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Measurement of the velocity and direction of flow of solid particles in a fluidized bed
Powder Technology, 0 ELsevier Sequoia
27 (1980)
S-A.,
1 - 6 Lausanne - Printid in the Netherlands
1
MeasurementoftheVelocityandDirectionofFlowofSolidParfic~esina Fluidizedfkd M. ISHIDA, Research
T. SHIRAI
Laborcfory
of Resources
Utilization,
Tokyo
of Technology,
Institute
Yokohama
(Japan
227)
and A. NISHIWAKI Department
(Received
of Industrial
December
Chemistry,
Oyama
Technical
College,
Oyama
(Japan
323)
17,1979)
SUMMARY
A new system for measuring the velocity and direction of flow of particles in violent unsteady-state motion was developed. It consisted of multi-fiber optical probes and a microcomputer data processor. By this system, various types of particle flow in a fluidized bed such as upward movement with a single rising bubble, oblique movement in a free bubbling bed, rapid upward movement with successive bubbles and downward movement near the column wail could be examined. The movement of particles in a dilute phase near the hole of a nozzle could also be detected.
INTRODUCTION
The behavior of bubbles in a fluidized-bed has been investigated by applying X-ray techniques [l] or various kinds of probes [ 2 - 83 _ However, the behavior of solid particles has not been elucidated because of the lack of good measuring systems. Recently, the authors have proposed real time measuring techniques for the solid particle velocity by developing a time-interval to voltage converter [ 91 or by applying a spatial filtering method [lo]. These are convenient to measure the velocity of particles in one-dimensional movement but not satisfactory to follow the velocity of particles in a fluidized bed, because the particles in it show threedimensional movement. In this study, a new system was developed. It consisted of multi-fiber optical probes and a microcomputer data processor. The former
was made to detect tlne velocity of particles as well as the direction of their flow in a two-dimensional domain. The latter was applied to process the observed signals and to output the calculated results by an X-Y plotter. The applicability of this system to detect the velocity and direction of flow of particles in extremely unsteady-state motion is discussed and example diagrams for various types of particle flow in a fluidized bed are illustrated_
1. MEASURING
SYSTEM
1_1 Multi-fiber optical probe Figure 1 shows the overall view of the probe used in this study. It consisted of two multi-fiber optical probes A and B. Probe A was composed of seven optical fibers. Each fiber was 0.2 mm in diameter and its core diameter was 0.13 mm. Light emitted by a lamp was guided through the central fiber to project onto the particles around the tip of the probe. The light reflected on the surface of each particle was received by the peripheral six fibers, A-l through A-6.
Fig_ 1. Multi-fiber optical probe to detect the velocity and direction of particle flow as well as the diameter and rising velocity of bubbles.
2
Probe B was composed of three optical fibers. One of them was used as light projector and the other two, B-7 and B-8, were light receivers_ The distance between these probes A and B was 2.13 cm. 1.2 Data processing ,Tstem Figure 2 shows the outline of the data processing system_ The light signals received by the optical fibers were converted to electric signals by phototransistors, amplified up to the voltage range between 0 and 2.5 V by operational amplifiers, and recorded by an analog data recorder-
Fig.
2. Flow
diagram
or
data
processing
system.
A-l plays the role of the reference signal. The required time and the flow direction are determined by finding the time displacement 7 and the pair of signals which made the following cross-correlation function or coefficient maximum.
(k = 2, 3, -., 6) where y1 denotes the intensity of the reference signal A-l, and yk denotes that of the master signals, A-2 through A-6. Then, the particle velocity can be obtained by dividing the distance between these two fibers, A-k and A-l, by the time displacement 5-_ Two kinds of summation are used: x
N
The data recorder was then connected to a disk-driven microcomputer with the processor Z-80, and the recorded analog data were converted to a sequence of S-bit digital signals. Since the data recorder and the analog to digital converter used in this study could receive only seven channels, the signals A-l through A-6 and B-7 were processed.
