PRESSURE FLUCTUATIONS IN A FLUIDIZED BED WITH AND WITHOUT SCREEN CYLINDRICAL PACKINGS W . K . K A N G , J. P. S U T H E R L A N D , A N D G. L. OSBERG
Dzz iston of ApfiliPd Chemzstrj, .Vatzonal Research Councll, O t t a a a , Canada
+
Pressure fluctuation data were obtained from an air-fluidized sand bed ( - 4 8 65 Tyler mesh) with openended cylindrical packing. The tests were made in a 5-inch diameter column, and with packings made from steel wire cloth 4-, 6-, or 14-mesh per inch and ’/? X ‘/2, ”4 X 3/4, and 1 X 1 inch in size. These data were analyzed to yield r.m.s. values, the probability density, and the normalized power spectral density functions. The r.m.s. values of the pressure fluctuations were lower for the packed fluidized beds than for the same bed fluidized with no packing. For each packing, a maximum was observed on a plot of r.m.s. vs. flow rate or bed expansion. When no packing was used, r.m.s. values increased continuously with gas flow or bed expansion; the distributions were Gaussian a t low flow rates, and skewed at high flow rates. The probability distributions of the differential pressure fluctuations were Gaussian for a fluidized b e d containing packings over the whole flow range tested. The normalized power spectral density functions were similar for the packed and unpacked fluidized beds, though peak frequencies showed some dependence on packing dimensions.
drop fluctu,ations in aggregative fluidized beds have been studied as a basis for defining a n index of fluidized bed quality (Fiocco, 1964; Shuster and Kisliak, 1952; Sutherland, 1964). In these studies. strip chart recordings of the pressure changes \vere analyzed in various ways to give peak counts, line-cut counts, average fluctuation, etc. These data are of limited value because of the arbitrary way in which the recordings Lvere analyzed. I n the present study, the pressure data were analyzed b;; a current spectral technique, which provides a more detailed examination of the data. T h e source of the pressure fluctuation is not yet fully understood. I n gas-solid fluidized beds, the pressure drop fluctuations correspond directly to the bubble flow, though the pressure drops are really a consequence of changes in gas flow through the dense phase. Reuter (1963, 1966) has reported that the axial pressure gradient in the dense phase near the bubble is larger than in the undisturbed regions of the bed, \vhile the gradient inside the bubble is nil. Though Reuter’s kvork provides a partial explanation for the pressure fluctuation in fluidized beds, the data are not yet sufficient for a complete interpretation of a fluctuating pressure signal. I n this paper. preliminary experiments are first reported on the correlation of pressure fluctuations \vith bed height fluctuations, and then o n the pressure change \vhich occurs when a single artificial bubble ]passesthrough a bed. Finally, data are given on the effect of screen packing on pressure fluctuations in a fluidized sand bed. Various packings, such as spheres, solid cylinders, Raschig rings, Berl saddles, and screen rings. have been used to improve fluidization. Data have been reported on the effect of packings on gas mixing (Chen and Osberg, 1967; Gabor and Mecham, 1964); solid mixing (Gabor, 1964, 1965, 1966; Kang and Osberg, 1966) ; segregation (Capes and Sutherland, 1966 ; Sutherland and Wong, 1964) ; heat transfer (Basakov and Vershinina, 1964; Gabor et a/., 1965 Sutherland et al., 1963; Ziegler and Brazelton, 1963); and chemical reaction (Gabor and Jonke, 1964; Ishii and Osberg, 1965; McIlhinney and Osberg, 1964; Mecham et al., 1964); but no data have PRESSURE
been reported on the effects of packing on pressure fluctuations. Open-end screen cylinder packings \rere selected for study, since these packings occupy a small volume ( 1.
