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N. C. MEHTA', J. M. SMITH, and E. W. COMINGS Purdue University, LafayeWe, Ind.
.,.
!.. Pressure Drop in Air-Solid ,Flow.Systems . ,
..
.
A method for predicting solids.flow rate in transport lines and fluidized systems satisfactorily handles air velocity, solids flow rate, and vertical and horizontal flow,' but requires knowledge of particle. velocity
.: '
. ' and. mugbm 3. VeWtyoffluid 4. Dcouityandhityoffluid
w
...
,
-
'entrainid by 'the aii were r e d in a second g h wdol filter. Neither filter is shown in the diagram. The air flow was then divided into an auxiliary stream, for premrizing the solids feed tank a d m y m e t e r bubblaa, and the rnah'8fnxri going to &,test sections uia ,the m u r e regulator%. Mt, leathe %t acrtions, the air pawd thmugh a cyclone scpiirarm' and then to the abnoaphere thmugh a, bag fille;. Rotameters m e d the flow
Properties of System Variabl 50
dl.
velocity PlrtiClS
diun-
%lids E o w ~ m t e
0.
5.
1199y*
theirsize. The study reported here included pmzkure drop and particle velocity measuments for fwo *de sizes. The purpose was to obtain a better 'undytanding of the relationship between particle and fluid velocities and to develop an improved method for pidieting the p m r e drop.
Apparatus The experimental equipment consisted of an air supply system, enlids feed and cpcovay m k a , and wtical and horizontal test sections. Air from the supply line pass& through a glass wool filter to remove water and oil droplets and then to a silica gel drying tower. Fine silica gel parti@=
Yatuiel. ScotcbUte l o t . Mining a d M a
Terminal velocity It 'IS' c., 1 am.)
0.315
1.:
6 &
PRESSURE REGWATM
GATE VALVE
1
I T 1
WICK OWNING VALVE
#elSTOP-M)CK UNIONS
.hc, OYCK VALVE
1
1 I
?ow dic----
,
,
.
of pneumatic transport systr
rata in the lines to the test scctiois and solids feed tank. The solids feed and recovery tanks were made from &inch standard steel had capacities of 0.75 and 0.55 w. fmt. The feed n o d e was connected
.pipe and
to *e feed tank by a '[rinch pipe union to the transport line by! a' '/r+b glagMtal union. The, key p & , d the nozzle was a glagl funnel glued to tbc metal wall and inserted so that the - , tapredsideoftheendwasinthedownstnam.direction. % miid particl-3 ace acceleratad to 1 their equilibrium velocity after .&,feed no+ in the straight, horiEontal pipe :.ai?r to the horizontal teat &&on. % maight w t i o n was 100 +hca -long, to enaurc that none of the preanne drop in the test section was due to ac., . ' deration of the panicla. Similarly, cbue Was a straight, vertical length of 100 inohm prior to,the vertical test sectton. Quick-opening values wen installed a t both en& of the t a t sections, to trap F the partrclcs within .the section. After the valves were clw, the'section was w o n n e c t a l " and' the solid partiela P were removd and wek&d. The hngms ofthe M O test a 0 M W e : BetwapuniolU 58 .inCbcs BehMm "dvcs 48 i n c h Betwempriauretaps , 36inchcs , he prasun drop meisurrmyt t k tqtsection is hiqhxrd by,tbe dog-, ging of the tap openings by sow..Tbis was pp2ntecl air.through a bubbler, hp@bthee:S-., aqd
.. ., fled ncnZI& were studied, iseluding an h t - g l a c a % h i ~graw . +> a,saide& stoel straight funnd;a ewed bel. to mm3duGe pp-ticle3 in the direcrion ,of aoW, and the straight
\
I(
'
,
AIR VELOCITY,
Figure 2.
% FT./SEC.
