A new data processing technique for noisy signals: application to measuring particle circulation times in a draft tube equipped fluidized bed

Powder Technology 92 (1997) 111–117

0032-5910/97/$17.00 q 1997 Elsevier Science S.A. All rights reservedPII S0032- 5910 (97)03222 -1

Journal: PTEC (Powder Technology) Article: 3275

A new data processing technique for noisy signals: application tomeasuring particle circulation times in a draft tube equipped fluidized bed

Michael Xu, Richard Turton U

Department of Chemical Engineering, West Virginia University, Morgantown, WV 26506-6102, USA

Received 25 March 1996; revised 15 January 1997

Abstract

The interpretation of signals obtained from a magnetic tracer particle passing through a detector coil surrounding the draft tube in a fluidizedbed is addressed. Due to the erratic motion of the particle as it passes through the coil, the signal obtained contains many peaks of differingmagnitude and frequency. Using a phenomenological picture of the process and probability theory, a new technique to deconvolve signals ofthis type is presented. This new data analysis tool allows the discrimination between signals caused by the circulation of the tracer particle inthe bed and by those caused by the unsteady motion of the particle in the detector coil. A simple cross-plot is presented to illustrate thetechnique.

Keywords: Data processing; Circulating beds; Fluidized beds; Noise

1. Introduction

Werther and Molerus [1] measured the bubble rise veloc-ity in fluidized beds using a needle capacitance probe. Theyfound that the signals generated from the bubbles passingthrough the probe and those generated from the variation ofthe voidage of the fluidized bed around the probe were mixedtogether. It was found that there was a statistically significantdifference in signal intensity between these two sources ofsignals. Thus, it was concluded that a cut-point for the signalintensity could be determined by plotting the signal intensityversus its occurrence frequency. This cut-point in signalintensity was quite sharp and allowed the accurate deconvo-lution of signals from the two different sources.

When two kinds of signals, with similar intensities and arandom number of occurrences, are mixed together the dataanalysis becomes more complicated. The purpose of thisresearch is to discuss a method to interpret such signals anda data processing technique to discriminate between them.

2. Source of the signals

A mixture of signals, generated from two different sourceswith similar intensities but different frequencies, was foundin the measurement of the mean solids circulation time in a

U Corresponding author. Tel.: q1 304-293-2111: fax: q1 304-293-4139.

draft tube equipped spouted bed. The circulation times of theparticles were found by tracking the motion of a single mag-netic tracer particle, using a detector coil wound around thedraft tube.

3. Experimental apparatus

The spouted bed, with a draft tube insert, is shown in Figs. 1and 2. The inside diameter of the bed was 15.25 cm (6 inch),and the total height was about 2 m (6 ft 6 inch). The lowerpart of the bed was made of aluminum tubing. One reasonfor choosing aluminum was that the metal wall could beelectrically grounded to shield partially the detector coil,wound around the draft tube insert, from environmental noiseand to eliminate static electrical charges. The upper enlargedsection of the apparatus was 22.9 cm (9 inch) in diameterand was made of transparent Perspex so that the flow patternin the bed could be viewed through the wall. The distributorplate was made of sintered stainless steel with approximately40 m pores. Beneath the distributor plate there was a splitm

plenum consisting of two concentric cylindrical tubes throughwhich the gas supplies were fed separately into the centralcore and annular regions of the bed. The draft tube insert wasmade of aluminum tube with an 8.89 cm (3.5 inch) insidediameter, an 11.43 cm (4.5 inch) outside diameter, and 25.4cm (10 inch) in length. The draft tube was suspended from

M. Xu, R. Turton / Powder Technology 92 (1997) 111–117112


Fig. 1. Sketch of the equipment.