Pressure changes were also observed when the artificial bubble was in motion. T h e bubble was pulled upward through the central axis of the column by winding an attached string on a motor-driven shaft. The velocity of the rising bubble was adjusted to the rise velocity calculated for a real bubble of equivalent size (Rowe and Partridge, 1965). The pressure difference between taps at 3 and 7 inches from the bottom was then measured by a pressure transducer. Figure 3 is a Brush recording of the pressure difference, AP,. against the position of the bubble when the bed is at minimum fluidization. The larger bubble exhibits a larger effect than the smaller one; and the differential pressure first decreases as the bubble approaches the lov..er tap, increases as the bubble passes the upper tap. and finally diminishes as the bubble rises to the top of the bed. ?io significant change of the pressure was obtained on lifting the nonporous ball. O n moving the bubble upward in other regions of the bed. it was also noted that the magnitude of the pressure changes was much larger when the bubble passed close to the pressure taps. From these preliminary experiments, it is postulated that the bubble causes some gas flow to short-circuit the dense phase; that the bed in the wake of the bubble is denser, which results in a n increase in the interstitial velocity of the gas flokving through the wake; that the pressure fluctuations are caused by a change in the gas flow and in the porosity of the dense phase; and that the pressure differences measured between pressure taps located in the wall of the column are a n integration of damped and delayed local variations throughout the bed.
BUBBLE
I 0
-
0.5 -
Ub
U/Umf
1.51~
181n/sec.
I
1.Oin.
14in.kec.
I
-
-I
-
PRESS. TAP
REFERENCE TAP
4
h
4
0
8
BED HEIGHT
+
12
16
20
BUBBLE CENTER POSITION, in.
Figure 3. Differential pressure change as an artificial bubble rises through center of fluidized b e d Bed.
500
l&EC FUNDAMENTALS
1 2 pounds of 48- to 65-mesh sand fluidized b y air in 5-inch diameter column
Measurement of Pressure Fluctuations
T h e experimental details of the main study are as follows. A 5-inch diameter Plexiglas column with pressure transducers mounted flush with the inside wall, as illustrated in Figure 4, was used. The bed was a narrow cut (-48 65 Tyler mesh) of Ottawa sand. Bed particles were approximately spherical, and had a specific gravity of 2.7. When packing was used, the column was filled almost to the top by dropping the individual packing into the column, so that the cylinders were randomly orientated in the bed. A screen baffle a t the top prevented any significant movement of the packing under fluidized conditions. T h e packing occupied less than 5% of the column volume. T h e bed when fluidized never went above the packed section of the column, and so occupied the void space within the packing. All packings \vere openended cylinders, I,'Z X I I ' Z , 3//4 X 3/4, and 1 X 1 inch, made of 4-, 6-. or 14-mesh per inch steel wire cloth.
+
(
~
J
B
P
G
FILTER
SCREEN CYLINDER PACK I NG
I
Air at about 3oyO relative humidity and a t room temperature was introduced to the bed through a porous plate at the bottom of the column. Air flow rates were measured with a rotameter at 10 p.s.i.g. and varied from 1.2 to 20 times the minimum fluidization flow rate. T h e minimum fluidization velocity was taken as the intersection of the fluidized and fixed bed pressure us. flow rate curves when decreasing the air flow rate. T h e minimum fluidization flow was 1.1 SCFM for the unpacked bed and 1.3 SCFM for the screen cylinder packed bed. Pressure taps were located a t 3 and 7 inches from the bottom plate and were connected to a differential pressure transducer (strain gage type, Statham Model P M l 3 l T C + 2.5 p.s.i.g. with about 0.005-inch H 2 0 error over 0- to 2000-C.P.S. frequency range). T h e sienal from the transducer was balanced and then amplified- T h e r.m.s. fluctuations of the pressure signal were obtained with a circuit involving a "chopper," a r.m.s. meter ,4.D. converter-counter system described elsewhere (Kang et al., 1966). This method was verified by recording the signal onto a tape recorder, then feeding the taped signal a t 40 times the recording speed to an r.m.s. meter which could measure the voltage of the random signals above 2 C.P.S. T h e relationship between the transducer output voltage and the applied differential pressure was determined for every run by recording an applied static pressure as measured with a water manometer and reading the corresponding output voltage on a Brush recorder. The relationship \vas linear over the entire range with less than 2y0 standard error. For a few selected runs, the probability density function \.vas determined with a probability density analyzer (Bruel and Kjoer Model 160) by running the recorded tape a t 40 times the original recording speed. T h e tape-recorded signal was digitized by an analog-digital converter and then fed into a digital computer (SDS920) to obtain the cormalized power spectrum density of the signal. Hamming's filter with filter band width of 0.65 C.P.S. was employed in programming the digital process (Blackman and Tukey, 1958; Funke, 1961). This band width, \vhich fulfilled satisfactorily the requirement of the present investigation, was chosen from the observations of the power spectrum density obtained by an analog method (speeded tape, Honeywell Model 9060 wave analyzer) Lvith 10 C.P.S.(equivalent to 0.25 C.P.S.in real time) window lvidth.