2. DATA
PROCESSING
2.1 Bubble uelocify While the tip of the optical probe is located in a bubble, only very weak light signals are received_ Hence, the bubble can be recognized clearly from the reflected light signals. When these raw signals A-l through B-7 are recorded by the X-Y plotter, the rising velocity of the bubble may be calculated from the time required for the bubble to travel from probe B to probe A. 2.2 Solid particie velocity The velocity of particles is measured by probe A. It is obtained by measuring the time required for the particles to travel from the position of the fiber A-l to that of the fiber A-2,3,4, 5, or 6, and uice versa, depending on the direction of the particle flow, where
go, = g,f i-&t,
--
f
.__
+&t
-_(IN12)--1)Atl
+((NI2)--1)Atl
+___
(3)
where g denotes ykyl, yg, or yq in eqns. (1) and (2), and At is the time interval for sampling each master signal, A-2 through A-6_ Equation (3) is an equally weighted summation of N pieces of terms, and the period for sampling data becomes IV X At. On the other hand, eqn. (4) is an exponentially weighted summation. When a new term is added, the weight of the old data is decreased by the rate of 1 - (l/K). Hence, more weight is put on the new data Then, the period for sampling data is not definite. The frequency of each reflected light signal is almost proportional to the velocity if the concentration of the particles is kept conscant. Consequently, the frequency of each signal of probe A is calculated by the fast Fourier transform method and the mean frequency of the six probe A signals is displayed by the X-Y plotter. 2.3 Sampling of tke data The 7channel analog data recorded by the data recorder were converted to a sequence of &bit digital signals in the following order:
3
A-l,
A-2,
A-l,
A-3,
A-l,
A-4,
A-l,
A-5,
A-l,
A-6,
A-l,
B-7,
A-l,
X,
A-l,
X,
___ The above sequence consisted of the repetition of sixteen terms. The letter X means free memory spaces. They do not contain any meaningful data at present but are included in the sequence to fit the hexadecimal counting system. In most cases, those data were sampled in the interval of 21.75 ps. Hence, the sampling interval for the reference signal A-l becomes 43.5 w and that for the master signals A-Z through B-7 was 348 ps. In the cross-correlation calculations, r was chosen as -21.75 X 767 w to -21.75 ~.lsand 21.75 ps to 21.75 X 767 p_ Since the calibrated distance between fibers A-l and A-4 is 0.25 mm, those ranges corresponded to -11.5 m/s to -1.5 cm/s and 1.5 cm/s to 11.5 m/s for the verticaI velocity_ However, the range of the plotter scale was set between 2 cm/s and 2 m/s, and the overscaled data were plotted on the line at 2 cm/s or 2 m/s.
3. EXPERIMENT
AND
EXAMPLE
DATA
3.1 Apparatus and particles A stainless steel column of 15 cm i-d. and 1 m in height was used as the fluidized bed cohunn. The air distributor set at the bottom of the bed was a perforated plate with 121
holes of 1.5 mm diam. in triangular configuration_ In some runs, to eject a single bubble or to form a spout, a nozzle of 4 mm i-d. and 6 mm o-d. was installed at,,the center of the column and at a height of ‘T-5 cm from the air distributor_ In most runs, the incipient bed height was set at 25 cm. Three kinds of particles, glass beads, alumina catalyst beads, and sand particles were tested. Their minimum fluidization vf?locities, U,, , were 11.5,6.8, and 8.3 cm/s, respectively. 3.2 Example data Figure 3 shows example data for the case when a single bubble is ejected from a nozzle into a fluidized bed. The ambient gas velocity is set at 1.12U,f. The tip of probe A is located at 12.5 cm above the nozzle. The upper-left fjgure in Fig. 3 shows the reflected light signals received by the master fibers A-2 through 6, the reference fiber A-l, and the bubble detector B-7. In the middle part of the chart, one can find a bubble which passes through probes B and A. By comparing the signals A-l and B-7, the bubble is found to rise in about 41 cm/s_ Frequent occurrence of high peaks around the bubble means that the particles around it move in high veIocity. The right figure in Fig. 3 shows the velocities based on the cross-correlation coefficient eqn. (2) and equahy weighted
Fig. 3. Movement of particles when a single bubble is ejected from a nozzle (glass beads, UlUd 25cm,L~=20cm,r=Ocm).
