Droplet Transfer from Suspending Air to Duct Walls L.0 .ALEXANDER' A N D C. L. COLDREN UNIVERSITY OF ILLINOIS. URBANA. ILL.
EPOSITION of a spray on the walls must be considered in the design and operation of several types of industrial equipment, including Venturi scrubbers and atomizers, combustion chambers in which liquid fuels are burned, and spray dryers. This investigation of the transport of small water drop]ets from a turbulent air stream to thewalls of astraight
D
duct was undertaken to elucidate the
T h e experiments were performed toelucidate the mechanism and t o measure typical rates of deposition, on the walls of a straight duct, of small (average diameter 27 microns) water droplets suspended in a turbulent air stream. From the shapes of the radial profiles of mass velocity of suspended matter, it was deduced that, with respect to a t least 30 t o 60% by weight (depending on t h e velocity) of t h e droplets in the spray used, the maJor resistance t o transfer from the air stream t o duct wall resided in a relatively thin layer of gas adjacent t o the wall. A mathematical relation based on this hypothesis correlated t h e data reasonably well in terms of an equivalent-film coefficient of mass transfer. The coefficient varied with the 1.17 power of t h e velocity, and was 10 t o 20 times greater, on a mass basis, ttian coefficients estimated for ammonia and carbon dioxide under comparable conditions. Transport and deposition of droplets are phenomena encountered in t h e operation of Venturi scrubbers, spray dryers, and combustion chambers employing injection of liquid fuels.
mechanism by which sprays are deposited in such systems. The water spray used in this research wasgenerated inan'Lair-atomi"ng''spray ImZle of the type studied by Nukiyama and Tanasawa ( 6 ) , and their correlation was used t o compute the mean drop size of the spray. The spray was injected axially into an air stream moving a t moderate velocities in a straight horizontal circular duct. Deposition on the wall began a t the entrance t o the duct. In the first third of the duct (Zone I) the Profiles of local mass v e h itY of Suspended matter were bell-shaPed, but in the last half (Zone 11) the profiles were substantially flat over 75% of the radius of the duct, falling toward zero near the wall (Figure 4). The first type of profile is characteristic of a system in which there is negligible resistance t o transfer a t the walls and the "eddy" diffusivity of the main body is controlling. The second is typical of systems in which the rate of transfer through the main body is high compared to the rate of transfer at the walls. By assuming that the resistance t o transfer Of water droplets a t the wall was negligible in Zone I, and high in Zone 11, equations were derived which successfully correlated the data for the two regions.
THEORY
Consider a system in which a spray of water is injected concurrently along the axis of a straight, circular duct through which air is flowing. The droplets will be accelerated or decelerated by the drag of the air until their velocities approach that of the air stream, provided the duct is sufficiently long. Very small droplets will attain substantially air stream velocity in a short time. I n the analytical development which follows, it is assumed that the spray is in the duct for time sufficiently short to make it possible to neglect the action of gravity. The problem of mass transfer from the main body of a gas stream to the walls of the confining duct may be treated mathematically in a manner that will yield a film coefficient of mass transfer. Such a treatment should be valid in cases in which the resistance t o mass transfer is concentrated near the wall. The rate of depletion of suspended matter in a differential section of the duct is equated t o the rate of transfer through the equivalent film a t the wall.
Q
HISTORY
1
Considerable research has been reported on the diffusion of gases in turbulent gas streams flowing in ducts of various shapes. Sherwood has summarized much of this work (8). Towle (10) and Woertz (g), working with Sherwood, studied systems in which eddy diffusion was important. Gilliland investigated the evaporation of liquids from a wetted-wall tube into a turbulent air stream (S),and correlated his data on the basis of the familiar concept of an equivalent stagnant film. Kalinske (6) studied the transportation of suspended material in rivers. Applying Taylor's vorticity transport theory, he derived equations describing the distribution of suspended matter and showed that, for particles having the same density as the fluid, the diffusion coefficients for mass and momentum should be equal. Experiments with oil droplets suspended in a turbulent .stream of water confirmed this deduction (6). Kalinske also reported diffusion coefficients for the sediment in the Mississippi River at Muscatine, Iowa, as a function of particle size. No trend with size ( 5 to 580 microns) was observed. 1 Present
address, University of Oklahoma, Norman, Okla.
