles for different mean flow velocities. Keywords: Pneumatic transport; Electrostatic induction; Electrostatic flow noise; Granular
solids; Flow measurement; Electrostatic flow probe
I. Introduction The solids m a s s flow rate or v o l u m e l o a d i n g in p n e u m a t i c t r a n s p o r t pipes can be m e a s u r e d using the electrostatic (inductive), n o n  c o n t a c t m e t h o d discussed elsewhere in detail [ 1  4 ] . A m i c r o p r o c e s s o r  b a s e d system b a s e d on this m e t h o d was built for i n s t a l l a t i o n in largescale i n d u s t r i a l o p e r a t i o n s [5]. T h e system p e r m i t s one to m e a s u r e the solids m a s s flow rate o r v o l u m e l o a d i n g as well as the m e a n flow velocity in a pipe q u i c k l y a n d in a q u a s i  r e a l  t i m e mode, H e r e are revealed the results of the m e a s u r e m e n t s where the m i c r o p r o c e s s o r  b a s e d m e a s u r i n g system c a l c u l a t e d the effective value U of a m e a s u r i n g ring p r o b e signal o r the m e a n value of a rectified p r o b e signal ( ] u ( t ) l ) for v a r i o u s values of the m e a n mass 03043886/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved P11 S 0 3 0 4  38 8 6 ( 9 6 ) 0 0 0 1 62
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flow rate (rh(t)) as measured simultaneously by weighing the mass of solid particles accumulated over a measured time interval. The calibration curves U = f [ ( n i ( t ) ) ] and £lu(t)J)  9 [~m(t))] obtained for different mean flow velocities @(t)) are of practical significance. The particulate materials used in those experiments were aluminosilicate powder and 9ranulated polypropylene.
2. Measurement method
The flow of charged solid particles is a multidimensional stochastic (stationary and ergodic) process. Random variables are generally functions of space (x, y, z) and time (t): f =f(x, y, z, t). Each probe averages some flow variable over a volume determined by the probe geometry [6] and produces as output a time varying function: f = f ( t ) . Each of the variables can be expressed as a sum of its mean value and an independent, superimposed, bandlimited Gaussian variable fluctuation [6,7]. This fluctuation, termed "flow noise", is generated by a small, irregular flow that is superimposed on the average flow [8, 9]. Since flow noise is strictly related to the charging of solid particles during a twophase pipe flow it is convenient to call this phenomenon "electrostatic flow noise". There is also the direct correlation between this noise and the mass flow rate [9, 10]. The method involves measurement of the potential induced in a specially designed metal ring probe by charged solid particles that flow through the probe section (or two probes, when the mean flow velocity is to be determined) mounted on a dielectric pipe section that separates the probe from the flow and is "transparent" with respect to the electric field. The dielectric pipe has the same inner and outer diameters as those of the pneumatic metal pipeline. It was shown that RMS voltage is proportional to the mass flow rate of solids in the case of the wellknown capacitance method [9] and to the root of the mass flow rate [10]. Accordingly, there are the following relations: Uocm,
(1)
U oc rh°5.
(2)
Models for the electrostatic (inductive), noncontact method of continuous and quasirealtime measurement of the mass flow rate or volume loading and mean flow velocity of solids have been presented elsewhere [1, 3, 11]. Mathematical relations between the electric signals (potential or voltage) of an inductive probe and the mass flow rate (volume loading) have been given. In general, those models predict similar dependences despite their different origins. The general time dependence of the potential of the measuring ring probe itself, when it is isolated from all other grounded conducting objects in space, or the voltage drop across the total impedance of the system: the probe  the input of a preamplifier, when it is connected directly with the preamplifier input, on the mass flow rate is expressed
J.B. Gajewski/Journal oJ Electrostatics 37 (1996) 261276
263
as follows: u(t) = kith(f),
(3)
m(t)
u(t) = k 2 v(0'
(4j
u(t) = k3f
15)
t , ~ ],
where kl, k2 and k3 are the calibration coefficients, rh(t) is the instantaneous value of the solids mass flow rate and v(t) is the instantaneous value of the solids flow velocity. Measurement of the instantaneous values of the mass flow rate and flow velocity is practically impossible but, furthermore, unnecessary. Thus the mean values of both quantities are used: Qh(t)) and (v(t)). The solids mean flow rate (rh(t)) is practically determined by measuring the mass Am of solid particles that fall down onto, e.g., a balance within a certain time At. The mean mass flow rate is easily calculated from the following formula: Oh(t))
Am At"
(6)
The solids mean flow velocity (v(t)) is measured using the crosscorrelation method. The two stochastic signals x(t) and y(t) of two probes separated by a distance L on a dielectric pipe are crosscorrelated by software to obtain any crosscorrelation function Rxy(r). An analysis of the crosscorrelation function course R~y(r) permits the transit time zo to be determined from the maximum of this function R~v(r} = ~ lira
x(t  r)y(t)dt = 7lim ~?,
x(t)y(t + z)dt.