= 1.12,
Ld
=
4
summation eqn. (3) with N = 96. Hence, the sampling period is 33.4 ms, and the crosscorrelation calculation was performed every 348 G_ In that figure, Us, means the velocity calculated from the time displacement r which made QCk.1. _, maximum- The direction of the flow is obtained from the pair of signals which gave the maxi-mum coefficient among the five values of oCi;.l_r) for k = 2 through 6. That pair is marked by the thick base line. As shown in the figure, vertical movement of the particle is predominant, and the velocity of the particles ahead of the bubble as well as within the wake is found to be detected clearly. When the vertical movement of the particles in the velocity u is observed by the other fiber pairs, say 3-l or 5-1, the velccity is calculated as u/cos 30” [lo] _ In some periods, one can find such values, but in most periods, the calculated velocities for other directions may become entirely erroneous values, especially when the sampling period is short The lower-left figure in Fig. 3 shows the variation in the mean frequency of the six probe-A signals. The Fourier transform calculation is based on sixty-four data, which corresponds to the sampling period 22.3 ms, and is performed every 696 ws. The similarity between the frequency f and the velocity u_+= indicates that the velocity is calculated correctly by the cross-correlation calculation_ The reflected light signals shown in Fig. 3 were processed by various correlation methods and the diagrams obtained are compared in Fig. 4. Figure 4 (III) is the same as uq_l in Fig. 3 but the period in which the
computer judged the vertical flow is marked clearly by the shaded baseline_ Figure 4 (I) shows the result by the crosscorrelation function eqn_ (1) Exponentially weighted summation, eqn. (4), with K = 64 is applied. When the peak height in the signals is not at the same level, the function often gives erroneous results. Moreover, the direction of the flow cannot be selected properly, since this function is not normalized. Figure 4 (II) is based on the crosscorrelation coefficient eqn. (2) with exponentially weighted summation for K = 64. It gives much better results than the previous one. For example, it gives the velocity at the top of the wake at the correct time_ In other words, this method gives the correct velocity when new reflected light signals are received after the continuation of extremely weak signals. In the other periods, however, about 13 ms delay is observed. This is in accord with the results of the delay test of the exponentially weighted cross-correlation coefficient for a stepwise change in velocity when random signals generated by a computer are used as input signals. Figure 4 (III) is obtained by the crosscorrelation coefficient and equally weighted summation, eqn. (3), with N = 96. The time delay is significantly shortened, and this case generally gives the best results for the velocity range between 2 cm/s and 2 m/s. It is noticed, however, that the velocity at the start of the wake appears at about 12 ms ahead of the real time. Figure 4 (IV) is obtained by the crosscorrelation coefficient with N = 64. When the particle velocity is higher than about 6 cm/s, this method has the highest capability for following the change in velocity. However, the lower velocity cannot be obtained correctly, since the particle moving at 2 cm/s travels only 0.4 mm in the sampling period, 22.3 ms.
4_ VARIOUS
TYPES
OF FLOW
IN A FLUIDIZED
BED
Pig. 4. Comparison of cross-correIation function coefficient with various summation methods.
and
Figure 5 shows the movement of the particles at the center of the column in a free bubbling bed. The gas velocity was set at 1.9U,f. At the start of the chart, a bubble is recognized_ However, the particles around it
E‘ _tdmdd,_mma>u_. .z- r b’_-+ = .:: ._ a _r: _ - _I ._; ; 2 !rt _.__. _ I- ;
+_-
?I -‘) -.
----r---___
-f+%P-,p~_ _._’
2
c= -bL
v5_-__A _-____ -,
-;
-
=a -=-
---= ----
_ ___._-__-- - .--__
:
= -c-_
CL c_
_ *----_ -.-_
--
__.
_
_-_-_
‘-_-
__-C--___-_
___ ___ __----.-
Fig. 5. Movement of particles at the center of the column at a iow gas velocity (glass beads, U/U, = 1.9, Ld = 25 cm, L, = 12 cm, r = 0 cm).