TRANSDUCER + -
Figure 4.
Results and Discussion
AIR
Fluidized bed column
-
PACKING 4 MESH
lin.
6 MESH
3 4 in.
14 MESH
'12 in.
o A
.
I
0.1
0.2
0.4 '3.6
I
2
4
6
IO
20
40
(&-I) Figure term
5.
R.M.S. of Pressure Fluctuation. The root-mean-square APd fluctuations, uAP,,,were tabulated and plotted as a function of the reduced velocity in Table I and Figure 5, respectively. From the iable or the figure. a maximum value of uAPdcan be observed at L'lc',, = 4 6 for the packed fluidized bed, whereas uAPdis a monotonic increasing function of the reduced velocity when packing is not present. At higher gas flow rates bubbles in the packed fluidized bed may be regarded as containing solid particles and so exhibiting some particulate nature. Such bubbles will have some pressure drop, and should cause less variation in the interstitial gas velocity in the dense phase, and hence lower AP fluctuations. Similar nonmonotonic trends have been reported (Chen and Osberg, 1967; Sutherland and lt'ong, 1964) with these packings. Since bubble size in the packed fluidized bed should increase with the packing size (Ishii and Osberg. 1965), the larger packings are expected to give larger APd fluctuations (see Figure 3). Also, in the packed fluidized bed. the mobility of solid particles should be reduced by smaller screen openings (Kang and Osberg, 1966) which should result in less variation in dense phase porosity. These two postulates agree well with the experimental data in Table I and Figure 3, which show u A p dincreasing with the packing size and with the screen opening. APd measurements in this study were made in the lower section of the column (between 3 and 7 inches from the bottom compared to about 20-inch bed height), where the screenpacked fluidized bed may be considered fully developed.
Pressure fluctuation as a function of flow rate
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501
Table I.
UiLTmj
R.M.S. APd in a Fluidized Bed" with and without Packingr Packing &mesh, ?&mesh, 7 inch 7 inch U A P A Inches H?O
4-mesh, 7 inch
,Tone
1.2 0.018 0.056 1.6 0.084 0.176 2.0 0,199 0.297 0.648 4.0 0.952 0.744 6.0 1.73 0.728 8.0 2.38 3.45 0,656 10.0 3.55 0.540 12.0 3.74 0.412 15.0 4.92 0.243 20.0 12 Pounds of 48- to 65-Tyler mesh Ottawa sand a Bed: sure drop: between 3 and 7 inches from bottom of column.
0.035 0,131 0.235 0.484 0.480 0.432 0.392 0.339 0,235 0.145
in 5-inch diameter column.
However, the unpacked fluidized bed in this region may still be developing, so that, at lower gas flow rates, the bubble size in the lower region could be smaller for the unpacked bed than for some packed ones. At flow ratios, U/Um, < 2, the r.m.s. values of the unpacked bed are smaller than those of 1-inch screen packing beds at comparable flow rates (see Table I and Figure 5). In Figure 6, the dimensionless r.m.s. term, U T , where 7 = A P , J D d is plotted against an expansion term, - Hmf)/HnL,. The expansion term is a n average volumetric ratio of the bubble to the dense phase. The maximum of UT for the packed fluidized bed is at 0.3 of the expansion term, regardless of the packing size or the screen opening in the range of the present investigation. Chen and Osberg (1967) have observed a minimum in their gas-mixing term at the same value of the expansion term. For the unpacked bed, however, U T is an increasing
(n
PACKING x
2
-.-
o o
I
--
0.6
--
A
NONE 4 MESH
/
I in.