(7)
The transit time r0 is a measure of the mean flow velocity (v(t)) which can therefore be calculated easily and exactly when the optimum, socalled correlated distance Lop, between the two probes is known. This distance can be determined experimentally and/or predetermined theoretically. The correlation coefficient px:.(ro) is a good optimization criterion and strongly depends on the distance L between the probes: p~,(ro) = f ( L ) for a fixed mean flow velocity (v(t)) when the distance L is a correlated one Lop,, then the correlation coefficient reaches its maximum (when the flow velocity increases, so does Lopt ). The criterion was used in all the experiments presented here. Before the experiments were performed with the use of a new particulate material, a series of measurements were made for different mean flow velocities and probe distances to obtain the set of characteristics: p~y(%) = f ( L ) , where (v(t)) is a parameter. The distance Lop, between the probes was predicted according to the following formula which was derived by analyzing the crosscorrelation function R~v(r) and verified experimentally [12]: (/;(t)) 2 Lop t = 0 . 8 8   , O'vO)0
(8)
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where av is the standard deviation of the flow velocity v(t) and COo( = 2nfc) is the upper cutoff angular frequency (electrostatic flow noise bandwidth) of the corresponding power density spectrum. Then the solids mean flow velocity (v(t)) is easily calculated from (v(t) ) 
Lop,
(9)
TO
3. Experimental installation and measuring system The experimental facility consists of the pneumatic transport installation and measurement subsystem which in turn consists of a measuring head and the microprocessorbased instrumentation. The overall experimental system is shown in Fig. 1. The pneumatic transport installation is made up of a compressor driven by an electric motor (1), a valve (2) for controlling the compressor output, a pressure vessel (3) with a weightedlever safety valve (4), another valve (5) for controlling the volumetric flow rate of air as a carrier of solid particles in a pneumatic pipeline, a solids feeder (6), the measuring system (7), a system of cyclones (8 and 9), a bag filter (10), a blower (11) for discharging the filtered air outside of a building, a tank receiving the tested loose material from cyclones and a bag filter, a simple, common balance used for measuring the mass flow rate (12), a storage silo (13) into which the tested material falls down after it has been weighed and in which one can maintain constant pressure by means of a valve (14) which controls the amount of air flowing into the silo. The measuring system consists of a measuring head (chamber) and the microprocessorbased system. The head consists of specially designed probes or transducers for
Fig. 1. Schematic diagram of the experimental pneumatic transport installation. Description in the text.