Fig. 2. Schematic diagram of the draft tube equipped fluidized bed.

a cross-bar in the expanded part of the bed by two rods securedby set screws, and the draft tube could be lowered or raisedto adjust the gap height between the bottom of the insert andthe distributor plate. There was a milled slot in the outsidewall of the draft tube for housing the detector coil (seeFig. 1). The draft tube was centered within the bed by threesmall spacers located between the outside wall of the drafttube and the inside wall of the bed column. All the internal

parts of the apparatus were made of PlexiglasTM and non-ferromagnetic metals in order to prevent the magnetic tracerparticle from adhering to them. A pair of centrifugal blowerssupplied air to the split plenum located beneath the distributorplate.

The gas flowrates to the central core and annular regionwere regulated independently by two valves and monitoredby two rotameters, one with a 0.0330 m3/s (70 SCFM) full-scale range, and the other with a 0.00472 m3/s (10 SCFM)full-scale range. The bed material consisted of approximatelyspherical sucrose particles (trade name Nu-Pareil, IngredientTechnology Co., Pennsauken, NJ) in the size range of 16y–18q mesh (1.18–1.00 mm diameter) with a density of 1526kg/m3 (measured by the displacement of water). The totalmass of the particles in the bed was 1.81 kg (4 lb).

Inside the central tube, the gas velocity was adjusted highenough to entrain the solids at the bottom and to convey thempneumatically through the draft tube. After leaving the drafttube, the particles eventually rained down into the annularregion outside the draft tube due to the reduced gas velocityin the upper expansion section. In the annular region, the gasvelocity was adjusted to be low enough so that the particlesmoved downward either as a moving packed bed or a movingincipiently fluidized bed. At the bottom of the bed, the solidsflowed radially into the center, under the draft tube, and werethen entrained upwards by the central gas. Thus, at the bottomof the bed, the particles were fed from the annular region intothe center, they were conveyed upwards through the drafttube, and then returned to the dense bed in the annular region.Thus, the solids circulated continuously in this manner. Fur-ther details of the experiment are given by Xu [2].

4. Solids circulation rate

The solids circulation rate is one of the most importantparameters to control in spouted beds. Mann [3] and Mann

M. Xu, R. Turton / Powder Technology 92 (1997) 111–117 113


Fig. 3. Typical raw signal from the detector coil.

and Crosby [4] developed a magnet-detector coil techniqueto measure the solids circulation time distribution in a spoutedbed. They used a magnetic tracer particle (0.952 cm diameter,0.926 g weight) to track the movement of bed material(0.635cm diameter, 0.15 g weight). They deduced that the differ-ences in size and weight of the tracer particle and the trackedparticles had only a small effect on the measured particlecycle time distribution in their system. The reason for thiswas that the main portion of the cycle time of particlesoccurred during the descent in the annular region of the bed,where the tracer particle followed the bulk movement of thebed particles. Cheng and Turton [5] further developed thistechnique in several aspects, such as making the tracer par-ticle much smaller (1 mm diameter) so that it was almostidentical to the bed particles both in density and diameter.Furthermore, they inlayed the detector coil in the draft tube,thus reducing interference with the movement of solids andgas. They made the data processing more convenient by usinga data acquisition system instead of a simple timer, thusimproving the repeatability of the experimental data. Themagnetic particle tracer technique is relatively simple, cheapand gives reproducible results. This technique was imple-mented in the present research.

A detector coil was constructed with approximately10 000turns of 36 gauge insulated copper wire wound around amilled slot which was located 6.35 cm (2.5 inch) above thebottom edge of the draft tube. The magnetic tracer particle(1 mm diameter) consisted of a small piece of a powerfulpermanent rare-earth magnet wrapped in a ball of hardeneddough of flour and water. The tracer particle was made to beapproximately spherical with a magnetic core and a hardeneddough shell, and was very close in both dimension and densityto the particles in the bed. When the tracer particle passedthrough the draft tube insert, it induced a signal in the detectorcoil. These signals were collected and recorded by anADALABTM PC data acquisition system with an interfaceboard and a 286 IBM compatible PC. The data acquisitionboard, which was used in this part of the work, featured adual-slope integrating analog–digital (A/D) converter. Pre-liminary tests were done to examine the response signals dueto the magnetic particle in the measurement system by drop-ping the particle through the draft tube coil. The ranges ofthe signal strength and the proper gain were determined by