-
l' ($)v
d(r2) = k,DAE
(1)
where k, is the film coefficient of mass transfer, D is the diameter of the duct, c is the ]oca] concentration of suspended matter, is the local air velocity, 5 and T are coordinates in the axial and radial directions, respectively, and AZ = E
- co
(2)
where cis the average concentration of suspended matter over the cross section of the duct and c0 is the concentration a t the wall. BY definition 1 = uc (3) where I is the local mass velocity of suspended matter, Consistently with this, the average mass velocity of suspended matter, t, is defined a5 i- E* (4) where ii is the volumetric-average air velocity.
1325
1326
INDUSTRIAL AND ENGINEERING CHEMISTRY
air velocity, U. A droplet suspended in a turbulent stream receives impulses from various directions. The impulses are not entirely random, for the "turbulent shearing stress" depends upon the degree of correlation between transverse and longitudinal velocity fluctuations. However, if it is aswmed that the impulses are nearly random, the net rate of mass transfer should be governed by a diffusion law of the form
FROM COMPRESSOR ~.
HOT OR COLD PRESSURE CONTROL VALVE
,~~
HEAT EXCHANGER
VENT FOR HUMIDITY MEASUREMENT
I
CRITICAL ORIFICE PLATE
1
$ l
j
ATOMIZING NOZZLE
1 Figure 1.
11 COLLECTION
u
Schematic Diagram of Experimental Apparatus
Assuming that the concentration a t the wall, ea is zero-i.e., that there is no tendency of the droplets to return to the main stream once they are deposited on the wall-and applying Equations 2, 3, and 4 to Equation l, followed by integration and rearrangement, the following relation is obtained. k a -
GDdlni 4 dx
The element of volume is considered t o move with velocity U, and diffusion of drops through the ends of the 'vas x
I
D ~ Ud ~n i 4Ri2 dx
a = - - -
=
(3A)
U6
where x is the distance the volume eleineiit travels from the origin in time 6. The boundary conditions are
-
(5)
The hypothesis that the effective concentration of water droplets is zero a t the walls lvas investigated in a preliminary experiment where in water, a t rates up to 300 ml. per minute, was allowed to flow uniformly distributed down the inside wall of a vertical tube 1.86 inches in inside diameter by 6 feet long. A4ir a t velocities up to 800 feet per second was passed down through the tube. The gas stream leaving the duct was sampled through a KO. 38 (0.101 inch) sampling probe over the cross section of flow. Although a fine mist was present in the air stream, the rate of collection of water by the probe was immeasurably sniall except near the wall where the probe entered the spray detached from the end of the tube. It was concluded that a negligible amount of water was detached from the wall by the action of the air stream. As and D are readily measured and 2 may be determined exaerimentallv bv a method described in the next section, Eauation 5 may be investigated conveniently. Equation 5 is not applicable t o cases \There the resistance a t the wall is not controlling. If the major resistance t o transfer is in the main body of the stream and not a t the wall, the proper relation involves the average apparent eddy diffusivity of droplets: "
where b X / b B is the radial inass rate of transport of droplets per unit area, a is the eddy diffusivity, and Dc/Dr is the radial gradient of concentration of liquid. Taking a mass balance on a volume element having a length 62, a diameter r , and a thickness dr, the following differential equation is readily obtained.
SECT'oN /
Vol. 43, No. 6
c = f ( r i when 6 = 60 c = '0 when 6 = c = 0 when r = D / 2
where D is the diameter of the duct. Solving Equation 2
Froin boundary cobdition ( c )
Jo(u.
%)= 0
and from condition ( a )
The average mass velocity of the liquid still in suspension a t any section along the length of the duct is given by the integral
where A is the cross-sectional area of the duct. Substituting from Equation 4A and integrating
c m
R here 01
is the average apparent eddy diffusivity of the droplets and R1is the first root of the zero-order Bessel function of the first kind. A derivation is given below. functions of 1,. hence, it is It is Seen that a and k , are not possible t o deduce from the linearity of graphs v, hich mechanism of transport is controlling. The shape of the concentiation profile is the criterion: ii flat profile falling rapidly toward zero near the wall indicates that resistance to transfer there is controlling. On the other hand, a bell-shaped profile would be equivocal in connection with the present experiments because center-line injection of water a a s used.
