Ind. Eng. Chem. Fundam. 1980, 19, 175-180
P e = Peclet number, dimensionless Q = volumetric feed rate of slurry cm3/s r = radial coordinate
R = total resistance to filtration, N m-2 cm-' s-l u = axial velocity, m/s Uo = inlet axial velocity, m/s u = transverse velocity, m/s V = (EM-E - Vw)/V,, dimensionless V , = filtration velocity at the wall, m/s x = axial coordinate X = dimensionless axial coordinate (= x / h ) y = vertical coordinate Y = dimensionless vertical coordinate (= y / h ) Greek Letters a = (EM-E - V,)/2U0, dimensionless (3 = 2(EM.E - V,).h.10-3/D, dimensionless y = V,/Uo, dimensionless
175
Literature Cited Edwards, M. S.,Rodgers, B. R., Salmon, R., "Supporting Research and Development on Separation Technology", Phase I Report, ORNL-TM-480 l (March 1975). Gorin, E., Kulik, C. J., Lebowitz, H. E., Ind. Eng. Chem. Process Des. Dev., 16, 95-105 (1977). G i s p o w , D., Lee, C. H., Wasan, D. T., U S . Patent Serial No. 861 254 (1978). Henry, J. D., "Cross-Flow Filtration", in "Recent Developments in Separation Science", Vol. 11, pp 205-225, Chemical Rubber Co., 1972. Henry, J. D., Jacques, M. T., AIChEJ., 23, 607-609 (1977). Henry, J. D., Lawler, L. F., Kuo, C. H. Alex, AIChEJ., 23, 851-859 (1977). Lee, Chang Ho, unpublished Ph.D. Thesis, Illinois Institute of Technology, Chicago, IL. 1978. Moulik, S. P., Cooper, F. C.. Bier, M., J . ColloidInterface Sci., 24, 427-432 (1967). Moulik, S . P., Environ. Sci. Techno/.,5 , 771-776 (1971). Snell. J. G., U S . Patent 3852 183 (Dec 1974). Sze, M. C., Snell, G. J., US. Patent 3852 182; 3856675 (Dec 1974a). Sze, M. C.. Snell, G. T., U S . Patent 3856675 (Dec 1974b).
Received for review May 11, 1979 Accepted January 22, 1980
6 = dimensionless thickness of boundary layer 6(x) = dimensionless thickness of clear boundary layer
Cross Correlation and Tracking for the Measurement of Particle Velocities Gary 8 . Tatterson,' John T. Heibel,* and Robert S. Brodkey' Chemical Engineering Department, The Ohio State University, Columbus, Ohio 432 10
A cross laser beam correlation technique was developed for the measurement of individual realization of particle vector velocities. The method was applied to the velocity measurement of particles in a stirred tank to demonstrate the adequacy of the technique.
New experimental techniques are often necessary to further our understanding of complex flow phenomena. The present work described the development, testing, and use of a relatively simple cross laser beam correlation technique which was used to obtain individual instantaneous realizations of the vector velocities of particle motions (Tatterson, 1977). The Cross Laser Beam Correlation Technique T h e cross laser beam correlation technique involves tracking of particle shadows. The general experimental scheme is shown in Figure 1. Two expanded and colliminated laser beams were placed orthogonally in the same horizontal plane and each beam was projected onto an array of seven sensors. A well-defined sampling volume was formed inside the intersection of the laser beams by the projections of two arrays. When a particle passed through this intersection, particle shadows were cast upon the arrays of photoelectric sensors as shown in Figure 2. The configuration of the arrays and the relative size between the particle shadows and the sensors are also shown. The output of the sensors provided signals which were used to obtain the entry and exit times of the particle shadows. Using this time information, the particle velocity in the plane of each of the arrays was calculated. For the resulting data to be considered as a point velocity, a particle Department of Chemical Engineering,Texas A&M University, College Station, Texas 77843. Industrial Data Terminals Corp., Columbus, Ohio 43220. 0196-4313/80/1019-0175$01.00/0
event required coincidence of the center sensors of the two arrays (Le,, both indicating particle shadows). Thus, the actual sampling volume was the intersection of the projections of the center sensors from the two arrays. The surrounding sensors were used for tracking and velocity calculation. Similar techniques are currently being investigated in Japan. One of the authors (R.S.B.) attended the 1979 meeting of The Society of Chemical Engineers, Japan, where preliminary reports on these measurements were reported. Yamomoto has reported on Lagrangian measurements in a mixing vessel where a large (7 mm), neutrally buoyant particle motion was tracted in an unbaffled vessel at a low speed of 76 rpm. Kamiwano reported similar Lagrangian measurements a t 250 rpm and also made average Eulerian measurements a t several points in the vessel. They used an array of sensors that