these preliminary tests. The data acquisition system was cal-ibrated by collecting the data with and without the magneticparticle in the bed. Software for data acquisition was writtenusing QuickBasicTM. This software allowed the system totake and store data continuously for long time periods withoutinterruption. It was found that five data files each containing2731 s of data were enough to obtain sufficient reproducibil-ity, giving a relative accuracy for the average cycle time ofparticles of "2.8%.

5. Signal interpretation

The signals from the detector coil, induced by the passageof the magnetic particle, were collected by the data acquisi-tion system, stored in data files, and were processed off-line.A typical signal is shown in Fig. 3. Two problems wereencountered in processing the raw data:

(1) In the data there are low frequency (less than 4 Hz)components which are artifacts of the data acquisitionsystem.The low frequency component is the background noise,which is the base signal without a magnetic particle in thebed. The amplitude of the noise is larger than that of thesignals generated by the magnetic particle, but its dominantfrequency is very much smaller than those of the signals fromthe tracer particle. Thus, the raw data consist of sharp positiveand negative pulses superimposed on a low frequency carrier-wave baseline (see Fig. 3). It should be noted that the carrierwave appears to have a very low frequency (approximately0.0025 Hz) but also contains some higher frequency noise(less than 4 Hz).

(2) Every time the tracer particle goes through the detectorcoil, it can generate several signals due to the irregular motionof the magnetic particle. Therefore, it is not clear how tointerpret the series of pulses comprising the signal due to themovement of the tracer particle.

The first problem was overcome by a digital filter similarto that used by Cheng [6]. First, the raw data (usually 16 384data taken at a sampling rate of 30 Hz) are transformed fromthe time domain to the frequency domain by a discrete for-ward fast Fourier transformation (FFT). Then by plottingthe magnitude of frequency versus its corresponding occur-rence frequency, it was found that the background noise had



Fig. 4. Typical signal after digital filtration.

frequencies less than 4 Hz. Finally, after the low frequencydata were set to zero, the data in the frequency domain weretransformed back to the time domain by the reverse FFT.These procedures were programmed using MathcadTM soft-ware, and they function as a simple high-pass digital filter. Atypical signal curve after filtering is shown in Fig. 4. Com-parison of Figs. 3 and 4 shows that the magnitude and numberof sharp spikes are preserved after filtering. A formal analysisof the phase lag and amplitude reduction of the signal afterfiltering was not carried out. However, comparison of thesignals before and after filtering show no difference in eitherof these quantities.

From Fig. 4 it can be seen that the digitally filtered signalmay be considered to consist of many groups of positive andnegative peaks sitting on an almost flat baseline. It was foundthat the number of positive peaks is almost equal to that ofthe negative peaks and the absolute value of the sum of theamplitudes of positive and negative peaks is almost equal tozero. This means that the signals are almost symmetric withrespect to the time axis. This is consistent with the physics ofthe detector system in which the direction of the inducedvoltage will change as the tracer particle passes through thecoil. Two problems are encountered in interpreting the sig-nals: first, the height of the signal in order for it to be countedas a pass of the particle through the coil; second, the closenessof the two successive peaks in order for them to be consideredto be different particle passages through the coil.