7
*,tD A,e-a2a'J1 L4
(SA)
1
If all terms in this series except the first can be neglected, - 4ZA1 l=-e D
-a:aQJ1
(u+)
(QA)
Differentiating with respect to 6 di
de
- 4UA1 D-
afae-a?aoJ1
('$)
(10A)
Substituting from Equation 9A CASE OF NEGLIGIBLE RESISTANCE T O TRANSFER A T WALL
It was assumed that the velocity of the sprag was substantially uniform over a cross section and equal to the volumetric-average
(11A)
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1951
1327
But, by Equation 3A
whence
By Equation 5h
2R1
u1 = -
D
where R1 is the first rpot of the zero-order Bessel function of the first kind. Substituting in Equation 13A d-l ni dx
- - -~
R ~ c Y 0%
According to Equation 6, a plot of the logarithm of the average mass velocity of liquid in suspension versus duct length should give a straight line having a slope of -4R:/D2G. The assumption that all terms in Equation 8A except the first are negligible is based on the expectation thdt, after a reasonable length of test section and regardless of the original distribution, the spray distribution approaches a form described by a single term of the Bessel series. There is no u priori justification €or this hypothesis, except the feeling t h a t the deposition probably is a first-order rate process, as implied by E uation G . The assumptions of (1) uniform air velocity across &e test section, and (2) absence of spattering effect, blow off, and other wall phenomena, make the diffusivity, C Y , an average, apparent diffusivity. Furthermore, LY is average with respect to drop size. APPARATUS A N D PROCEDURE
Figure 3.
Figure 1 shows a schematic diagram of the apparatus, comprising an air compressor and auxiliary equipment, pressure control and air metering equipment, heat exchangers, a water supply and metering system, a spray nozzle together with control and metering equipment, a straight, horizontal circular duct having an enlarged approach section, and an impact-tube, spray collection rake. Air was supplied b y a Diesel-driven reciprocating compressor equipped with aftercooler, surge tanks, filters, heat exchangers, and pressure-controlling devices. The air was metered through a set of orifices centered in a flange connection in such a manner t h a t the plates could be installed in only one orientation. Nine plates covering the range of flow from 0 t o 330 standard cubic feet per minute were calibrated t o *0.5% against a standard flow nozzle (4). Critical flow was maintained at all times. Water for the spray was supplied from a 350-gallon tank maintained under a pressure of 30 pounds per square inch gage by compressed air. This system provided sensibly steady flow at the atomizing nozzle. The water was metered through an orifice calibrated within 1%. II
The spray was produced in an air-atomizing nozzle of the type used by Nukiyama and Tanasawa in some of their experiments (6). Figure 2 shows the details of the design. 4 4 T R E A M L I N E D SUPPORT
\
AIR
-&,,,I
40.787k
............................
Figure 2.
T
Air-Atomizing Nozzle
Dimensions i n inches
Water flows through the central tube and is injected along the axis of the air stream flowing through the nozzle. Air was supplied t o the nozzle from a side t a p on the main air line and was metered through the nozzle orifice. During calibration, water was ejected through the orifice a t the same rate as in subsequent experiments.
Spray Collection Rake
The test duct consisted of sections of seamless steel tubing 1.86 inches in inside diameter and of various lengths. These were connected through a 13-inch convergent section t o a plenum chamber 18 inches long and 6 inches in diameter. The convergent section and plenum chamber were made of sheet steel and connected by 12-bolt steel flanges. The test sections were soldered t o the convergent section. The end of the plenum chamber opposite the convergent section was closed by a steel plate bolted t o a flange, and the plate was fitted with a packing gland. The atomizing nozzle was inserted through the gland on the axis of the plenum chamber with its outlet 2.125 inches from the entrance t o the test section. The main air stream was admitted to the chamber through a 1.5-inch opening near the upstream end of the plenum chamber. A collection rake (Figure 3), consisting of nine impact tubes arranged across a diameter of the duct, was clamped to the outlet of the test sections, which discharged directly to the atmosphere. T h e tubes were of steel tubing 2 mm. in inside diameter and the ends were tapered to knife-edges. The area of the mouth of each tube was determined by microscopic measurement. The tubes were connected by rubber hose t o short sections of 8-mm. glass tubing provided with drip points. The glass tubes served as decelerating chambers for the air stream passing through them. I n reaching them, the air stream underwent a 180” change in direction, and substantially all the water in the stream was deposited on the walls and dripped off the drip points into calibrated glass collection cylinders. These were supported under the drip points in a rack that could be placed in position and removed rapidly. From measurementi of the rate of accumulation of water in the cylinders, the local mass velocity of suspended water droplets was computed for nine points across a diameter of the duct.