Ld=7cm,r=7cm).
Fig_ 6. Movement of particles at the center of the column at a high gas velocity (glass beads, iJ/U~ = 4.2, Ld = 25 cm, Ld = 12 cm, r = 0 cm).
Fig. 8. Dilute phase flow in a spout (glass beads, VW, = 1.12, UN = 58 m/s, Ld = 16.6 cm, Ld = 12.7 cm, I- = 0 cm).
show oblique flow. Also, downward flow is observed_ Such abrupt change in the velocity and flow direction takes place quite fi-equently in a fluidized bed. Figure 6 shows the tax at a higher gas velocity, U = 4.2U,f. Also, the probe is set at the center of the column. Swarms of particles rise in high velocities between successive bubbles like a runnin g fire_ When the equally weighted summation with N = 64 is used, the velocity of the particles within a bubble is sometimes measured satisfactorily. Figure 7 shows the movement of the particles near the wa.U. In almost all periods, the particles move downwards but the velocity itself often changes abruptly_ Figure 8 shows the flow of particles when a spout is formed in a fluidized bed kept at
incipient
Fig. 7. Downward movement of particles near the column wall (glass beads, U/U, = 2.8, Ld = 25 cm,
fluidization.
The
probe
A
is set
at
3.7 cm from the top of the nozzle, and the bed height is 16.6 cm. The velocity of gas at the exit of the nozzle is 58 m/s. Since this is a kind of dilute phase flow, the frequency does not give the velocity directly. The crosscorrelation calculation with N = 64 shows that the velocity of the particles carried in the dilute
phase
is higher
than
that
of the
rising
swarms of particles. Figure 9 shows the case when
the nozzle gas velocity is lowered to 34 m/s and the bed height is increased to 25 cm. Then, the separation between the dense and dilute phases
progresses
and
air bubbles
are formed.
fire flow of swarms of particles with successive bubbles is observed very clearly.
The
running
6
LIST OF SYMBOLS
f Ld
L rnf f P
u
Fig. 9_ Running fire flow of swarms of particles above nozzie (gl-ss beads, Uli/v, = 1.12. UN = 31 mfs, Ld = fo cm. Ld = 20 cm, r = 0 cm).
frequency of reflected light signals height from gas distributor bed height at incipient fluidization time radius superficial gas velocity minimum fluidization velocity gas velocity at nozzle particle velocity time displacement cross-correlation coefficient cross-correlation function
REFERENCES 1
2 3 CONCLUSION
4
A system to detect the velocity and direction of unsteady-state particle flow was developed, and various types of flow in a fluidized bed were detected based on the cross-correlation coefficient with equally weighted summation. The sampling period was selected to fit the range of the velocity. The mean frequency of the reffected light sign& was used to check the result of the cross-correIation calculation_
5 6 7 8 9 10
P. N. Rowe and B. A. Partridge, Trans. Insf. Chem. Eng., 43 (1965) T157. W. H. Park et al., Chem. Eng. Sci.. 24 (1969) 851. P. W. Heertjes et al.. Powder Technol.. 4 (19701 71) 38. J. Werther and 0. Molerus, Inf. .J_ MuZtiphase FZow. 1 (1973) 103. T. Hirama, M. Ishida and T. Shirai, Kagaku Kogaku Ronbunshu. i (1975) 272. P. H. Calderbank, FZuidizafion Technology. Vol. 1, Hemisphere Publ. Corp., 1976. p. 115. U. Mann and E. J_ Crosby, Ind. Eng. Chem. Process Des. Dev.. 16 (1977) 9. M. Yamazaki et al.. Kagaku Iiogaku Ronbunshu. 3 (1977) 266,272. K. Ogawa, H. Sato, M. Ishida and T_ Shirai, J_ Chem. Eng. Jpn.. I I (19’78) 410. M. Ishida, K. Ogawa. A. Nishiwaki and T. Shirai, Kagaku Kogaku Ronbunshu. 5 (1979) 487.