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measuring the mass flow rate and mean flow velocity in a pneumatic pipeline. The probe signals are amplified for transmission to the microprocessor unit which is usually located rather far away from the head. The measuring head provides mechanical support, thermal protection and electromagnetic screening. The head must be grounded very carefully. As shown in Fig. 2, it is made up of the following parts: a housing (1), a dielectric pipe (2), the measuring metal ring probes (3), flanges (4), the preamplifiers (5), electric connection wires 16), power leads (7), BNC connectors (8), coaxial cables (9) for connection to the microprocessorbased measuring system, and a metal guard ring or partition (10). The guard ring, mounted on a dielectric pipe between the sensing electrodes and grounded. reduces capacitive crosscoupling that may disturb the probe signals and increase the resolution error. The partition is especially useful when the probe spacing is small. The microprocessorbased measuring system for convenience is shown in the block diagram in Fig. 3. The microprocessor plays the most important role, as it receives analog electric signals from the probes and converts them into a digital form for processing. The unit gathers data for calculation of: • the delay in samples of a Y signal in relation to X for the maximum correlation coefficient value, • the delay in time, i.e. the time delay or transit time, • the mean value of the flow velocity of solid particles in a pipe. The system collects all the data related to the signals themselves and obtained from the calculations, and stores them in the internal memories. The microprocessorbased measuring system consists of an analog signal conditioning section and an analogdigital part in which analog signals are converted into digital ones and then processed by a microprocessor. In each of the four measuring heads, as shown in Fig. 3, there are the measuring probes which are mounted on dielectric pipes and directly connected with the inputs of identical emitter follower preamplifiers (1). The signals are then transmitted by coaxial cables to the 5
9 jJ
J /j
J
J
//JJ
Fig. 2. Measuringhead. Description in the text.
7 6
/i, 1 J J~
2
266
J.B. Gajewski/Journal of Electrostatics 37 (1996) 261 276 1
,
2
'
3
"

1
Output O
•
04"Input
4
43
l Outpuot
Measuring heads 1,2or4
Analog part
o
~ ~
o
fJ [ L.... a I I ]
Analogdigital part
Fig. 3. Schematic block diagram of the microprocessorbased measuring system. Description in the text. P1 4: measuring probes in individual measuring channels, M: multiplexer, A/D: A/D converter, laP: microprocessor, D: alphanumeric LCD, 1M: internal memories: SRAM and EPROM, K: keyboard, SI: serial interface RS232, PI: parallel interface (optionally). Digits 14 at the measuring inputs before the probes and at the preamplifiers mean the numbers of each of the four independent measuring channels.
analogdigital part directly to the inputs of four amplifiers which along with amplitude limiters and other amplifiers are the block of amplifiers (2); the signals are properly scaled to utilize the full dynamic range of an A/D converter to minimize resolution errors. In both blocks (1) and (2) the channel gains are automatically controlled. The microprocessor block (3) consists of an A/D converter and digital signal processing sections. The analogdigital subsystem consists of a multiplexer and an A/D converter. The digital subsystem is an independent unit in which the main part is a microprocessor with SRAM (1 MB) and E P R O M (64 KB) memories. This block carries out all the monitoring, collecting, processing, calculating, controlling, and storing procedures. The last block (4) contains two power supplies for energizing the analog and digital circuits. To illustrate the function of the microprocessor unit on the probe electric signals, sample computer printouts of processed data are shown in Fig. 4. Below the plots of signals and crosscorrelation curves, as one can see on the monitor screen, there are the legends in which the abbreviations of different names of data, parameters, quantities, etc. are used. The explanations of those abbreviations are the following: NAME the name entered of a given data set, NPNTS the number of the samples collected of the signals X and Y in a set of sequences, SFREQ the sampling frequency, DPROB the probe spacing (a distance between probes), START the starting point, i.e. the number of a first sample in the set X, from which the calculation of the autocorrelation and crosscorrelation functions starts,
J.B. Gajewski/Journal of Electrostatics 37 (1996) 261 276
120110II]OS08070<~5040
267
a
1
0 1020. 30" 40 E~O. 60. 70. 80 90 lO0 Ii0 120
moo
io~o
NPNT~= SFREQDPROB:
Coo
4000 3 9 4 : 3 Hz O.lOIDa
.~
i~o
$1~NPD= 1 NUSCtO= 4 0 0 0 INOEL= 0 IIDEL = ;lO00
i~o
13~o
NU~ILI=O .036 U IMUft.IL = 0 . 6 4 2 U fl11~.1. = 0 . 7 9 2 U
13~
14~
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15~o
I H ~ A I  ~ =  O .O~E, U IIUR2 = 0.~,23 U I~115 ~' : 0 . 7 7 8 U
i~
DEL = 33 TP.~NT= lB.3? ~s UELOC: 11.55m/ts
I
1.0, 0.~.
b
0
.