It was assumed that all droplets in the cylindrical volume having the mouth of the tube for a base entered the tube as the air carrying them flowed over the mouth of the tube. The greater part of the air probably flowed through the tubes, as these were short in comparison with their diameter. Spray collection probes of this type were studied by Amstead ( 1 ) . The efficiencies of “spillover” types, such as used here, and of “nonspillover” types, in which air is drawn through the probes a t a rate such that there is no disturbance in the streamlines a t the entrance, were compared and found t o be substantially equal a t
INDUSTRIAL AND ENGINEERING CHEMISTRY
1328
I
1
Vol. 43, No. 6
I
the local mass velocity was assumed to be zero AVERAGE A I R V E L O C I T Y 0 7-5/8 IN. a t the wall of the duct, 0 - 297 FT./SEC. 0 - 13-5/8 11 IW 0 - 19-5/8 ' 1 corresponding to the A - 25-518 ' 1 n A - 126 - 31 5 / 8 hypothesis that there - 79.8" 495/8 J is no tendency for a 55-518 1 1 n 03 n 0 67-5/8 '1 0 droplet to return to the 1//1t 0 00.2 air stream once it has been deposited. The logarithms of t h e average maas velocity were t h e n p 1o t t e d against distance from the atomizing nozzle, as shown in Figure 7. Two regions of the curves obtained appeared to correlate b e s t a s f a m i l i e s of s t r a i g h t lines. The slopes of these lines were determined and are t a b u l a t e d in I I I 1 I Table I. I 0.2 0.4 0.6 0.8 From these slopes D I S T A N C E F R O M W A L L OF DUCT, IN. D I S T A N C E FROM W A L L OF D U C T , I N and the corresponding Figure 4. Radial Profiles of Local Mass VeFigure 5. Radial Profiles of Local Mass Vevalues of G and D , the locity of Suspended Droplets a t Various Dislocity of Suspended Droplets a t Various eddy diffusivities, 01, tances from Nozzle Average Air Velocities for Zone I, and the Average air velocity 186 feet per second Distance from nozzle 43.626 Inches film coefficientsof mass transfer, k,, for Zone 98%. In analyzing the data obtained here, this small correction I1 were calculated by Equations 5 and 6. These are tabulated was neglected. in Table I1 and are shown plotted against the velocity, U,on In this research, the diameter of the duct and the mean drop log-log coordinates in Figures 8 and 9. size were not varied. The water rate was held constant a t 400 ml. A reasonably good straight-line correlation was obtained for per minute, and the velocity of the air in the atomizing orifice n-as the film coefficient, k,, to which the equation maintained a t 800 feet per second in all experiments. The mean k , = 0.00335 ? i l * l r (7) diameter of the droplets was calculated by the equation of Nukiyama and Tanasawa (6) to be 27 microns. Five air velocities corresponds. On the other hand, the plot of a , although having were used in the duct: SO, 132, 185, 239, and 295 feet per second, a small positive slope a t low velocities, tends to become horizontal each being reproducible within 2.5%. Mass-velocity profiles of a t higher velocities. the spray were obtained a t each of eight distances from the atomizing nozzle: 67.625, 55.625, 43.625, 31.625, 25.625, 19.625, 13.625, and 7.625 inches. When the measurements a t 67.625 M NOZZLE inches were complete, the test section was shortened by cutting off the desired amount, and so on. I n this way, the entrance to the test section was left undisturbed. Air was admitted t o the atomizing nozzle and test section a t 86' F. It was assumed that the temperature of the air a t the exit was always near its wet-bulb temperature. Velocity profiles were taken a t selected air velocities and length? of test section by the use of a traversing impact tube.
1
D I S T A N C E FROM N O Z Z L E
l l
--
RESULTS OF EXPERIMENTS
Figure 4 shows typical mass-Gelocity profiles of suEpended water corresponding to various lengths of test section. The volumetric-average air velocity was 185 feet per second. It is seen that the profiles flatten out rapidly in the first 18 inches from the spray nozzle. Beyond this point there is little change in shape. I n Figure 5 are shown mass-velocity profiles for various velocities a t a single test-section length, 43.625 inches. The profiles are all similar. Velocity profiles corresponding to various distances a t a bulk velocity of 295 feet per second are presented in Figure 6. Profiles similar to those shown in Figure 4 were obtained at five air velocities for each of eight lengths of test section. The profiles were integrated graphically to obtain the average mass velocity of suspended water, i. In performing the integration,
D I S T A N C E FROM W A L L OF DUCT. IN.