are commercially available. The details of the methods involved have not as yet been published to our knowledge. Distributions of the velocities at the points were not reported and comparisons could not be made since all the work reported was for unbaffled vessels in contrast to the baffled vessel work done by us. Velocity Calculation. For the calculation of the velocity, each array was considered separately and velocities were calculated from all possible sensor combinations in open and closed triad patterns by the equations shown in Figures 3 and 4. For each sensor in the path of the shadow, the entry and exit times were averaged together to give a specific time at which a line vector from the center 0 1980 American Chemical Society
Ind. Eng. Chem. Fundarn., Vol. 19,
176
No. 2, 1980
Center o f Shadow Path
Figure 4. Velocity equations using a closed triad.
Figure 1. The cross beam correlation technique.
, Poth
Beorn A l i g n m e n t
Figure 5. Beam misalignment and alignment.
7
I 59mm
Laser Beam # 2
Sensor A m y # 2
‘.,f
Lnser Beom # I
Sensor Arroy # I
Figure 2. Particle shadows correlated in time.
(3)
‘
Center ot Shadow P a t h
Figure 3. Velocity equations using an open triad.
of the sensor was assumed perpendicular to the center line of the shadow path. With this assumption, the time of the particle shadow for each sensor was related to the geometry of the array. The velocity calculation involved two additional assumptions: (1)a constant velocity through the arrays and (2) straight particle paths. These were reasonable assumptions since the overall size of the array was small compared to the scale of turbulence to be studied. The ordering of the sensor times from the beginning of the event to the end resulted in values for the ratio (T2T1)/(T3 - T,) which ensured convergence on the angle 0. The velocity ’magnitude was then calculated using the equations given in the figures. The transformation of velocity into laboratory coordinates was done by relating the angle to the specific sensor combination and then correcting the angle for the orientation of the sensor combination to laboratory coordinates. The velocity was obtained directly from distance and time without the necessity of difficult calibration. The calculations did not need a definite particle shadow size
or an initial shadow position with respect to the array sensors. Vertical Velocity Equality. Since the laser beams were in the same horizontal plane, two independent values for the vertical velocity could be obtained, one from each array. For any particle which passed through the sampling volume, these two values should be equal. Beam Alignment and Misalignment. The overlapping in time of the center Sensor signals from the two arrays helped significantly, although not completely, to ensure that the velocity being measured was for a particle in the sample volume. It was possible for two or more particles outside the sampling volume to correlate in time and have the same vertical velocity (Le., a false event). Beam alignment--misalignment experiments, as shown in Figure 5 , were used to determine statistically the number of false events and to minimize these. During beam alignment, a sampling volume was formed and both false events and true events were recorded. During beam misalignment, the laser beams were slightly ajar, which prevented the formation of a sampling volume. Under this condition the laser beams passed through the same flow conditions but only false events would be recorded. By comparing the two sets of data, the frequency of the true events was determined. By using a low enough particle concentration, the false events had an insignificant effect on the results. Experimental System and Evaluation Data Acquisition Equipment. For accurate measurement of the particle velocity, the time resolution measurement must be of the order of microseconds. There are two methods to obtain such high resolution. The first method would be a direct AID conversion at the high rate and storage of the resulting data when a suspected event occurred. Such a high rate would probably require captive use of the computer which would represent for our PDP/ 15 system considerable overkill. Furthermore, for our normal multiuser use, the computer A I D conversion rate was set at 1 kHz. The second method involved the development of a small “interface computer” that would provide the required time resolution and signal the main
Ind. Eng. Chem. Fundam., Vol. 19, No. 2, 1980 I4 Individual Sensor
~~~~
...-
1
14 Individual Transition Circuit
Circuits
Encoder
Type o f Transition
Transition Clear
Buffer
Sensor
Sensor
Data Read
to Disk
+
Figure 6. Data acquisition system.