6 MESH 14 MESH 6 MESH
3/4in.
I in. I in.
I 4 MESH
' / z In. '/z in.
/I'
0.4 -.
0,032 0.125 0,202 0.399 0,396 0.375 0.315 0.295 0.193 0.146 Packing:
6-mesh, "4 inch
4-mesh, ' / n inch
0.021 0.015 0,078 0.069 0.176 0.166 0,389 0.336 0,389 0.372 0.340 0.312 0,267 0.233 0.218 0.189 0,132 0.107 0.078 0.067 open-end screen cylinder, height
14-mesh 1 / 2 inch
=
~
0.011 0.032 0.052 0.132 0.126 0.117 0.086 0.063 0.042 0,029 diameter. Pres-
function of the expansion term and u, even exceeds unity when the bed is slugging vigorously. Probability Density Function of Pressure Fluctuations. Figure 7 shows the probability density functions for APd derived from data obtained with unpacked and packed fluidized beds, respectively. For the packed fluidized beds, the probability density functions are fairly close to a normal distribution in the range of the present investigation. For the unpacked beds, however, the distribution becomes skewed to the lower side when c'/C,,> 4 and the skewness is more pronounced as the flow rate increases. From the unsymmetrical shape of the differential pressure trace shown in Figure 3, it is predicted that the probability density of the differential pressure caused by a single bubble should be skewed. However, when the bed contains a large number of such bubbles between the pressure taps, the distribution of the pressure fluctuations should become normal according to the central limit theorem of statistics. The distributions for the packed fluidized bed (Figure 8) and the unpacked bed a t relatively low gas flow rates (Figure 7) can be explained on this basis. For the unpacked bed at higher gas flow rates, however, the distribution should become skewed as shown in Figure 7 since the bubbles are large and only a relatively few bubbles can be contained in the bed between the pressure taps.
0.7
0.6
0.5
>
0.04
k
t
9
0.4
w n
b
0.3
a iT
0.2
0.0 i 0.006
0.004
0.002
0. I
t I
I
I
I
I
I
I PRESS. DROP/RMS,(Apd-
(n'-Hmf)/Hmf Figure 6. 502
l&EC
uT as a function of an expansion term
FUNDAMENTALS
ATd!/gApd
Figure 7. Probability density function of pressure fluctuations of unpacked fluidized bed
Table II.
Peak and Average Frequencies of Power Spectral Density of Pressure Drop Fluctuation in Fluidized Bedsn
Packing -~ c'/Vrnf
AVone
1.6 2.0 4.0 6.0
2.3 2.3 2.6 2.2
8 .n
6-mesh, "4 inch Peak Frequency, C.P.S.
2 3 ~.
BPd:
,Vone
6-mesh, 3 / 1 inch Aaerage Frequency, C.P.S.
... 1.3 1.3 1.2 1.3 1.3 1.3 1.3 0.5
3.5 4.1 3.8 3.2 3.4 3.5 3.5 3.8 3.5
2.7 2.7 3.8 4.0 3.9 4.3 4.4 4.5 3.3
2.6 2.0 2.8 3.9 2.6 3.8 2.9 3.6 1.3
1.9 2.9 3.3 3.3 12pounds of 48-to 65-Tyler mesh Ottawa sand in 5-inch diamPtPr column.
10.0 12.0 l5,O 20.0 a
7 4-mesh, inch
Spectral Analysis osf Pressure Fluctuations. Previous studies on the frequency of the pressure fluctuation in fluidized beds have been based on strip chart traces of the pressure changes, and the obserired frequencies have been determined 0.7 0.6
--- NORMAL DISTRIBUTION 6 MESH-'/4 in.PACKlNG, U/U,( - 14 MESH- '12 in.PACKING, U/U,f
=IO 10
0.5 t.