Figure 6. Radial Profiles of Local Air Velocity a t Various Distances from Nozzle Average air velocity 295 feet per second
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1951 Table I.
Logarithmic Deposition Rates Computed from Figure 9
Table Ill.
-
Expt.O.10
u, Average Air Velocity, Feet/Sec. 80 132 185. 239 295
Table II.
-
(*i), Inches-' -0.0615 -0.0497 -0,0395 0.0324
-
Eddy Diffusivities and Film Coefficients of Mass Transfer
Averzke Air Velocity, Feet/Sec. 80 132 185 239 295
a,Sq. Feet/Sec.
Zone I,
Zone I1 ko, Feet/de'eo.
0.088 0.101 0.115 0.118 0.119
0.58 0.92 1.49 2.11 2.69
Tables 111, IV, and V give data on local mass velocity of suspended droplets, average air velocity, distance, and average mass velocity of suspended droplets, and local air velocity. DISCUSSION O F RESULTS
From Figure 6, it is seen that, in Zone 11, profiles of the mass velocity are flat, as would be expected in a system in which there is appreciable resistance t o transfer a t the wall, and the concept of a semistagnant film at the wall having a resistance equivalent t o the entire resistance of the stream appears applicable. The data are well correlated on the basis of this concept by Equation 5 . On the other hand, in the region near the nozzle (Zone I), the profiles are not flat. This condition results from the center-line injection of the water, regardless of the relative magnitude of the resistance to transfer at the wall. It does not seem p,ossible to estimate the wall resistance from these data. Qualitatively, it may be of the same magnitude as elsewhere (Zone 11),for inspection shows t h a t the concentration gradient near the wall was approximately the same in Experiments 21 and 51. The data for Zone I are equivocal for several reasons. There may have been a selective action by which the larger drops were deposited more rapidly, thus accounting for the high rates of
IAVERAGE 0
0
A
A I R VELOCITY 295 FT./SEC. 240 14 19 185 11 11 I 34
'1
Local Mass Velocity of Suspended Droplets y, Inch 0.54 0.72 0.91 0.75 0.56 1, Pound per Second per Square Foot 0.191 0.205 0.222 0.226 0.220 0.202 0.205 0,236 0.226 0.218 0.196 0.200 0.217 0.228 0.212 0.190 0.185 0.198 0.215 0.202 0.179 0.169 0.193 0.188 0.178 0.160 0.167 0.168 0.162 0.152 0.149 0.152 0.150 0.145 0.140 0.164 0.169 0.177 0.171 0.166 0.185 0.183 0.192 0.185 0.190 0.181 0.182 0.192 0.177 0.178 0.112 0.114 0.117 0.106 0.104 0.194 0.187 0.204 0.198 0.195 0.217 0.197 0.241 0.224 0.2Q3 0.231 Q 227 0.236 0.261 0.247 0.271 0.287 0.271 0.298 0.302 0.267 0.230 0.250 0.261 0.269 0.238 0.223 0.241 0.231 0.242 0.179 0.180 0.179 0.172 0.175 0.178 0.168 0.177 0.171 0.172 0.132 0.131 0.129 0.125 0.125 0.329 0.313 0.329 0.365 0.370 0.310 0.270 0.300 0.318 0.335 0.261 0.250 0.270 0.263 0.272 0.210 0.217 0.225 0.210 0.208 0.150 0.150 0.144 0.140 0.149 0.373 0.385 0.407 0.434 0.431 0.359 0.324 0.407 0.391 0.396 0.350 0.313 0.411 0.395 0.386 0.290 0.289 0.325 0.323 0.327 0.235 0.242 0.248 0.235 0.233 0.158 0.168 0.159 0.157 0.154 0.200 0.209 0.204 0.201 0.195 0.302 0.326 0.333 0'.329 0.319 0.234 0.342 0.463 0.401 0.434 0.462 0.457 0.525 0.552 0.530 0.477 0.474 0.533 0.585 0.574 0.655 0.768 0.874 0.911 0.693 0.661 0.743 0.899 0.886 0.768 0.575 0.686 0.824 0.786 0.655 0.435 0.549 0,603 0.547 0.485 0.275 0.316 0.318 0 , 3 0 1 0.281 0.705 1.27 1.58 1 . 3 6 0.874 0.905 1.69 2.50 1.15 2.03 1.03 2.38 1.25 1.69 2.08 1 . 9 1 2.46 1.08 2.15 1.29 1.07 1 . 8 2 2.56 2.13 1.34
0.31
No.