27 (1980)
S-A.,
1 - 6 Lausanne - Printid in the Netherlands
1
MeasurementoftheVelocityandDirectionofFlowofSolidParfic~esina Fluidizedfkd M. ISHIDA, Research
T. SHIRAI
Laborcfory
of Resources
Utilization,
Tokyo
of Technology,
Institute
Yokohama
(Japan
227)
and A. NISHIWAKI Department
(Received
of Industrial
December
Chemistry,
Oyama
Technical
College,
Oyama
(Japan
323)
17,1979)
SUMMARY
A new system for measuring the velocity and direction of flow of particles in violent unsteady-state motion was developed. It consisted of multi-fiber optical probes and a microcomputer data processor. By this system, various types of particle flow in a fluidized bed such as upward movement with a single rising bubble, oblique movement in a free bubbling bed, rapid upward movement with successive bubbles and downward movement near the column wail could be examined. The movement of particles in a dilute phase near the hole of a nozzle could also be detected.
INTRODUCTION
The behavior of bubbles in a fluidized-bed has been investigated by applying X-ray techniques [l] or various kinds of probes [ 2 - 83 _ However, the behavior of solid particles has not been elucidated because of the lack of good measuring systems. Recently, the authors have proposed real time measuring techniques for the solid particle velocity by developing a time-interval to voltage converter [ 91 or by applying a spatial filtering method [lo]. These are convenient to measure the velocity of particles in one-dimensional movement but not satisfactory to follow the velocity of particles in a fluidized bed, because the particles in it show threedimensional movement. In this study, a new system was developed. It consisted of multi-fiber optical probes and a microcomputer data processor. The former
was made to detect tlne velocity of particles as well as the direction of their flow in a two-dimensional domain. The latter was applied to process the observed signals and to output the calculated results by an X-Y plotter. The applicability of this system to detect the velocity and direction of flow of particles in extremely unsteady-state motion is discussed and example diagrams for various types of particle flow in a fluidized bed are illustrated_
1. MEASURING
SYSTEM
1_1 Multi-fiber optical probe Figure 1 shows the overall view of the probe used in this study. It consisted of two multi-fiber optical probes A and B. Probe A was composed of seven optical fibers. Each fiber was 0.2 mm in diameter and its core diameter was 0.13 mm. Light emitted by a lamp was guided through the central fiber to project onto the particles around the tip of the probe. The light reflected on the surface of each particle was received by the peripheral six fibers, A-l through A-6.
Fig_ 1. Multi-fiber optical probe to detect the velocity and direction of particle flow as well as the diameter and rising velocity of bubbles.
2
Probe B was composed of three optical fibers. One of them was used as light projector and the other two, B-7 and B-8, were light receivers_ The distance between these probes A and B was 2.13 cm. 1.2 Data processing ,Tstem Figure 2 shows the outline of the data processing system_ The light signals received by the optical fibers were converted to electric signals by phototransistors, amplified up to the voltage range between 0 and 2.5 V by operational amplifiers, and recorded by an analog data recorder-
Fig.
2. Flow
diagram
or
data
processing
system.
A-l plays the role of the reference signal. The required time and the flow direction are determined by finding the time displacement 7 and the pair of signals which made the following cross-correlation function or coefficient maximum.
(k = 2, 3, -., 6) where y1 denotes the intensity of the reference signal A-l, and yk denotes that of the master signals, A-2 through A-6. Then, the particle velocity can be obtained by dividing the distance between these two fibers, A-k and A-l, by the time displacement 5-_ Two kinds of summation are used: x
N
The data recorder was then connected to a disk-driven microcomputer with the processor Z-80, and the recorded analog data were converted to a sequence of S-bit digital signals. Since the data recorder and the analog to digital converter used in this study could receive only seven channels, the signals A-l through A-6 and B-7 were processed.