~
:
'
[?.7, 0.6 0.~', 0.3' (?.2 O.l'
0.2 0.3 ' 0.+ 0.5 0.6 0.7 0.~ •
•
l.O 0
NAME NPNTS= SFFII='Q= DPflOB
OX20 ,41.O00 : 3 9 4 3 Hx O..I.OON
~TART= 1 :SAMPle1 NUSI~= 4000
¢II'IPLi.= " ~ , 3 4 4 V HUALt=O ,O36 P H U R l  0 . 6 4 2 U
I~IMPL2= 2,3B'.'~ U 14~AL2='O .O~15 U HEIR2 = 0 . 6 2 3 U
]NDEL:
RllS/
RI15:2
IIDEL
0
=
0.792U
:
0.778U
.
COCOR= 0.894 DEE 33 TI~INTG .3"? ms =
UIE.LOC:
11.Cj~ln/S
= 2000
Fig. 4. Representative computer printouts (the copies of a monitor screent of the digital processing of analog probe signals and the other data collected: (a) the time variations of two measuring probe signals (1) x(t) and (2) y(t), and (b) the courses of two crosscorrelation functions calculated using the I l) 8bit and (2) 1bit correlation procedures. Description in the text.
SAMPD
NUSAC
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 Y taken for calculations of the crosscorrelation function,
268
~LB. Gajewski/Journal of Electrostatics 37 (1996) 261~76
INDEL
the initial delay in samples  a shift of the beginning of the sequence of the signal Y samples in relation to the sequence of the signal X samples, MDEL the maximum delay in samples, AMPL the maximum amplitude of a signal within a whole analyzed range of samples, MVAL the mean value of a signal, MVR the mean value of a rectified signal, RMS the effective value of a signal, COCOR the correlation coefficient, DEL the delay in samples of a signal Y in relation to X for the maximum value of the correlation coefficient, TRANT the delay in time, i.e. time delay or transit time, VELOC the mean value of the solids flow velocity. In general, the digits 1 and 2 in both plots of Fig. 4 correspond to the number of the probes or measuring channels. The two curves of the crosscorrelation functions are different and marked with the digits 1 and 2 which mean that the first function has been obtained with the use of the 8bit correlation procedure while the second, using the 1bit procedure of the auto and crosscorrelation functions calculations.
4. Results The granular solids used in the experiments were aluminosilicate powder and 9ranulated polypropylene. The results presented here are plots of the effective values U and the mean values of the rectified signals ([u(t)l) as functions of the mean mass flow rates (rh(t)) for the different mean flow velocities (v(t)) as the parameters. The solids mean flow rate was determined by a weighing method (simultaneous weighing and timing). The method employed is based upon the measurement of a mass Am of solid particles that fall down from a bag filter into a container connected with a balance within a certain time At measured with a stopwatch  a computer clock was sometimes used as well. The mean mass flow rate (rh(t)) was calculated from Eq. (6).
4.1. Aluminosilicate powder The aluminosilicate powder particles used were of rather regular shape sized less than 0.001 m. The quantity of the aluminosilicate powder in the storage silo was about 25 kg. The powder under test was fed into the pneumatic transport system in times ranging from 5 to 20 min to achieve different mean mass flow rates. During those tests the probe signals were sampled about 10 times, depending on the sampling frequency f~. Before each test the optimum, correlated distance Lop t between the two probes was determined using the correlation coefficient pxr(Z0) as an optimization criterion. In Fig. 5, a typical curve of the dependence of pxy(ro) on the probe spacing L is shown. From such curves, one can easily determine the correlated distance Lop t between the
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269
0.90 0.88
i
0.86
T I
Z bc~
0.84 0.82
 ;
0.80

0.78 0.76
I
0.74 0.00
0.05
0.10
J
i
O.15
0.20
0.25
L [ml Fig. 5. Dependence of the correlation coefficient Px~.(%) on the probe spacing L for a mean flow velocity (v(t)) of 13.20 m s 1.