$,
0.4
z
w n
8
0.3
a
a
0.2
0. I
PRESS. DROP/RMS, (hp,-
Figure 8.
Aid)/Qhpd
Probability density function of pressure fluctua-
0
5
14-mesh, inch ... 2.4 2.7 3.3 4. . 4.
5.0 4.9 3.3 2.6
from the number of significant pressure drop fluctuations (Shuster and Kisliak. 1952). or the number of line cuts a t a fixed pressure level (Sutherland, 1964), or the number of line cuts at 10% maximum pressure fluctuation (Fiocco, 1964). These latter data could have been a combination of the fluctuation intensity and the real frequency. In the present investigation, the spectral analysis was carried out by a digital method to produce a normalized power spectral density function, which is the power spectral density divided by (r.m.s.)2. T h e curves shown in Figure 8 illustrate the data from three runs. I t can be seen that the power spectrum becomes negligible when the frequency exceeds 15 C.P.S. and that the packing does not make significant changes in the frequency system of the pressure fluctuation in fluidized beds. I n the preliminary study, it was noted that the pressure fluctuations \yere induced by changes in the dense phase properties which, of course, are caused by the bubbles. Thus, the frequency of the pressure fluctuation should depend on the frequency of the dense phase change-Le., the cycle of forming and releasing the wake-ithich appears not to be much affected by screen packings. Table I1 is a summary of the power spectrum analysis. T h e major peak of the power spectrum and the average frequency (which divides the area equally under the spectrum curve) are shown. No significant change in the peak frequency with the gas flow rate can be observed, but the average frequency for the packed fluidized bed exhibits a slight tendency to increase
IO
15
20
FREQUENCY, cps.
Figure beld
9. Normalized power spectral density of pressure drop fluctuations in fluidized
VOL. 6
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NOVEMBER 1 9 6 7
503
with the gas flow rate. T h e peak frequency with 14-mesh, ‘/?-inch packing is lower than that with 6-mesh, 3/4-inch packing. This difference is probably due to the more restricted movement of solid particles Tvith the smaller packing. Acknowledgment
The authors are indebted to E.R.R. Funke for helpful discussions on the analysis of the random signal and to A. Shewchuk for his valuable technical assistance in the computer processing of the data. Nomenclature
H -
A
= = = = = =
U
=
H
H,, AP APd
zd = urn,ub H
uZ
= = =
bed height, inch average bed height, inch bed height at minimum fluidization, inch total pressure drop, inch H20 differential pressure, inch HzO average total pressure drop, inch H20 average differential pressure, inch HzO superficial gas velocity, inch,’sec. superficial gas velocity a t minimum fluidization, inch/sec. bubble -velocity, inchlsec. APd/APd r.m.s. fluctuation of x
Capes, C. E., Suthrrland, J. P., IND.ENG.CHEM.PROCESS DESIGN DEVELOP. 5 , 330 (1966). Chen, B. H., Osberg, G. L., Can. J . Chem. Eng. 45, 90-4 (1967). Fiocco, R. J., Sc.D. thesis, Stevens Institute of Technology, Hoboken, N. J., 1964. Funke, E. R. R., “Correlation Function and P.S.D. Analysis with Emphasis on Numerical Technique,” Internal Circulation of Canadian National Research Council, 1961. Gabor, J. D.,A.I.Ch.E. J . 10, 345 (1964). Gabor, J. D., A.I.Ch.E. J . 11, 127 (1965). Gabor, J . D., Chem. Eng. Progr. Symp. Ser. 62, 32 (1966). Gabor, J. D., Jonke, A . A . , Chem. Eng. Progr. Symp. Ser. GO, 96 (1964). Gabor, J. D., Mecham, it-. J., I ~ DENG. . CHEY.FwDAhfENTALs 3, 60 (1964). Gabor, J. D., Strangeland, B. E., Mecham, \\’, J., A.Z.Ch.E. J . 11, 130 (1965). 1shii.T.. Osberp. G. L.. A.I.CI1.E. J . 11. 279 11965’3. Kang, 11’. K., ?bin, V. 3. H., Osberg, G. L., unpublished note, 1966. Kang, LV. K., Osberg, G. L., Can. J . Chem. Eng. 44, 142 (1966). McIlhinney, A. E., Osberg, G. L., Can. J . Chem. Eng. 42, 232 (1964). Mecham, \V. J., Gabor, J. D., Jonke, A . X., C h m . Eng. Progr. Svmb. Ser. 60. 76 (1964’3. Re;&, H., Chbm. Eng. Progr. &‘>nip.Ser. 62, 9 2 (1966). Reuter, H., Chem.-Ing.-TPch. 35, 98 (1963). Rowe, P. N., Partridge, B. A , , Trans. Inst. Chem. Engrs. 43, T157 l,l ~ c ) 6, 5-) ~
,.