Particle velocity data VOL49,NO. 6
JUNE I957
987
$:mI S O L l b S M A S S VELOCITY - L B S /(sa FTI(SEC 6 8 - 5I 9 {
-
+ 32.2-12.9
2
0 39.7. 40.4 8
10
I5
20
30
40
SUPERFICIAL AIR VELOCITY
II 5 I2 2 230 - 2 3 5 322 - 3 2 9
$3
60
80 100
2
- F r / SEC.
39 7
a
IO
15
20
so
40
SUPERFfCtAL AIR VELOCITY
-
60
40 7
80 100
- FT/SEC
Figure 3. Pressure drop for horizontal transport of 97-micron spheres
Figure 4, Pressure drop for vertical transport of 97-micron spheres
glass funnel finally used. The hourglass type operated intermittently because of the formation of a solids bridge across the narrow opening. Vibration of the nozzle improved the operation but not to a satisfactory level. The stainless steel funnel gradually eroded, changing the calibration. The curved nozzle did not operate well, presumably because of carbon deposition in the curved part, which developed as a result of electrostatic ignition of oil particles contained in the air stream. The straight glass funnel performed satisfactorily and three sizes were calibrated for each particle size. In the beginning the test sections were borosilicate glass pipe. Electrostatic charges and the resulting spark discharges between the tube wall and the solid particles prevented reproducible measurements of solids flow rate or pressure drop. Plugging of the pressure taps and tubes to the manometer also prevented accurate measurement of the pressure drop. Installation of the air system with bubblers kept the pressure taps free. The solids trap shown in the diagram prevented plugging of the manometer lines. Using this arrangement the maximum fluctuation in pressure drop was ‘ / z inch of water, and the average s’,1 inch. I t was necessary to clean the system each day to maintain this precision.
determined by collecting the solids in a bag filter a t the end of the horizontal test section. Preliminary experiments showed that variations in air velocity in the transport line and height of solids in the feed tank had no measurable effect on the calibration curve. The calibration tests were repeated a t the end of the pressure drop measurements across the test sections and found to be reproducible within the error of measurement, estimated to be less than 5%. To test the functioning of the pressure taps in the horizontal and vertical sections, pressure drop and total pressure were measured for the flow of air alone. To obtain data consistent with the results for flow with solid particles, it was necessary to pretreat the test sections by passing suspensions of the solid particles through them. The pressure drop measurements, plotted as A P / p , us. u, on logarithmic paper, gave well defined straight lines, confirming the correct functioning of the pressure taps. As a matter of interest, roughness factors were determined by comparison with the Fanning equation. A value of E / D equal to 0.0026 correlated the data in the horizontal section after pretreatment with 97-micron particles; a roughness of 0.0022 was indicated after pretreatment with 36micron particles.
Calibration Procedures and Data
Particle Velocity
The solids flow rate through the nozzle was a function of pressure drop across the nozzle, nozzle size, and particle diameter. The calibration curves of pressure drop us. solids flow rate for each nozzle and particle size were
Determination of the mass of solids in the test sections permitted direct calculation of solid particle concentration, Pda. Then from the measured flow rate of solids and the continuity equation,
988
INDUSTRIAL AND ENGINEERING CHEMISTRY
IO
15 20
30
40
60
SUPERFfCfAL AIR VELOCfTY
-
a0 100
Fr/SEC.
Figure 5. Pressure drop for horizontal transport of 36-micron spheres
the average velocity of the solid particles, us, was computed. Figures I and 2 show particle velocity as a function of air velocity for the two particle sizes in vertical flow. The scatter in the data is partially due to the manual operation of the quick-closing valves. Reproducibility of any one run may be as low as 25%. Nevertheless the curves show that there is considerable slip between solid and fluid and that the degree of slip varies with air velocity and particle size. For example, with the 97-micron particles Figure 3 indicates that the particle velocity approaches a maximum of about 20 feet per second, regardless of further increases in air velocity. I n contrast, for the 36-micron particles the particle velocity increases linearly throughout the range of air velocity. In other words, the extent of slip, ug - u,, increases much more rapidly for the large particles. As expected, the velocity of the 36-micron particles is greater than that for 97-micron particles throughout the range of air velocity. These observations suggest that the nature of the flow of particles is different for the two sizes, The data in Figure 3 agree with the conclusions of Hariu and Molstad (70), Culgan ( 5 ) , and Uspenskii (76) that particle velocity is independent of solids flow rate. The results for horizontal transport gave curves similar in shape to the curves in Figures 1 and 2. However, the particle velocity for horizontal flow was always somewhat higher than for vertical transport.