probes. In this experiment, the mean flow velocity (v(t)) was 13.20 m s  1. The signals of both probes were sampled with the sampling frequency of 10 k H z and one obtained 16 000 signal samples for each probe (measuring channel) signal samples set. In Fig. 5, the correlated distance Lopt is seen to be approximately 0.15 m. For the mean flow velocity of 10.44 m s  1 the experiments were carried out in which the effective values U and the mean values of the rectified signals (lu(t)]) were calculated for the different mean mass flow rates Qh(t)). The results of those measurements are collected in Fig. 6. A similar diagram, obtained for a mean flow velocity of 13.20 m s~, is shown in Fig. 7. The curves obtained serve as calibrations for subsequent experimental runs (calibration curves). The data presented in Figs. 6 and 7 were sampled at frequencies of 1 and 10 kHz, respectively. For the velocity of 10.44 m s  1 the correlated probe spacing was 0.12 m for pxy(r0) = 0.904 while for the other case the correlated coefficient was a little bit smaller and is 0.858 for the correlated distance of 0.15 m.
4.2. Granulated poIypropylene These particles were almost monodisperse at 0.0044 m in diameter. Their shape is regular and similar to the flat pellets (pills). Their thickness ranged from 0.0024 to 0.0028 m. The mass of the polypropylene granules used also was 25 kg and they were fed into the experimental installation in the same way, as was the aluminosilicate powder. As before a test was first carried out to find the correlated distance Lop t for the measuring probes. In the case of polypropylene the probe correlated distance was 0.2 m. The correlated distance was obtained for the correlation coefficient value of
270
.~B. Gajewski/Journal of Electrostatics 37 (1996) 261276 1.6 1.5 1.4 1.3
E
1.2
A
1.1 v
1.0 0.9 0.8 0.7 0.6 19
20
21
22
23
24
25
26
27
II0 3kgs 11 Fig. 6. The effective value U and the mean value of a rectified signal (pu(t)l) versus the mean mass flow rate (rh(t)) for a mean flow velocity (v(t)) of 10.44 m s ~.
0.95 0.90 0.85 0.80 A
v
0.75 0.70 0.65 0.60 0.55 0.50 57
58
59
60
61
62
63
[10 3kg.slJ Fig. 7. The effective value U and the mean value of a rectified signal (Ju(t)l) versus the mean mass flow rate (rh(t)) for a mean flow velocity (v(t)) of 13.20 m s  i
0.63 a n d f o r t h e m e a n f l o w v e l o c i t y o f g r a n u l e s o f 8.50 m s  1. F o r p o l y p r o p y l e n e , t h e s i g n a l s o f b o t h p r o b e s w e r e s a m p l e d w i t h t h e s a m e f r e q u e n c y o f 10 k H z in all t h e e x p e r i m e n t s p e r f o r m e d . A s a m p l e p l o t o f t h e c o r r e l a t i o n c o e f f i c i e n t v a l u e pxr(Zo) d e p e n d e n c e o n t h e p r o b e s p a c i n g L is s h o w n in Fig. 8.
.LB. Gajewski/Journal of Electrostatics 37 (1996) 261 276
271
0.64 0.62 k
0.60 0.58
Z
0.56 0.54 i
0.52 0.50

0.48 0.46 0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
/~ Iml Fig. 8. Dependence of the correlation coefficient px~(ro) on the probe spacing L for a mean flow velocity ( v ( t ) ) of 8.50 m s  ~.
0.40 0.38 0.36 0.34
>z
0.32
A
0.30
V
0.28 0.26 0.24
+j
0.22
+,j
t__+
0.20 0.18 52
54
56
58
60
62
64
[10 3kg.s 1] Fig. 9. The effective value U and the mean value of a rectified signal (lu(tJ]) versus the mean mass flow rate ~rh(t)) for a m e a n flow velocity (v(t}) of 8.28 m s  1.
The dependences of the RMS value U of the probe signals monitored and the mean value of the rectified signals {lu(t)]) of the probes upon the mean mass flow rates Qh(t)) as measured by weighing and timing are presented as the calibration curves in Fig. 9. These results were obtained at a mean flow velocity (v(t)) of 8.28 m s  1.