computer when data should be transferred a t the normal 1 kHz rate. The second method was chosen, since it allowed high time resolution compatible with our normal main computer operation. The data acquisition system (interface computer), shown in Figure 6, was designed to form a seventeen-bit word which was divided into three subsections. The first subsection recorded the sensor number, the second recorded the type of transition (i.e., entry or exit), and the third recorded the clock counter time at which the transition occurred. The coincidence of the two center sensors was developed into a hard-wired flag to signal the computer program to acquire data. The acquisition system consisted of fourteen sensor digitization circuits with accompanying transition detectors and clear circuits. In addition, a FIFO (First In, First Out) storage buffer with inputs from a priority encoder, clock, and a transition selector were used. The fourteen individual sensor circuits used optical fibers to form the close packed detection arrays, shown in Figure 2, and to transmit the light signal to phototransistors. The current signals from the phototransistors were the inputs to operational amplifiers. The voltage signals from the operational amplifiers were compared to a reference voltage using a comparator which formed the digitized signal. A more detailed description of the detection sensor system is provided by Tatterson (1974). The outputs from the comparators were stored and continuously updated in dual bit memories. The first bit contained the present comparator level and the second contained the previous comparator level. If there was a level difference between these two bits, a transition had occurred and an exclusive-or circuit set a single-bit memory of the transition detection circuit. The output from this single bit memory in turn caused the priority encoder to output a four-bit number specific to the sensor that underwent the transition. The four-bit sensor number was also the input to a data selector circuit which passed the level of the comparator as one bit. This indicated the type of transition (Le., an entry or exit).
177
The priority encoder also issued a flag which loaded the entire data word into the FIFO storage buffer and cleared the one-bit memory of the transition detection circuit. The data word, located into the FIFO buffer, consisted of the four-bit sensor word, the one-bit transition type, and a twelve-bit clock time. After the loading operations, the acquisition system was ready to handle another transition signal. The priority encoder also had the ability to break ties if two transitions occurred simultaneously. The entire circuit (excluding the operational amplifiers, comparators, and storage buffer) was driven by a twophase clock which could provide a time resolution of 2 p s , if required. This clock circuit drove and set the times at which the various memory loadings, updating, and clearing operations were conducted. Computer Interfacing and Acquisition Program. The FIFO buffer was read continuously by a real-time data subroutine at a rate of 1 kHz with a dual processor PDP/15 computer. The data were stored in a software buffer by means of a Fortran computer program. The computer flag of the center sensors was also read continuously by the same real-time subroutine. This flag, when set to one, indicated coincidence of the center sensors and signaled the execution of the data acquisition program. This program took the output from the FIFO buffer used by the real-time subroutine and filled an event buffer with the serial data of the entire event. The computer acquisition program sorted the event data according to sensor number and type of transition and formed a matrix of entry and exit times, This matrix was stored and later used to calculate velocities. The acquisition program then issued a digital output to clear the computer flag and was then ready to handle the next event. The data acquisition was accomplished with a small program which remained in the foreground of the multitask, multiuser system. This permitted long-term continuous data logging and greatly enhanced the data acquisition capability.