A closer look at the behavior of the magnetic particle iswarranted. When the magnetic particle goes through the coil,it induces signals in the coil due to the upward motion of themagnetic particle. However, besides the upward motion, themagnetic particle may also be rotating and the motion maynot be smooth due to collisions with other particles. Thisirregular particle motion generates a series of signals in thevery sensitive detector coil. The magnitude of the inducedsignals depends on the velocity, the relative position in thecoil, and the orientation of the magnetic particle. In otherwords, the movement of the tracer particle gives multiplesignals during a single passage through the coil, and thenumber of the signals is a random number which depends onthe path of the motion of the tracer particle through the coil.Therefore, it is difficult to distinguish between signals due tothe main upward motion of the tracer particle from those due

to the irregular motion in the draft tube, based only on theamplitude or frequency of the signal peaks. For most casesthe peak height for both the regular and the irregular signalsis between 6 and 20 computer counts, which is equivalent to7.3 and 24.4 mV. After the tracer particle passes through thedraft tube it goes to the annular down-comer. The particletakes a relatively long time to travel back down the down-comer. Since the magnetic particle is moving slowly in theannular region and lies outside the detector coil, it is unableto produce a detectable signal in the coil and, thus, the outputsignal is essentially zero during this time.

6. Data processing technique

Physically, there must exist a minimum time period forwhich it is impossible for the tracer particle to circulatearound the bed. This time period is called the critical or cut-off time, tc, with an empirical value around 1 s. When a signalpeak appears, a determination must be made whether theparticle has finished one cycle and begun a new cycle sincethe last peak occurred, or if it is still inside the draft tube andactually indicating the same event as the previous peak(s).This critical time classifies all the times elapsed betweensuccessive peaks into two groups. The group with valuesgreater than the critical time is called Group A, which rep-resents the time the particle spends in the down-comer. Thegroup with values less than or equal to the critical time iscalled Group B, which represents the times that the particlespends inside the draft tube. Every element in Group A refersto one cycle that the particle completes, but every element inGroup B refers to only a fraction of the time that the particlespends inside the draft tube. The smallest value in Group Amay be close to the largest value in Group B due to thediversity of the ways that the particle travels. The criticaltime, tc, is the cut-off point between the two groups. Its valuelies between the maximum time elapsed between two suc-cessive peaks, due to the irregular motion of the magneticparticle, and the minimum time needed for the tracer particleto travel through the down-comer.

Based on the physical picture of the particle motiondescribed above, it was postulated that the cycle time of thetracer particle can be decomposed into the sum of severaltime intervals as defined by Eq. (1) and illustrated in Fig. 5:



Fig. 5. Diagram illustrating notation used in describing the digitally filteredsignals.

tsTqt qt q«qt (1)1 2 n

where t is a random cycle time that is independent of thethreshold peak height, h. It can be expressed by the sum ofindependent random variables T, t1, t2, «, tn and n, which arefunctions of the threshold peak height. Between T and t1, t2,«, tn there is a clear cut-off point tc. Thus:

T)t (2)c

t Ft is1, 2, «, n (3)i c

Over a long time period, the mean cycle time is

# ##tsTq#nPt (4)

and the total number of time intervals between successivepeaks is

NsmqmP#n (5)

where and are the mean of t and T, respectively; m is the##t Tnumber of time periods in Group A; is the average number#nof time periods in each Group B; N is the total number oftime periods. The formal proofs of Eqs. (4) and (5) are givenin Appendix A.

The time periods T and ti (is1, 2, «, n) are determinedby the number of peaks on the signal curve. In order to getthe number of peaks, a minimum acceptable peak height mustbe chosen. This height is called the threshold peak height, h.If a peak has a height less than the threshold peak height, itis ignored. It is assumed that within a certain range of thresh-old peak heights [ha, hb], the cycle time is measurable andstill satisfies the above model, Eq. (1). Obviously, if thethreshold peak height is increased, the total number of peaks,N, will change dramatically, since some of the peaks with aheight less than the threshold peak height will be ignored.However, the number of time periods which the particle

spends in the down-comer, m, will be almost constant since,during these time periods, the particle does not yield anysignal. On the other hand, the average number of time inter-vals spent by the particle inside the draft tube, , will change#nsignificantly due to the change in the number of peaks withheight less than the threshold peak height. Thus, no matterhow the threshold peak height is changed within a reasonableregion, [ha, hb], the value of m will be almost constant.