Zone I1 -0,0154 -0.0150 -0.0173 -0.0190 -0.0196
Zone I
-0.0878
-
'1
I O 2 0 30 40 50 60 70 D I S T A N C E FROM N O Z Z L E , IN.
Figure 7. Distribution of Average Mass Velocity of Suspended Droplets along Duct a t Various Average Air Velocities
0.107 0.105 0.081 0.088 0.086 0.110 0.119 0.086 0.100 0.112 0.084 0.099 0.114 0.142 0.204 0.161 0.142 0.140 0.135 0.102 0.280 0.216 0.178 0.163 0.142 0.332 0.246 0.244 0.197 0.182 0.157 0.173 0,207 0.221 0.285 0.365 0.353 0.290 0.249 0.222 0.178 0.156 0.176 0.129 0.137 0.135
Table I V .
1329
0.36
0.15
0.197 0.200 0.188 0.170 0.150 0.134 0.129 0.137 0.167 0.162 0,111 0.176 0.208 0.241 0.289 0.255 0.230 0.176 0.171 0.125 0.353 0.311 0.263 0.210 0.149 0.416 0.371 0.364 0.304 0.235 0.161 0.198 0.287 0.373 0.447 0.499 0.599 0.554 0.495 0.416 0.260 0,485 0.604 0.604 0.613 0.636
Average Air Velocity, Distance, and Average Mass Velocity of Suspended Droplets E = feet per seoond 5 = inches = pound per seoond per square foot
'i Expt. No. 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 31-A 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
-u
300 296 239 239 167 143 90.9 166 166 139 80.4 183 239 291 297 240 185 121 131 79.8 293 238 185 132 80.4 297 240 240 186 132 80.4 81.4 134 189 245 297 292 237 182 129 78.2 79.3 131 185 238 293
5
-2
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
1330
Table V.
‘ Expt. A
Expt. B
288 302 317 326 330 332 332 328 321 309 297 281
-
c
Expt.
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
09 7 2 . 6 13 75.3 19 7 8 . 0 24 7 9 . 3 34 8 1 . 2 44 8 2 . 8 55 8 2 . 8 69 83.6 85 8 3 . 7 83 8 3 . 7 63 8 3 . 7 42 8 3 . 0 30 82.:. 20 8 0 . 0 10 7 3 . 3 06 6 8 . 5
Expt. D
0.06 0.14 0.22 0.31 0.43 0.55 0.69 0.87 0 . 84 0.72 0.49 0.33 0.20 0.08
246 290 309 312 317 320 322 324 324 324 321 315 302 276
Expt. E
0 0 0 0 0 0 0 0 0 0 0 0 0
05 11 17 22 33 46 63 83 85 57 33 19 09
Local Air Velocity Expt. F Expt. I
275 290 299 304 309 313 317 320 321 319 313 301 280
272 305 313 320 323 325 325 320 315 306
0.20 0.34 0.56
O.GQ
0 88 0 83 0.86 0.44 0 23 0.09
0 . 0 8 279 0 . 2 2 298 0 . 3 2 308 0 . 4 9 326 0 . 6 8 341 0 . 8 8 349 0 78 345 0 . 6 3 338 0 . 4 2 319 0 . 2 8 306 0 . 1 7 292 0 . 0 7 262
Expt. J
0.13 76.6 0.24 78.2 0 . 3 7 77.7 0.65 77.7 0 . 9 3 77 7 0 . 5 2 78.7 0.26 81.3 0.15 81.3 0.06 77.4 0.87 77.4 0.13 7 7 . 4
Vol. 43, No. 6
Expt.