Experimental Details The configuration of sensor arrays was shown in Figure 2. Each sensor was about 1.0 mm (40 mils) in diameter and the center-to-center distance was 1.27 mm (50 mils). The active sensor area was the end of an optical fiber which transmitted the laser light to phototransitors, which were VT1113 lens type obtained from Vactec, Inc. The particles were nylon precision ball bearings, 1.59 mm (62.5 mils) in diameter, with a specific gravity of 1.14. To check for equal sensor spacings, photographs were taken of each array. The spacings were within 0.002 cm (about 1 mil) and the configuration symmetry was excellent. The flow system was an open batch mixing vessel, 29.5 cm (1ft) in diameter filled with water to a 29.5 cm (1ft) height. Four baffles (width 3.5 cm and height 32 cm) were mounted a t the tank wall symmetrically with respect to the center of the tank. Both a pitched blade turbine and a bladed disk impeller, placed about one-third above the bottom of the tank, were studied. Both mixers were 10.2 cm (4 in.) in diameter, with the blades of the turbine 1.75 cm wide and pitched at 45O, while those of the disk impeller were 2.5 cm long by 1cm wide. A square glass tank, filled with water, surrounded the round tank to minimize distortions and beam refractions due to curvature. Calculations and visual observation showed that the distortions and beam refractions were unimportant, and except index of refraction matching between the fluid and glass was not required. The agitator was a 1/4-hpChemineer Experimental Mixing Unit ELB maintained a t 300 rpm. For the alignment of the arrays, a needle was placed in the intersection of the laser beams and shadows were cast onto
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Ind. Eng. Chem. Fundam., Vol. 19, No. 2, 1980
Table I. Data Summary vector vel0 ci t y magnitude, cm/s position 1, 536 data points
position 2, 341 data points
position 3, 499 data points (overall)
position 3, 55 data points, positive V ,
position 3, 444 data points, negative V ,
position 4, 421 data points
av std dev min rnax av std dev min max av std dev min max av std dev min max av std dev min rnax av std dev min max
47.6920.89 9.25 105.81 34.00 10.30 12.13 69.08 23.88 9.39 4.26 58.70 32.21 14.89 9.23 58.70 22.84 7.91 4.26 52.01 77.31 29.24 13.72 216.07
radial tangential velocity, cm/s velocity, cm/s 20.25 21.64 -32.32 85.99 0.076 10.43 -30.17 25.34 6.18 9.66 -26.15 42.15 4.58 13.22 -22.25 42.15 6.38 9.13 - 26.1 5 37.10 65.74 30.61 - 13.93 177.50
vertical velocity, cm/s - 30.60 14.75 - 82.40 41.68
19.53 17.25 - 39.32 75.08 5.23 11.24 -23.36 41.17 3.63 11.66 -38.91 38.99 0.61 15.86 - 31.45 38.99 4.0 1 11.00 -38.91 36.71 16.74 24.13 -76.45 112.99
29.53 11.32 -17.12 61.07 -11.98 15.32 -40.44 58.67 23.17 16.82 0.15 58.67 -16.35 7.53 -40.44 -0.37 -3.51 26.55 -72.01 63.14
Table 11. Overall and False Event Rates vs. Position and Concentration ~~
position 1 position 2 position 3
position 4 a
~
~~
type of event rate
no. of particles/ tank
no. of event rate estimates
event rate eventsih
std dev eventslh
total no.a of events
total time,a h
overall false overall false overall overall overall false overall false
75 75 75 75 75 125 175 175 75 75
5 4 3 1 2 4 1 1 3 3
8.0 0.5 11.5 0.7 4.5 7.2 9.5 1.5 9.3 0.4
0.8 0.4 0.6
358 17 327 7 74 29 3 171 11 366 4
45 32 29 9 16 40.5 18 7.5 41 10
..
0.5 0.5
.. ..
2.0 0.4
These were the data to establish event rates only. Total event number and total acquisition time were larger than these.
the arrays. The arrays were then aligned by adjusting their heights until the shadows were in the same horizontal plane in each array. Tests. Various tests on the operation of the system were conducted by using a rotating wire to simulate particle events. For these tests, the coincidence of the wire shadows on the center sensors of the two arrays was used. The response times and saturation limits of the computer flag and data acquisition equipment were found to be sufficient to meet the expected event frequency. For testing of the velocity calculation program, the shadow of the wire was made to cross the arrays vertically and the agreement among the vertical velocities, calculated as previously described, agreed to within 5 % . The velocity of the rotation was of the same order of magnitude as the highest velocity encountered in the flow experiments. The absence of any directional bias was established by rotating the wire at different angles to the beam. Results Figures 7 and 8 illustrate the location of the positions, the coordinates used, and the general velocity vector distributions observed for the four positions studied. An overall data summary is given in Table I. Position no. 3
I
t:?.