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5. Analysis and discussion The results presented here reveal an approximately linear dependence for both the RMS value U of the probe signals u(t) and the mean value of the rectified signals ([u(t)]) upon the mean mass flow rate (rh(t)). Such a dependence is predicted by different models Eqs. (1), (3), and (4), though (2) shows the nonlinear dependence of the RMS value U of a signal on the mass flow rate n~ and (5) is a certain implicit function, where the relationship between the RMS voltage U and the mass flow rate rh(t) and flow velocity v(t) is not expressed in a direct way. There are two possible explanations of the dependences U = f [ ( n ~ ( t ) ) ] and (Ju(t)J) = g[(n~(t))] obtained and presented here for different mean flow velocities (v(t)). One possibility is that the changes of both electrical parameters U and ([ u(t)l) of the probe signals detected and monitored may be assumed to be approximately linear or nonlinear with the same probability since the range of variations of (th(t)) seems too narrow to permit one to state unequivocally that the dependences should be linear according to Eqs. (1), (3), and (4) or nonlinear according to Eqs. (2) and (5), if the latter is nonlinear. On the other hand, if one assumes that the range of variation of (n~(t)) is sufficient to interpret the results obtained, one could also find that all the relationships obtained should be only nonlinear as predicted by Eqs. (2) and (5) as the most probable explanation of such variations of those curves from the physical point of view. The tendency of U and ~]u(t)l) to decrease with the increasing (rh(t)) can be explained in the following way: when the solids volume loading (and mass flow rate) is low, the mean free path of particle motion is rather long and the random particle motion is not damped by particle collisions. Along with an increase in the solids loading (the high mass flow rate) the mean free path decreases and impacts between particles begin to damp out the motion. This phenomenon is more noticeable especially for the range of lower velocities since the particles are then relatively close together. At the high flow velocities the average distance between the particles is greater and the damping of their motion occurs at relatively higher volume loadings. Both kinds of the influences are well noted in Figs. 6 and 7. The second interpretation is valid for both the aluminosilicate powder particles and polypropylene granules, though in the case of the latter, the more regular, almost linear dependence of U and (]u(t)]) upon Qh(t)) can be explained in terms of the identical dimensions of those granules that are practically monosized, and of their larger size and greater mass than in the case of the aluminosilicate particles. The granules supposedly move only along the rectilinear trajectories parallel to the pipe axis because of their inertia and regardless of their mean flow velocity within a range of velocities covered in the experiments, and therefore the random particle motions do not occur at all. An increase in fluid resistance and drag is also observed and considered as the main and key factor which is responsible for a decrease of the mean flow velocity of the polypropylene granules for the same volumetric flow rates as were used for conveying the aluminosilicate particles. It is interesting that for the relatively large, heavy, and regularly shaped polypropylene granules the correlated probe distance Lop ' is somewhat larger than for the
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273
aluminosilicate particles, and for the lower mean flow velocity (v(t)), namely of 8.50 m s1. A possible explanation for this may be that the frozen flow pattern I6, 7, 13] is travelling downstream between the probes rather slowly and steadily, and therefore the time variations of the flow velocity v(t) and thus its standard deviation av are very small  the standard deviation is relatively smaller than the mean flow velocity (v(t)), resulting in the greater probe spacing Lopt according to Eq. (8). If the polypropylene granules motion is smooth and steady, then the probe distance L might also be shorter. But there is one serious lower limit: the two probe signals may overlap in wh,~ii case the resolution may also decrease while the resolution error increases at the same time.Fig. 8 shows that the correlation coefficient value px~,(r0) decreases, as the distance L goes below its optimum value Lop,. Steady motion of the granules also results in reduced electrostatic flow noise fluctuations, i.e. the amplitude of the time variations of the electric field generated by the flow of the charged granules. These signals are much smaller for the polypropylene than for the aluminosilicate powder. It seems that this is the only and plausible reason of the much lower correlation coefficient value in the case of the polypropylene granules. The dependences U = f E ( r h ( t ) ) ] and (lu(t)l) g1(rh(t))] can be used as calibration curves for a given, welldefined powder or granular solid pneumatically conveyed in a pipe and also for given, welldefined and rather constant conditions under which solids transport is carried out, i.e. the volumetric flow rate of air and flow velocity, air carrier temperature and humidity, type and material of which the pipeline is made, etc. Even if the above dependences are not exactly linear, the microprocessorbased measuring system is capable of: • analyzing the data obtained after the calculation of the values of U. (lu(t)t), and