FLUID MECHANICS ~~
~~
Experimental Pressure Drop Data for Horizontal Flow
60
(0.097-mm. diameter Scotchlite glass beads in l/n-inoh standard steel pipe with 36-inch
50
test section) Air Mass Velocity
Total
Ft./Sec.
Lb./Sq. Ft.
78.0
33.8
5.81
4.24
24.9
7.33
15.4
77.0
28.1 31.1 29.0 32.6 29.8 33.1
5.86 5.92 5.86 5.92 5.91 5.86
7.93 6.16 7.56 5.08 7.05 4.88
56.0 39.3 51.8 30.9 47.0 29.3
17.2 11.0 15.5 8.07 13.9 7.63
18.9 17.8 18.8 16.7 18.5 16.3
30.0 36.4 31.2 35.8 33.7 34.8 28.7 31.1 27.9 30. I 33.2 35.4 37.5 34.9 37.4
5.77 5.91 5.94 5.94 5.94 5.92 5.92 5.86 5.94 5.94 5.86 5.94 5.94 5.92 5.94
6.43 9.21 11.5 9.55 11.2 10.6 13.1 12.2 13.5 12.6 4.98 3.52 2.04 3.91 2.88
42.7 50.3 73.0 53.0 66.0 60.2 90.9 78.0 96.4 83.0 29.8 19.8 10.8 22.3 15.3
12.4 16.4 26.6 17.5 23.5 21.2 36.4 26.9 39.0 32.5 8.48 5.38
18.0 18.8 19.4 18.8 19.0 19.0 20.0 19.6 20.0 19.8 16.3 13.9
5.93 4.52
14.7 12.0
78.0
Air
Velocity
ffav
Lb./Sq. Ft. Seo.
5.
Pressure Drop
Pressure drop was measured over the range of conditions listed above for both vertical and horizontal transport, and the data are plotted as pressure drop us. gas veiocity in Figures 3 to 6. Typical results are given in the table above for a low solids flow rate in the horizontal transport of 97-micron particles. Pressure drop, particle velocity measurements, and calibration results are tabulated by Mehta (73). Analysis of Datq
Contributions to Total Pressure Drop. I n the general case of transport of solid particles by a fluid flowing through the pipe, the total pressure drop may be considered as the sum of the following contributions : 1. Acceleration of air to carrying ve-
locity
2. Acceleration of solid particles, by a momentum balance
Gaus APs8 = .Ca
(4)
3.
Su port of column of air (in vertical
4.
Apho = P d u ) (5) Support of solids (in vertical trans-
transport7
u,r
Pressure
V,
Particle Velocity, US, Ft.ASec.
T, F. *
Abs. Solid Pressure Feed Inlet to Rate, G,, Test Section, Lb./Sq. Ft. Seo. Lb./Sq. Inch
4 0:
drop, Apt,
...
40
30
\
2 20 I
P
s
IS
u6
IO
$
8
cg
E 8
A II 2 - 1 2 0 5
10
15
20
30
40
60
SUPERFICIAL AIR VELOCITY
-
8 0 100
F r/SEC.
Figure 6. Pressure drop for vertical transport of 36-micron spheres
...