2. DATA
PROCESSING
2.1 Bubble uelocify While the tip of the optical probe is located in a bubble, only very weak light signals are received_ Hence, the bubble can be recognized clearly from the reflected light signals. When these raw signals A-l through B-7 are recorded by the X-Y plotter, the rising velocity of the bubble may be calculated from the time required for the bubble to travel from probe B to probe A. 2.2 Solid particie velocity The velocity of particles is measured by probe A. It is obtained by measuring the time required for the particles to travel from the position of the fiber A-l to that of the fiber A-2,3,4, 5, or 6, and uice versa, depending on the direction of the particle flow, where
go, = g,f i-&t,
--
f
.__
+&t
-_(IN12)--1)Atl
+((NI2)--1)Atl
+___
(3)
where g denotes ykyl, yg, or yq in eqns. (1) and (2), and At is the time interval for sampling each master signal, A-2 through A-6_ Equation (3) is an equally weighted summation of N pieces of terms, and the period for sampling data becomes IV X At. On the other hand, eqn. (4) is an exponentially weighted summation. When a new term is added, the weight of the old data is decreased by the rate of 1 - (l/K). Hence, more weight is put on the new data Then, the period for sampling data is not definite. The frequency of each reflected light signal is almost proportional to the velocity if the concentration of the particles is kept conscant. Consequently, the frequency of each signal of probe A is calculated by the fast Fourier transform method and the mean frequency of the six probe A signals is displayed by the X-Y plotter. 2.3 Sampling of tke data The 7channel analog data recorded by the data recorder were converted to a sequence of &bit digital signals in the following order:
3
A-l,
A-2,
A-l,
A-3,
A-l,
A-4,
A-l,
A-5,
A-l,
A-6,
A-l,
B-7,
A-l,
X,
A-l,
X,
___ The above sequence consisted of the repetition of sixteen terms. The letter X means free memory spaces. They do not contain any meaningful data at present but are included in the sequence to fit the hexadecimal counting system. In most cases, those data were sampled in the interval of 21.75 ps. Hence, the sampling interval for the reference signal A-l becomes 43.5 w and that for the master signals A-Z through B-7 was 348 ps. In the cross-correlation calculations, r was chosen as -21.75 X 767 w to -21.75 ~.lsand 21.75 ps to 21.75 X 767 p_ Since the calibrated distance between fibers A-l and A-4 is 0.25 mm, those ranges corresponded to -11.5 m/s to -1.5 cm/s and 1.5 cm/s to 11.5 m/s for the verticaI velocity_ However, the range of the plotter scale was set between 2 cm/s and 2 m/s, and the overscaled data were plotted on the line at 2 cm/s or 2 m/s.
3. EXPERIMENT
AND
EXAMPLE
DATA
3.1 Apparatus and particles A stainless steel column of 15 cm i-d. and 1 m in height was used as the fluidized bed cohunn. The air distributor set at the bottom of the bed was a perforated plate with 121
holes of 1.5 mm diam. in triangular configuration_ In some runs, to eject a single bubble or to form a spout, a nozzle of 4 mm i-d. and 6 mm o-d. was installed at,,the center of the column and at a height of ‘T-5 cm from the air distributor_ In most runs, the incipient bed height was set at 25 cm. Three kinds of particles, glass beads, alumina catalyst beads, and sand particles were tested. Their minimum fluidization vf?locities, U,, , were 11.5,6.8, and 8.3 cm/s, respectively. 3.2 Example data Figure 3 shows example data for the case when a single bubble is ejected from a nozzle into a fluidized bed. The ambient gas velocity is set at 1.12U,f. The tip of probe A is located at 12.5 cm above the nozzle. The upper-left fjgure in Fig. 3 shows the reflected light signals received by the master fibers A-2 through 6, the reference fiber A-l, and the bubble detector B-7. In the middle part of the chart, one can find a bubble which passes through probes B and A. By comparing the signals A-l and B-7, the bubble is found to rise in about 41 cm/s_ Frequent occurrence of high peaks around the bubble means that the particles around it move in high veIocity. The right figure in Fig. 3 shows the velocities based on the cross-correlation coefficient eqn. (2) and equahy weighted
Fig. 3. Movement of particles when a single bubble is ejected from a nozzle (glass beads, UlUd 25cm,L~=20cm,r=Ocm).