Top V i e w
,K.011 Flow
Radial V i e w
I
1 1
?W l i
c2
I
A
P # I C h e d Blade T u h n e Flow
--_.
_J
Figure 7. Approximate flow distribution with position using a pitched blade turbine.
is subdivided in the table because of the intermittency of the flow data. To obtain valid particle event data, the event rate during beam alignment must be considerably greater than that obtained during beam misalignment. Therefore, at each of the four data positions, estimates of both the overall and false event rates were obtained as shown in Table 11. Since the false event rates were small in comparison to the
Ind. Eng. Chem. Fundam., Vol. 19, No. 2, 1980
179
Table 111. Percent Error between the Two Estimates of Vertical Velocity vs. Position I_______-
-
--
.
__
I _ I _
position position position position
1
pitched blade turbine jet
L. wall flow
3. intermittent flow region 4 Rushton jet
% error % error in relation to in relation t o vertical overall velocity velocity vector av vertical component magnitude velocity, cm/s -10.1 5.1 -30.6 4.5 3.8 29.5 15.4 6.0 -12.0 102.0 5.9 3.5 I
1
1
av vector velocity magnitude, cm/s 47.7 34.0 23.9 77.3
1
1
'
A
80
ew
Radial View
ti
~
Figure 8. Approxiniate flow distribution with tank position using a Rushton turbine, ,
'-401
\ ,
,
20
0
-40 -20
60
40
IO0
80
Radial Velocity (crnlsec)
Porticles/Tank
Figure 9. Overall and false event rate as a function of particle concentration.
overall rates for all positions studied, true particle event data could be obtained directly. The particle concentrations, experimental times, and event numbers used to establish the event rates are also given in Table 11. In three of the four positions studied, there was a substantial vertical velocity component. Because of this, the vertical velocity estimates were used t o establish the validity of each event. In this initial work, however, the final decision about the validity of the event was checked by the experimenter. Table I11 summarizes the average error between the two vertical velocity estimates for each position. The agreement for position 2 , the wall flow, was expected and was similar to the agreement between the vertical velocity estimates obtained from the rotating wire tests previously described. The percentage error for the pitched blade turbine jet (no. 1)and the intermittent flow region (no. 3) was higher primarily because these flows contained substantial horizontal components. Position 4 for the bladed disk impeller was in a horizontal jet, and the vertical velocity criterion was not used since its magnitude was too small to be accurately determined. The horizontal jet was at a high enough speed that the coincidence requirement for data acquisition was sufficient to insure the validity of the detected events. At position 3 the particle concentration was varied to determine the proper range to be used for the acquisition of true particle event data. The rate for true particle events should be a linear function of concentration with a zero event rate at zero particle concentration (Figure 9). For low concentrations, false event rates were impractical to measure because of the long times that would be involved.
-80
11
!
-40
C
-20
20
40
60
80
I00
Radio1 Velocity (cm/sec)
401 '
! v)
20
I 1 -40
I
1
1
1
-20
0
20
40
I
60
, J 80
Tangential Velocity (crn/sec) Figure 10. Velocity distribution projections at position 1 in the discharge flow of a pitched blade turbine.
Figures 7 and 8 contain approximate flow lines at the various points in the mixing vessels. The actual data obtained were three-dimensional vector velocity distributions from which momentum and energy distributions were obtained. The complete analysis can be found in the dissertation of Tatterson (1977). Only one example, for the pitched blade turbine jet, will be presented here in Figure 10. The data for other positions and the threedimensional plots for the mass, momentum, and energy
180
Ind.