Specific Pressure Ratio and Solids Friction Factor Concepts. If it is assumed that the pressure drop due to solids friction can be represented by a Fanning-type expression,
Friction between air and pipe wall
6 , Particle-particle friction and particle-wall friction,APf8 Contributions 5 and 6 deserve explanation. The friction factor in Equation 7 is a function of the turbulence level in the flowing stream. This may be influenced by Reynolds number, pipe roughness, and other obstructions, fixed or moving, in the stream. Hence the magnitude of the air friction contribution may not be the same with air alone flowing through the pipe as with air and solid particles. Contribution 6 measures the pressure drop due to collisions between particles and between particles and the wall. The result of these processes is development of a slip velocity between particle and fluid. Several methods of treating this contribution have been suggested and two of these, involving a drag coefficient and solids friction factor, are analyzed below. If the flowing system is considered at a point where the acceleration is zero, and measurements are made by a differential manometer whose lead lines contain the same fluid, the total pressure drop may be written A p t = Aph,
+ APfu + A P f 8(vertical flow) (8)
port) or Apt = APf,
+ A P f , (horizontal flow)
(9)
where fs is a solids friction factor analogous to f, for fluid flow. Combining Equations 7, 9, and 10, the specific pressure ratio may be written
(for horizontal flow) (11) The slopes of a curve of a us. loading R is then equal to fsu,/fgug. Gasterstadt (9) found that S was constant for a given air velocity. Later studies (7, 77) failed to confirm the constancy of S. Equation 11 indicates that fau,/fpu, would have to be nonvariant for S to be constant at a fixed air velocity. The fluid friction factor, f,, may be a variable at constant ua because the turbulence in the fluid is expected to be a function of the solids loading, R, and solids velocity, u,. Similarly, fa and u. would be expected to vary as the nature and velocity of the solid particles changes. Hence this method of correlation is not promising. Hinkle ( 7 7 ) used the specific pressure correlation m.ethod but evaluated the variation in slope with solid properties through Equation 11. The solids friction factor was determined from Equation 11 by subtracting AP,, from A p e to obtain A P f 8 . This is a n improved approach over assuming S is constant at a given air velocity but still retains the assumption that the value of AP,, is the same with and without solids. This assumption is necessary in evaluating AP,, by VOL. 49, NO. 6
JUNE 1957
989
c
Y
1.0-
>
0.8~
E " *L
0.6-
0 Y
-
-
0
for a significant part of the total prck aurc drop.
MLhuc Friction Factor Qsrelntion. In view ofthe diffieutiw with the udsting d a t i o m j u a t desaibed, it isdcsirable to dnrelop a pmcedure which docs not assume that the pressure drop due to air
is un&ected by the solid partides and which taka into account dXer=nt particle flow patterns for different size solids. In Bccordancc with previous wncepts it wiw be supposed that the partide flow may be of the following thrretypes:
!
:
1. For small p article of low density there will be 110 slip and the solid-fluid miztun will Bow as a single fluid. 2. For solids of intermediate size and daaity, the partides flow in ry aLspcoded wndition, the bite slip velocity maintaining the suspended flow E6w). ( and mre d e w particle will have an unsteady motion. In a region whem the fluid velocity is high, they will be carrledaloag bysuspm9ion. Reaching a law vdocity region, the pmjde will d d e r a t e until again they are picked up' b M y moVing fluid. &winswith Xe may w u r at large angle. Such motion will be
. ? -
characterized as bouncing flow. From analysis of the partide velocity curves (pigum 1 and
2) it is postulated that the 97-miuon Bolids were primariI9 in bouncing b v , while the 36miaon size followed suspension flow.