= 1.12,
Ld
=
4
summation eqn. (3) with N = 96. Hence, the sampling period is 33.4 ms, and the crosscorrelation calculation was performed every 348 G_ In that figure, Us, means the velocity calculated from the time displacement r which made QCk.1. _, maximum- The direction of the flow is obtained from the pair of signals which gave the maxi-mum coefficient among the five values of oCi;.l_r) for k = 2 through 6. That pair is marked by the thick base line. As shown in the figure, vertical movement of the particle is predominant, and the velocity of the particles ahead of the bubble as well as within the wake is found to be detected clearly. When the vertical movement of the particles in the velocity u is observed by the other fiber pairs, say 3-l or 5-1, the velccity is calculated as u/cos 30” [lo] _ In some periods, one can find such values, but in most periods, the calculated velocities for other directions may become entirely erroneous values, especially when the sampling period is short The lower-left figure in Fig. 3 shows the variation in the mean frequency of the six probe-A signals. The Fourier transform calculation is based on sixty-four data, which corresponds to the sampling period 22.3 ms, and is performed every 696 ws. The similarity between the frequency f and the velocity u_+= indicates that the velocity is calculated correctly by the cross-correlation calculation_ The reflected light signals shown in Fig. 3 were processed by various correlation methods and the diagrams obtained are compared in Fig. 4. Figure 4 (III) is the same as uq_l in Fig. 3 but the period in which the
computer judged the vertical flow is marked clearly by the shaded baseline_ Figure 4 (I) shows the result by the crosscorrelation function eqn_ (1) Exponentially weighted summation, eqn. (4), with K = 64 is applied. When the peak height in the signals is not at the same level, the function often gives erroneous results. Moreover, the direction of the flow cannot be selected properly, since this function is not normalized. Figure 4 (II) is based on the crosscorrelation coefficient eqn. (2) with exponentially weighted summation for K = 64. It gives much better results than the previous one. For example, it gives the velocity at the top of the wake at the correct time_ In other words, this method gives the correct velocity when new reflected light signals are received after the continuation of extremely weak signals. In the other periods, however, about 13 ms delay is observed. This is in accord with the results of the delay test of the exponentially weighted cross-correlation coefficient for a stepwise change in velocity when random signals generated by a computer are used as input signals. Figure 4 (III) is obtained by the crosscorrelation coefficient and equally weighted summation, eqn. (3), with N = 96. The time delay is significantly shortened, and this case generally gives the best results for the velocity range between 2 cm/s and 2 m/s. It is noticed, however, that the velocity at the start of the wake appears at about 12 ms ahead of the real time. Figure 4 (IV) is obtained by the crosscorrelation coefficient with N = 64. When the particle velocity is higher than about 6 cm/s, this method has the highest capability for following the change in velocity. However, the lower velocity cannot be obtained correctly, since the particle moving at 2 cm/s travels only 0.4 mm in the sampling period, 22.3 ms.
4_ VARIOUS
TYPES
OF FLOW
IN A FLUIDIZED
BED
Pig. 4. Comparison of cross-correIation function coefficient with various summation methods.
and
Figure 5 shows the movement of the particles at the center of the column in a free bubbling bed. The gas velocity was set at 1.9U,f. At the start of the chart, a bubble is recognized_ However, the particles around it
E‘ _tdmdd,_mma>u_. .z- r b’_-+ = .:: ._ a _r: _ - _I ._; ; 2 !rt _.__. _ I- ;
+_-
?I -‘) -.
----r---___
-f+%P-,p~_ _._’
2
c= -bL
v5_-__A _-____ -,
-;
-
=a -=-
---= ----
_ ___._-__-- - .--__
:
= -c-_
CL c_
_ *----_ -.-_
--
__.
_
_-_-_
‘-_-
__-C--___-_
___ ___ __----.-
Fig. 5. Movement of particles at the center of the column at a iow gas velocity (glass beads, U/U, = 1.9, Ld = 25 cm, L, = 12 cm, r = 0 cm).