However, the value of m is the number of time periods inGroup A and in order to classify the time periods into the twogroups, the critical time must be known first. The critical timeand the number m are physically meaningful constants inde-pendent of the threshold peak height, but N and change#nwith the threshold peak height. In other words, is the char-#nacteristic of the irregular motion of the particle, but m is thecharacteristic of the regular motion of the particle. Therefore,if a plot of the number of peaks in Group A (m) versus tc ismade, curves with different threshold peak heights should allconverge to a single point. From this point the true value oftc and m can be found. The above analysis infers that theremust be a critical time tc, such that the number of time inter-vals in Group A is a constant, although the total number oftime periods and the number of time periods in each groupchange with the change in the threshold peak height. Themain objective of this work is to develop an unbiased tech-nique to estimate tc and m.

7. Results

In order to implement and test the above theory, the fol-lowing procedure was adopted and applied to experimentaldata:1. Choose a threshold peak height, h.2. Evaluate all peaks with magnitude greater than h.3. Choose a critical cut-off time, tc.4. Evaluate the number of peaks in Group A and Group B.5. Repeat steps 3 and 4 for different cut-off times.6. Repeat steps 1–5 for different values of h.7. Plot the results as number of peaks in Group A (m) versus

tc for each value of h.A data processing program was written to implement the

seven-step procedure given above. A series of experimentswas performed and a total of 11 sets of data were obtainedfor particle circulation rates at different operating conditions.For all the data sets, the m versus tc curves, for different hvalues, crossed at a single point. The coordinates of this pointchanged with the conditions used in the experiments but allgave values of tc on the order of 1 s. Four typical plots of mversus tc are shown in Fig. 6. It can be seen that for each setof experimental conditions all the curves go through onepoint. At this point, the corresponding abscissa is the correctcut-off point, tc, between the two groups, and the correspond-ing ordinate is the number of cycles made by the particle, m.The values of tc for the 11 data sets vary between 0.60 and1.23 s, while values vary between 2.39 and 4.33 s.#t



Fig. 6. Four typical plots of critical time vs. number of peaks in Group A for magnetic tracer particle in a draft tube equipped fluidized bed: d, threshold peakheight, hs6; s, threshold peak height, hs8; ., threshold peak height, hs10; ,, threshold peak height, hs12 computer counts.

The average cycle time for particles is found by dividingthe total time by the number of peaks recorded during thattime. The total mass of the particles in the bed divided by theaverage cycle time gives the mass circulation rate, Ws, ofparticles.

8. Conclusions

A new data processing technique has been developed toestimate the circulation time of a magnetic particle from anoisy signal. The technique is based on a phenomenologicalmodel for the movement of the magnetic particle in a drafttube equipped fluidized bed. The model assumes that thesignal can be partitioned into two parts, namely, that due tothe movement of the particle in the dense annular bed andthat due to the motion within the draft tube. The techniquewas applied successfully to a body of data for a specific seriesof experiments, namely, the signals induced by the movementof a magnetic particle through a detector coil wound arounda draft tube. It may be possible to extend this work to othersignal sources, with an appropriate change in the phenome-nological picture used to describe the process.