Thus
Figurc4ahowsalinearincrrane in partide d a c i t y with air docity# wmapondjng to the quimncnts of the
Mcond type of flow. By contrast, dip docity inmasea much more sharply with air d o c i t y for the 97-micmn partides, and the sound of the particles bouncing against the wall was dearly audible in this case, both facts suggesting the thid type of motion. These concepts arc included in a wrd a t i o n which is based upon the e x p sion
(for horizontal Bow)
This expression was developed by applying the Fanning equation to the combined flow of solids and fluid in the following way:
.f may be called a mixture friction factor. Equation 16 includes the p" tide velocity, ,.u and pmpoaes to account for the dfect of the density of the wmbined ayrtem, pu, oq the pnssure drop. Rnrious invedtigations (1, 2) using a combined solid-fluid friction factor have been haned upon the velocity and density of the Euid phase done. Equation 16 m e s that the fraction ofthekineticemrgyco rtedtoother forma through friction 18 the same for fluid as for aolid particles. 'Ihia would not be # to hold for M e r e n t types of particle Eow. This is recognized by exponent I). If the theory is wrrect, the exponent should be a
function of those variables which determine the type of solid flow. For a given fluid, it should be possible in thenry to predict I ) from the size, density, and ahape of the solid particles. From the point of view of the type of flow, n should be laIgeat for bounciug flow, leas for flow in suspcnaion, and zero for flow as a single fluid. Figurn 10 and 11 depict mixture friction factors as a function of fluid Rcynolds numba for horiwnd and vatied flow for both particle sizes. The CUNw d p o n d to the beat cornlation and were obtained with I ) 1.0 for the 97micron particle (bouncing flow) y d 4 = 0.3 for the 36-micron partides ( a w pension Bow). Figure 10 for horizontal Eow indicates that f., is independent of splid flow rate for both particle sizes and that most of the data are wnsistent with the correlation within &15%. The shape of the curves is in agreement with the results expacted by analogy to homogeneous Bow-that is, the friction factor deweases with in~ M M in ReynoMB number and appmache a constant value as the Rtynold8 number continues to incrtase. The expression comsponding to Equation 15, but for vertical flow, is
-
";"
This equation was used to calculate the points in Figure 11. The results iddieate a constant friction factor at high Reynolds numbers, aa expected VOL49.NO.6
JUW l9W
991
0 10
I 1 PAR 006
E
c
PIPE DIA
M M
0097
& I I
SIZE
POSITION
I
12 0 234
0 0
A/
1/2’STD
STEEL
VERTICAL
237
0.04
a”
PV
d z
0 t-
on LL
00 2
0.01 4300 top00
“ e.
I
REYNOLDS
Figure 1 1 ;
!
o
I
20,000
40,000
60,000
80,000 100,000
NUMBER, Re,
AP,, = pressure drop for acceleration of air, lb./(sq. ft.) AP,, = pressure drop due to acceleration of solid, lb./(sq. ft.) AP,, = pressure drop to support fluid column, lb./(sq. ft.) APhs = pressure drop to support solid particles, lb./(sq. ft.) AP,, = pressure drop due to friction for flow of air, lb./(sq. ft.) APr, = pressure drop due to friction for flow of solid particles, ab./ (sq. ft.) R = loading, G,/G,, dimensionless S = slope in specific pressure drop equation (Equation 1) I(, = air velocity, feet per second u, = particle velocity, feet per second o! = specific pressure drop, A p t / AP, E = equivalent height of roughness fcature, feet pa = density of fluid, lb./cu. foot ps = density of solid particles, lb./cu. foot pds = dispersed density of solid particles, Ib. of solids/cu. foot pg = viscosity of fluid
Friction factor as a function of Reynolds number
Literuture Cited