Eng. Chem. Fundam. 1980, 19, 180-185
radial velocity (in Figure 10A, labeled as 11),indicates that the main turbine jet flowed out radially and downward in the direction of turbine rotation. The momentum and energy content of the flow are obtained by squaring and cubing the velocity vector, respectively. The diagrams presented by Tatterson (1977) indicate that the main transport of momentum and energy is in the high speed turbine jet, which also flows out radially and downward in the direction of the turbine rotation.
distributions can be found in the dissertation of Tatterson (1977). Two-dimensional views of the vector velocity distributions are the method of data display used. In the plots, only the last one-fifth of each velocity vector is shown, and all of the vectors originate from the point (0,O) marked with a plus sign. The scales of the graph are the same in all directions to preserve the visual correctness of the vector angles. It should be kept in mind that the two-dimensional plots are not plots of particle paths; nor can these plots be interpreted, necessarily, as illustrations of flow structure because of the limited view of point velocity measurements. The tip speed of both the pitched blade turbine and the bladed disk impeller was about 150 cm/s, which serves as a reference point for the data. The velocity vectors are in the cylindrical coordinate system (i.e., radial, tangential, and vertical velocity components) with respect to the agitator shaft. The displayed data are raw velocity vector data without any attempts to eliminate vectors that differ from the main flow direction. The discharge flow of the pitched blade turbine is a good example of the method of data display since it is extremely complex due to the different flows caused by the turbine. In Figure 10, the views of the particle velocity distribution show a predominantly negative vertical velocity and a well distributed radial velocity component. The distribution of the tangential component (see Figure lOC) is skewed positively (labeled as I). The distribution of the radial component and the skewness of the tangential component with respect to the vertical velocity in Figure 10B and 1OC indicate the existence of multiple flows of varying speeds passing through the location. The observation agrees with visual studies that identified high speed jets in positive radial and tangential directions and more vertical, low speed flows through the turbine. The top view of the distribution (i.e., tangential vs. radial velocity plot in Figure 10A) shows strongly the influence of the impeller. The large tangential velocity, combined with the large positive
Conclusions The cross laser beam method has been developed as a technique to obtain velocity distributions of individual particle velocity vectors. The velocities are not viewed as random fluctuations in the flow about a single average velocity. Instead, each particle velocity measurement is indicative of the large-scale flows and transitions between these flows passing through the point during the time of measurement. The distribution of the radial velocity of the pitched blade turbine shows a dual flow system originating from the turbine: one system has low radial velocity and low momentum and energy content; the other has high radial velocity and high momentum and energy content. Acknowledgment The authors would like to acknowledge the current support of the National Science Foundation under whose sponsorship the cross-correlation concept is being further developed. Mr. M. Kulka was most helpful in providing advice associated with our PDP-15 system.
Literature Cited Tatterson, G. B., M.S. Thesis, The Ohio State University, 1974. Tatterson, 0.B., Ph.D. Dissertation, The Ohio State University, 1977.
Received for review May Accepted January
29, 1979 17, 1980
Liquid-Phase Oxidation of Phenol in a Rotating Catalytic Basket Reactor Hideki Ohla, Shigeo Goto,” and Hldeo Teshlma Department of Chemical Engineering, Nagoya University, Chikusa. Nagoya, 464, Japan
Catalytic oxidation of phenol in aqueous solution over supported copper oxide by oxygen was studied both in a slurry reactor and in a rotating catalytic basket reactor (RCBR). When the experiments in a RCBR were repeated two or three times at the same operating conditions, the catalytic activity became stable and the kinetics of phenol consumption were determined. The intermediates of phenol oxidation were identified as hydroquinone, pyrocatechol, maleic acid, and oxalic acid by a liquid chromatographic technique.
Introduction Liquid-phase oxidation of organic pollutants over a solid catalyst has been proposed as an alternative to conventional biological oxidation. To investigate the kinetics, mass transfer effects, and performance of reactors for this process, some organics have been treated as typical pollutants, e.g., formic acid (Baldi et al., 1974; Goto and 01 96-431 3/80/1019-0180$01 .OO/O
Smith, 1975), acetic acid (Levec and Smith, 1976; Levec et al., 1976), and phenol (Sadana and Katzer, 1974a,b; Sadana, 1978; Sadana, 1979; Njiribeako et al., 1978a,b; Katzer, 1978). Phenol seems to be most promising for the catalytic oxidation process because it may be difficult to oxidize biologically. Sadana and Katzer (1974a) studied catalytic 0 1980 American Chemical Society