Ld=7cm,r=7cm).
Fig_ 6. Movement of particles at the center of the column at a high gas velocity (glass beads, iJ/U~ = 4.2, Ld = 25 cm, Ld = 12 cm, r = 0 cm).
Fig. 8. Dilute phase flow in a spout (glass beads, VW, = 1.12, UN = 58 m/s, Ld = 16.6 cm, Ld = 12.7 cm, I- = 0 cm).
show oblique flow. Also, downward flow is observed_ Such abrupt change in the velocity and flow direction takes place quite fi-equently in a fluidized bed. Figure 6 shows the tax at a higher gas velocity, U = 4.2U,f. Also, the probe is set at the center of the column. Swarms of particles rise in high velocities between successive bubbles like a runnin g fire_ When the equally weighted summation with N = 64 is used, the velocity of the particles within a bubble is sometimes measured satisfactorily. Figure 7 shows the movement of the particles near the wa.U. In almost all periods, the particles move downwards but the velocity itself often changes abruptly_ Figure 8 shows the flow of particles when a spout is formed in a fluidized bed kept at
incipient
Fig. 7. Downward movement of particles near the column wall (glass beads, U/U, = 2.8, Ld = 25 cm,
fluidization.
The
probe
A
is set
at
3.7 cm from the top of the nozzle, and the bed height is 16.6 cm. The velocity of gas at the exit of the nozzle is 58 m/s. Since this is a kind of dilute phase flow, the frequency does not give the velocity directly. The crosscorrelation calculation with N = 64 shows that the velocity of the particles carried in the dilute
phase
is higher
than
that
of the
rising
swarms of particles. Figure 9 shows the case when
the nozzle gas velocity is lowered to 34 m/s and the bed height is increased to 25 cm. Then, the separation between the dense and dilute phases
progresses
and
air bubbles
are formed.
fire flow of swarms of particles with successive bubbles is observed very clearly.
The
running
6
LIST OF SYMBOLS
f Ld
L rnf f P
u
Fig. 9_ Running fire flow of swarms of particles above nozzie (gl-ss beads, Uli/v, = 1.12. UN = 31 mfs, Ld = fo cm. Ld = 20 cm, r = 0 cm).
frequency of reflected light signals height from gas distributor bed height at incipient fluidization time radius superficial gas velocity minimum fluidization velocity gas velocity at nozzle particle velocity time displacement cross-correlation coefficient cross-correlation function
REFERENCES 1
2 3 CONCLUSION
4
A system to detect the velocity and direction of unsteady-state particle flow was developed, and various types of flow in a fluidized bed were detected based on the cross-correlation coefficient with equally weighted summation. The sampling period was selected to fit the range of the velocity. The mean frequency of the reffected light sign& was used to check the result of the cross-correIation calculation_
5 6 7 8 9 10
P. N. Rowe and B. A. Partridge, Trans. Insf. Chem. Eng., 43 (1965) T157. W. H. Park et al., Chem. Eng. Sci.. 24 (1969) 851. P. W. Heertjes et al.. Powder Technol.. 4 (19701 71) 38. J. Werther and 0. Molerus, Inf. .J_ MuZtiphase FZow. 1 (1973) 103. T. Hirama, M. Ishida and T. Shirai, Kagaku Kogaku Ronbunshu. i (1975) 272. P. H. Calderbank, FZuidizafion Technology. Vol. 1, Hemisphere Publ. Corp., 1976. p. 115. U. Mann and E. J_ Crosby, Ind. Eng. Chem. Process Des. Dev.. 16 (1977) 9. M. Yamazaki et al.. Kagaku Iiogaku Ronbunshu. 3 (1977) 266,272. K. Ogawa, H. Sato, M. Ishida and T_ Shirai, J_ Chem. Eng. Jpn.. I I (19’78) 410. M. Ishida, K. Ogawa. A. Nishiwaki and T. Shirai, Kagaku Kogaku Ronbunshu. 5 (1979) 487.