sary to establish the nature of the reand as found for horizontal flow. between type of flow and However, the data at low values of ~ V R lationship ~ ~ properties. scatter badly and suggest a trend for The best correlation of the pressure the friction factor to increase with an drop data was obtained by proposing a increase in N R ~ ~This . behavior for modificaiion of the Fanning equation vertical flow results from the combined that includes particle velocity. The effects of the increase in concentration proposed method satisfactorily handles of solid particles accompanying a deair velocity, solids flow rate, and vertical crease in air velocity and the necessity and horizontal flow but requires a for subtracting AP,, in applying Equaknowledge of the particle velocity. tion 17. Because of the increased I t is believed that further progress in solids concentration, the pressure drop the study of solid transport behavior to support the particles closely apwill depend upon the development of a proaches the total AP. For this reason method for predicting the particle velocthe values of the left side of Equation 17 ity from the properties of the system. are not reliable at low Reynolds numbers. The magnitude of the error increases as the solids flow rate increases. Figures 10 and 11 indicate that the Acknowledgment mixture friction factor is essentially The Texas Co. and the Engineering the same for vertical and horizontal Experiment Station, Purdue University, flow and independent of solids flow rate. provided the financial support for this The use of Figure 8 for both horizontal work. and vertical flow is therefore recommended. Conclusions
The pressure drop in air-solid transport systems is dependent upon the type of particle flow. Two types, bouncing and suspension flow, have been observed with the particles studied. For bouncing flow the pressure drop is directly proportional to the solids flow rate; for suspension flow the pressure drop is proportional to the 0.3 power of the solids rate. The type of flow and its effect on the pressure drop should be determined by the size, density, and shape of the particles for transport with the same fluid and pipe size. Additional work with other particles is neces-
992
Nomenclature
exponent in Equations 15 and 17 drag coefficient, dimensionless D pipe diameter, feet D, particle diameter, feet fo fluid friction factor f, solids friction factor f, mixture friction factor g, = conversion factor, 32.17 lb. mass (ft.)/(lb. force) (sec.2) G, = fluid mass velocity, Ib./(sec.) (sq. ft.) G, = solid mass velocity, lb./(sec.) (sq. ft.) AL = increment of pipe length, feet NRep= particle Reynolds number A p t = total pressure drop for flow of solid-fluid system, lb./(sq. ft.) a
C
INDUSTRIAL AND ENGINEERING CHEMISTRY
= = = = = = =
(1) Albright, C. W., Holden, J. H., Simons, H. P., Schmidt, L. D.,
IND.ENG.CHEM.43,1837 (1951).
(2) Belden, D. H., Kassel, L. S., Zbid., 41,1174 (1949). (3) Chately, H., Engineering (1940).
149,
230
Cramp, ’ W., Priestly, A,, Engineer 137,89 (1924).
Culgan, J. M., Ph.D. thesis, Chemical Engineering, Georgia Institute of Tech., 1952. Davis, R. F., Engineering 140, 124 (1935).
Farbar, L., IND. ENG. CHEM.41, 1148 (1949).
de Frondeville and Siegfrid, Ann. bonts et chausskes 1. Part 2 (19391. Gherstadt, J., Z.’Ver. d&t. Ing. 68, 617 (1924).
H a r i u 2 ’ 0 . - ~ Molstad, *, M. C., IND. E m . CHEM.41,1148 (1949). Hinkle, B. L., Ph.D. thesis, Chemical Engineering, Georgia Institute of Technology, 1953. Korn, A. H., Chem. Eng. 57, No. 3,108 1950). (13) Mehta,”.
C., Ph.D. thesis, Chemical Engineering, Purdue University, January 1955. (14) O’Brien, M. P., Folsom, R. G., Univ. Calif. Eng. Pubs. 3, 343 (1937).
( 1 5 ) Se ler, G., Z. Ver. deut. Zng. 79, 5 5 8 f1935)
(16) Uspenskii, V. A., Ekon. Toplt’va, Za. 8, No. 3,26 (1951). (17) Vogt, E. G., White, R. R., IND. EN^. CHEM. 49,1731 (1948). (18) Wood, S. A., Bailey, A., Proc. Znst. Mech. Engrs. (London) 142, 149 (1979’1. ,---_ (19) Zenz, F. A., I N D . ENG. CHEM. 41, 2801 (1949). 3.
RECEIVED for review October 15, 1956 ACCEPTED April 3, 1957 Division of Industrial and Engineering Chemistry, ACS, Symposium on Fluid Mechanics in Chemical Engineering, Lafayette, Ind., December 1956.