9. List of symbols

E expectation function of a random variablef probability density function of random variable T

(sy1)

g probability density function of a sum of randomvariables ti (sy1)

h peak height of signals (cm or computer count)ha, hb lower and upper limits of peak height (cm or

computer count)m number of time periods in Group An random number of time periods in Group B#n average number of time periods in each Group BN total number of time intervals between successive

peaksp probability density function of the sum of

t1qt2q«qtk (sy1)q probability density function of random variable ntc cut-off time between Groups A and B (s)ti random time spent by a particle between

successive signal peaks (s)#t mean of ti (s)T random time spent in the down-comer by a

particle (s)#T mean of T (s)Ws mass circulation rate of particles (kg/s)x random time (s)X random time between two successive signal peaks

(s)

Greek letters

e voidage in the central coret random cycle time of particles (s)#t mean of random cycle time (s)



f probability density function of the random timebetween two successive signal peaks (sy1)

v probability density function of the randomvariable x (sy1)

Acknowledgements

The authors would like to acknowledge that this work wasmade possible by NSF Grant No. CST8657548. The supplyof the Nu-Pareil particles by Ingredient Technology Co.,Pennsauken, NJ, is also gratefully acknowledged.

Appendix A

The qualitative description of the particle motion may beformalized using probability theory. The probability densityfunction of a random variable T is assumed to be f(x,h), andthe probability density functions of random variable ti (is1,2, «, n) are assumed to be the same, g(x,h). The probabilitydensity function of the sum of random variablest1qt2q«qtk is a conditional probability under the condi-tion nsk, expressed by the following convolution, Eq. (A1)(Ross [7]). For xFktc and haFhFhb:

p{x/nsk,h}sg(x,h)=g(x,h)=«=g(x,h) (A1)

where h is added to express the parameter of threshold peakheight. The probability density function of t1qt2q«qtk isa sum of a series of weighted conditional probabilities, eachterm being weighted by the probability of the event on whichit is conditioned. Thus, the probability density function ofrandom variable t can be derived as

w(x)sf(x,h) p{x/nsk,h} p{nsk,h} (A2)8k

and the mean cycle time is expressed by

E(t)s x w(x) dxsE(T,h)qE(n,h) E(t ,h) (A3)i|

We note that for a given value of h, E(T,h)s ,#TE(n,h)s and E(ti,h)s , and substituting these values into##n tEq. (A3) gives Eq. (4).

The measured time between every two successive peaks isanother random variable X that can be any one of T, and t1,t2, «, tn and is defined by

Xs{T, t , t , «, t } (A4)1 3 n

with its probability density function:

E(n,h) 1v(x,h)s g(x,h)q f(x,h) (A5)

E(n,h)q1 E(n,h)q1

with mean:

E(X,h)s xv(x,h) dx|

1 E(n,h)s E(T,h)q E(t ,h)iž / ž /E(n,h)q1 E(n,h)q1

(A6)

Combining Eqs. (A6) and (A3) yields

E(t)s[E(n,h)q1] E(X,h) (A7)

which relates the mean cycle time E(t) to the measured meantime E(X,h).

We note that for a given value of h, E(n,h)s and#nE(X,h)sm /N and substituting these values into Eq. (A7)#tgives Eq. (5).

From Eq. (A7) it is concluded that E(n,h)q1 and E(X,h)are functions of threshold peak height h, but their product isnot. This also means that, at the cut-point, this product tendsto converge to one single point for different threshold peakheights, h.

References

[1] J. Werther and O. Molerus, Int. J. Multiphase Flow, 1 (1973) 103.[2] M. Xu, A theoretical and experimental investigation of spouted beds

with draft tubes, Ph.D. Dissertation, West Virginia University,Morgantown, 1994.

[3] U. Mann, Coating of particulate solids by air suspension, Ph.D.Dissertation, University of Wisconsin, Madison, 1972.

[4] U. Mann and E.J. Crosby, Can. J. Chem. Eng., 53 (1975) 579.[5] X. Cheng and R. Turton, AIChE Symp. Ser., 90 (1994) 142.[6] X. Cheng, Studies of uniformity of particle coating in fluidized beds,

Ph.D. Dissertation, West Virginia University, Morgantown, 1993.[7] S. Ross, A First Course in Probability, Macmillan, New York, 2nd edn.,

1984.

Documents

A new data processing technique for noisy signals: application to measuring particle circulation times in a draft tube equipped fluidized bed