Shuster, \V. I V . , Kisliak, P., Chem. Eng. Progr. 48, 455 (1952). Sutherland, J. P., Vassilatos, G., Kubota, H., Osberg, G. L., A.I.Ch.E. J . 9, 437 (1963). Sutherland, J. P., IVong, K. Y . , Can. J . Chem. Eng. 42, 163 (1964). Sutherland, K. S., Argonne National Laboratory, Rept. ANL-6907 (19641
\ - ‘ I . / ’
Literature Cited
Basakov, A . P., Vershinina, V . S., Intern. Chem. Eng. 4, 119 (1964). Blackman, R. B., Tukey, J. LV., “The Measurement of Power Spectra,” p. 14, Dover Publications, Xew York, 1958.
Zeigler, E. N., Brazelton, I$. T., Ind. E t g . Chem. Process Design Develop. 2, 276 (1063). RECEIVED for review January 31, 1967 A C C E P T E D July 13, 1967
EVAPORATION COEFFICIENT OF LIQUIDS J E R RU M A A Distillation Research Laboratory, Rochester Institute of Technology, Rochester, A’. Y .
Thermal gradient calculations have been made in an attempt to place the technique of the jet tensimeter on a quantitative basis. Families of curves have been derived with which experimental data can be compared. Using the jet tensimeter, evaporation rates of water, isopropyl alcohol, carbon tetrachloride, and toluene have been examined at various liquid temperatures, times of exposure, and back pressures of vapor. The experimental results agree satisfactorily with the thermal gradient calculations, making the assumption that the evaporation coefficient is unity. This shows that there is little or no resistance to molecules crossing the vapor-liquid interface in addition to the natural resistance imposed by the gas laws. As a corollary, when any vapor molecule strikes at the interface, the chance of failing to cross is small. No significant difference in the behavior of evaporation due to the difference in molecular structure or chemical properties was observed.
HE attempt of Hickman (1 965) to determine theoretically Tand experimentally the true evaporation rates (coefficients) of liquids using the technique of the jet tensimeter is continued here. A prerequisite for the calculation of coefficients is precise knowledge of the temperature of all areas of the interface and since these cannot yet be measured precisely, resort is made to calculation. A nonturbulent jet of well mixed liquid projected into its own vapor, as shown in Figure 1, has a uniform temperature and a clean surface and is believed to present the simplest model for the calculation of surface temperature, free from the artifacts that complicate usual engineering systems.
504
l&EC FUNDAMENTALS
After emergence from an orifice, evaporation or condensation occurs according to the pressure of the surrounding vapor, and the stream acquires a thickening sheath of cooler or warmer liquid. The depths and intensities of the thermal gradients in the liquid skin are paralleled by density gradients and velocities of the vapor near the stream. As Hummel has remarked (1966), a n observer equipped with infrared vision would see a cylinder of constant temperature liquid encased in a tapered thermal “can:” itself enveloped in a truncated cloud of vapor, as suggested in Figure 2 . For his first approximate test of this concept, Hickman (1965) substituted a cylindrical thermal skin (Figure 3), designated the (E)quivalent