0.07 0.20 0.35 0.64 0.71 0.91 0.76 0.66 0.47 0.40 0.30 0.19 0.08
K
52.7 5s. 7 81.6 130 166
189 176 151 108 88.3 68.8 50.0 43.9
Exnt. L
0.0 16 9
272 252
0 . 3 3 307 0 . 4 5 341 0 . 6 2 385 0 . 7 6 420 0 . 8 6 434 0 . 9 3 438 0 . 7 9 427 0.65 392 0 48 340 0 28 286 0.13 254 0 05 227
u = feet per second u = feet per second x = inches g = inch All local air velocity mieasure rnents M ere taken with no water drop1ets prese n t in a.ir &rea .m
transfer observed in Zone I. Again, the turbulence in Zone I was undoubtedly greater than in Zone I1 because of the action of the air-atomieing nozzle. It is reasonable to suppose that the root mean square velocity of the droplets was proportional to the absolute intensity of turbulence of the gas stream in nhich they were BUSpended. Furthermore,
vf
$
2S Y.30
0.2
L m
L
>
0;20
O.I5
I-L
>
w z a.I5
G13 o I O
-
: j i
008
q l o
0.06
h-depend on factors that were neither measured nor controlled-e.g., design of the atomizing nozzle and its location relative to the entrance of the duct, velocity of the atomizing air relative to secondary air, diameter of the atomizing orifice relative to the duct diameter, etc. The apparatus was not designed for the study of eddy diffusivities, and the results obtained were only incidental to the programmed study of the deposition from streams in ordinary turbulent flow, as in Zone 11. The magnitude and behavior of the film coefficients, k,, are thought to be reasonably reliable for the drop size used and level of turbulence existing. The latter !\as not measured, but the profiles of velocity indicate that the flow was approximately normal for pipes. On a mass basis, the coefficients observed were 10 to 20 times larger than the coefficients for the transfer of ~
L
O4 61 0
4I 1 1 11 I
60 100 200 300 AVERAGE A I R VELOC I T Y F T. 1 S E C .
gaseous ammonia or toluene under the snnie conditions, as estimated from Gilliland’s coirelation (3). T h e coefficient is probably sensitive to the level of turbulence, and the I?sults o b t a l n e d h e r e should be applied only qualitativelj to systemsnot providing the same c o n d i t i o n s of flom-.
Figure 9. Film Coefficient of Mass Transfer
CONCLUSIONS
This research has shown that, under conDroplets of 27-micron mean diameter suspended i n air stream flowing w i t h ditions O f normal pipe n o r m a l pipe turbulence (Zone I I ) i n flow a t m o d e r a t e d u c t 1.86 inches i n inside diameter velocities, the resistance t o the transport of water droplets of 27 micron mean diameter is high near a pipe a all compared to that in the main body of the gas stream. The coefficient of mass transfer, k,, calculated from the data on assumption that the resistance resides entirely within an equivalent laminar gas film a t the wall, is 10 to 20 times as great as the coefficients of common gases under the same conditions, and varies with the bulk velocity t o the 1.17 power. ACKNOWLEDGMENT
This paper contains a part of the results obtained in an investigation in the Engineering Experiment Station of the University of Illinois on a contract with the Office of Naval Research, S o . S6-ori-71, Task Order XI, entitled “Mising of Fluid Streams.” The comments and suggestions of H. F. Johnstone and E. K. Coniings are gratefully acknowledged. NOMENCLATURE
A = cross-sectional area of test duct, length squared A,, = arbitrary constants in Bessel’s series a, = arbitrarg. constants in Bcssel’s series F = average concentration of matter suspended in air stream, weight per unit volume c = local concentration of matter suspended in air stream, weight per unit volume D = diameter of duct k , = mass transfer coefficient across equivalent gas film, weight per unit time per unit area per unit difference in concentration, or length per unit time 1 = average mass velocity of suspended matter in air stream weight per unit area per unit time
June 1951
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INDUSTRIAL AND ENGINEERING CHEMISTRY
= local mass velocity of suspended water, weight per cent area
per unit time M = mass of suspended matter transported radially per unit area r = coordinate perpendicular t o axis of duct, length R1 = first root of zero-order Bessel function of first kind = local velocity of air stream, length per unit time u = average air velocity, length er unit time z = coordinate parallel t o axis ofduct, with origin at nozzle g = distance from duct wall, length, g = D / 2 - r = eddy diffusivity, length squared per unit time e = time Jo = zero-order Bessel function of first kind J 1 = first-order Bessel function of first kind BIBLIOGRAPHY
Amstead, B. H., “Techniques for Determining Liquid Droplet Concentration in High Velocity Air Streams,” M.S. thesis, Univ. of Texas, Austin, Tex., 1949. (2) Coldren, C. L., M.S. thesis in chemical engineering, University of Illinois, Urbana, 1950.