(v(t)), • determining the appropriate analytical or numerical forms of each of the mathematical relations: U = f [ ( r h ( t ) ) ] and (lu(t)[) = g[(~h(t))] for a given mean flow velocity (v(t)) as a parameter, • compiling, building the function tables for a family of different mathematical relations to enable the proper identification of a curve for a given mean flow velocity and/or for other calibration parameters, also the determination of a mass flow rate when the values of U or ([u(t)]) are known, • storing all the data obtained after the above procedures have been done to identify interesting dependences and to determine the mass flow rate accurately during each measurement series in a given industrial pneumatic transport installation and for a welldefined material under test. The balance and stopwatch accuracy were +_0.1 kg and +_0.2 s, respectively. The maximum relative error of the mass flow rate determination, when one assumes that the container was filled with the mass of 10kg within 120s, does not exceed 1.2%. At this stage of the research it is impossible to make a thorough analysis of the microprocessorbased measuring system and to assess uncertainties and all the possible measurement errors since the system is still restructured and perfected. The influence of temperature and relative humidity of the air carrier in a pipe and the equilibrium moisture contents of solid particles, particle type and size, particle and
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piping material and others on the mass flow rate measurement will be examined at the later stages of this research the results of which along with the final analysis of the system will be presented later.
6. Conclusions
The experiments performed on the electrostatic (inductive), noncontact method and the microprocessorbased measuring system prove the value of using the electrostatic flow noise generated by the flow of charged solid particles in pneumatic transport in monitoring and measuring flow parameters such as mass fow rate, volume loading and flow velocity. The system permits one to measure indirectly the solids mass flow rate (rh(t)) and the mean flow velocity (v(t)) in any pneumatic pipeline quickly and in a quasirealtime mode. The system is suitable for implementation in largescale, industrial installations after the calibration procedures have been carried out. The calibration procedures are necessary to determine • the correlated distance Lop, between the probes and • the adequate relations U = f [ ( m ( t ) ) ] and ([u(t)l) = g [(rh(t))] for the given mean flow velocities (v(t)) as parameters. The method in itself is very simple and reliable, and its practical application requires only simple measuring probes for detecting and monitoring the electrostatic flow noise. The necessary microprocessorbased measuring system is not unduly complicated. One important advantage is that the system is completely unaffected by vibration, a very important factor in industrial plants. All the experiments were performed quickly and reliably, and the results obtained revealed good repeatability and show promise in the design and construction of a new class of noncontact flowmeters. The microprocessorbased measuring system can be used where a monitoring of the emission of solid pollutants to the atmosphere is necessary, One very important problem is the ESD dust ignition hazard associated with pneumatic transport of solids. Using this system, such hazards should be assessed quickly and reliably, making it possible to control solids flow parameters. The system is similar to that for measuring the net electric charge on particles flowing in a pipe, as described in detail earlier [14, 15], and it could be applied for controlling fire and explosion hazards in many types of installations according to the socalled dynamic' safety criteria established and presented in [16].
Nomenclature
.f~ .f~
cutoff frequency sampling frequency kl, k2 and k3 calibration coefficients L probe spacing Lop, optimum, correlated distance between the two probes
J.B. Gajewski/Journal of Electrostatics 37 (1996) 261276
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mass of solid particles mean mass flow rate instantaneous value of the solids mass flow rate crosscorrelation function Rxy(Z) t time T sampling time (the crosscorrelation function is calculated within this time) U effective (RMS) probe voltage mean value of a rectified probe signal (voltage)
re, A m
(rh(t) ),
Acknowledgements The author acknowledges with thanks the financial support of the Committee of Scientific Research, Warsaw, Poland. Most of the work presented here was carried out under Grant No. 8 8525 91 02.
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