(1)
1331
(3) Gilliland, E. R., and Sherwood, T. K., IND.ENG.CHEM.,26,
516 (1934). (4) Grimmett, H. L., “Entrainment in ilir Jets,” Ph.D. thesis,
University of Illinois, 1949. (5) Kalinske, A. A., “Investigations of Fluid Turbulence and Suspended Material Transportation” in “Fluid Mechanics and Statistical Methods in Engineering,” Philadelphia, University of Pennsylvania Press, 1941. ( 6 ) Nukiyama, S., and Tanasawa, Y., Trans. SOC. Mech. Engrs. ( J a p a n ) ,4, No. 15,86 (1938). (7) Schubauer, C. B., Natl. Advisory Comm. Aeronaut., Tech. Rept. 524 (1935). (8) Sherwood, T. K., “Mass Transfer and Friction in Turbulent Flow” in “Fluid Mechanics and Statistical Methods in Engineering,” Philadelphia, University of Pennsylvania Press, 1941. (9) Sherwood, T. K., and Woertz, B. B., Trans. Am. Inst. Chem. Engrs., 35,517 (1939). (10) Towle, W. L., and Sherwood, T. K., IND.ENG.CHEM.,31,457 (1939). RECEIVED January 3, 1951.
Preparation of Solid- and Liquid-in-Air Suspensions For Use in Air Pollution Studies R. D.CADLE AND P.L. MAGILL S T A N F O R D R E S E A R C H I N S T I T U T E . S T A N F O R D . CALIF.
A
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N OVER-ALL investigation of air Artificial smogs have been found useful i n verifying the accuracy of current pollution calls for a number of distinct knowledge of the composition of natural smogs. The preparation of atmosstudies, including meteorology, methods pheres containing gaseous additives is usually relatively simple, b u t t h e prepof collection, and physical and chemical aration of atmospheres containing dispersed liquids and solids is much more analysis, These studies reveal much difficult. This paper describes techniques for preparing such atmospheres about both the mechanism of occurrence on a continuous basis. and the nature of smog, but they do not Aerosol generators were developed, which disperse liquids by an aspirating directly explain its disagreeable effects. action and can also be used for dispersing certain solids. I n a device for conSynthetic smogs are, therefore, useful in tinuously dispersing powders a t a uniform and easily controllable rate, t h e verifying the accuracy of current knowlpowder is spread on a long brass trough which is drawn beneath an airedge of the true composition and physoperated glass aspirator. Chambers i n which t h e atmospheres are blended ical make-up of natural smog. Experiand tested are described. ments with such smogs are valuable beThe methods and equipment developed have been very useful i n air pollucause the mechanisms by which natural tion studies, and should be useful i n many more studies of dispersions i n air. smog exerts its effects are not well understood and can best be studied empirically. Synthetic smogs may be considered as atmospheres prepared prepared in this laboratory had a median particle size less than 50 microns, and many less than 1 micron. under carefully controlled conditions and containing one or more of the constituents of natural smog. These constituents DISPERSION OF POWDERS can be in gaseous or aerosol form, or both. The preparation of atmospheres containing gaseous additives of known type and The dispersion of powders into air has been discussed by a composition is usually relatively simple; the problems involved number of authors. Dautrebande ( I , 2 ) and Sinclair (4, 9 )have have been studied in detail (8). However, the preparation of described methods which depend on pneumatic dispersions. T h e atmospheres containing dispersed liquids and solids of definite physiological and optical properties of aerosols are often studied concentration and physical form is a much more difficult task. more conveniently on continuously renewed systems than on It is with the latter problem that this paper is primarily conrelatively “static” systems that change by settling and coagulacerned. The main contribution is a description of techniques for tion. The powders may be continuously dispersed a t a uniform uniformly dispersing particles into a moving air stream, as conand easily controlled rate. A relatively simple device was found trasted with the preparation of relatively static aerosols. t o be especially effective for this purpose (Figure 1). The extent to which the atmospheric dispersions can be conThe powder to be dispersed was spread on a brass trough about sidered aerosols is a matter of definition. The upper particle 1.5 meters long and 6 mm. deep which was drawn mechanically size limit for aerosols has been defined as 50 microns (9) and 1 at a rate of about 4 em. per minute beneath an air-operated glass micron ( 1 ) . Both limits are higher than those usually accepted aspirator. The sides of the trough made a 90’ angle where they for colloidal particles in general. Practically all of the dispersions came together. The aspirator sucked the powder from t h e
