ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
Xo'
of liquid water and liquid organic component a t eutectoid temperature, Ib. /hr. = IPb - p a [ : lb./cu. ft. = latent heat of vaporization of condensate of a single component vapor, B.t.u./lb. = latent heat of vaporization of organic component, B.t.u./lb. = latent heat of vaporization of water, B.t.u./lb. = B.t.u./lb.
p, pa
= viscosity of organic film, lb./(hr.) (ft.)
p
=
pa
= density of organic component, lb./cu. f t . = density of water, lb./cu. ft.
hxu
= heat transfer coefficient determined by Equation 2,
Ay
h,
using assumptions similar t o those implied in Nusselt equation for single component condensation, B.t.u./ (hr.) (sq. ft.) ( O F.) = experimentally observed heat transfer coefficient, B.t.u./(hr.) (sq. f t . ) ( " F.) = heat transfer coefficient of organic component calculated from Nusselt equation, B.t.u./(hr.) (sq. ft.)
X
ho'
/ o n 1 I 1 .I
= heat transfer coefficient of condensing steam, B.t .u./
(hr.) (sq. ft.) ( O F.)
= water side heat transfer coefficient, B.t.u./(hi.) (sa.
ft.) ( O F . ) thermal conductivity of condensate film, B.t.u./(hr.) (ft.) ( O F.) = thermal conductivity of organic film: B.t.u./(hr.) =
AP
A, Ah
= difference between surface tension
U
pb
=
(ft.) ( O F.)
= thermal conductivity of water, B.t.u./(hr.) (ft.) ( O F.) = distance from top of vertical condenser surface t o any
kb
L
= =
+2
point, it.
density of condensate, lb./cu. ft. function representing net effect of water drops on film of organic condensate function representing "disturbing" effect of water drops function representing "blanketing' effect of water drops
= weight rate of condensation of organic component on
literature Cited
test tube, lb./hr.
= weight rate of condensation of water on test tube, lb./hr. = rate of heat transfer by condensation of organic vapor
(Kirkbride equation), B.t.u./hr. = rate of heat transfer by condensation of steam (Kirk-
bride equation), B.t.u./hr. = principal radii of curvature at a point on the interface
of two immiscible liquids (Equation 8) = inside wall temperature minus '/z (mean wall-to-water temperature difference), O F. = maximum thickness of organic film a t a given height, ft. = over-all heat transfer coefficient, B.t.u./(hr.) (sq. ft.)
V,
x
(, O F-., " 1 = water velocitv, ft./sec.
( m a " h h.:)i'2 (Figure 2 ) m5 p a k zl, zz = thickness of materials having conductivity ICl and k z , respectively (Equation 9), f t . Y = 1 (Figure 2) = -A-y S A P
g p4
.""
= distance t o a point on interface of two immiscible liquids from a given datum (Equation 8 ) , ft.
2
yL
At
= interfacial surface tension, lb./hr.e = average temperature drop across condensate film,
eutectoid temperature minus average tube surface temperature, O F.
(1) Adam, N. K., "Physics and Chemistry of Surfaces," Oxford, The Clarendon Press. 1930. (2) Cooper, A . H., Morrison, R. IT.,and Henderson, H. E., IND. ENG.CHCM., 34, 79 (1942). (3) Edwards, D. ii., Bonilla, C. F., and Cichelli, M. T., Ibid., 40,
1105 (1948). (4) . . Hazelton, R., and Baker, E. M., T,.ans. Am. Inst. Chem. Enars.. - . 40, l(1944). ( 5 ) Jeffrey, Joseph 0.. Cornel1 Univ., Eng. Sta., BuU. 21 (March 1936). (6) Kirkbride, C. G., ISD. EM. CHEM.,25, 1324 (1933).
(7) Kolb, F. J., and Weeks, J. R., h1.S. thesis in chemical engineering, Massachusetts Institute of Technology, 1939. (8) Mueller, A. C., and Baker, E. M., 1 s D . ENG.CHEM.,29, l\Q67
(1937).
(9) Nusselt, W., 2. Trer. deut. Ing., 60, 541 (19183. (10) Palmer. G.. IND.ENG.CHEM..40. 89 (1948) (11) Parr, S. W., Engineer, 131, 559 ( 1 9 5 1 j . ~ (12) Perry, J. H., ed., "Chemical Engineers' Handbook," 2nd ed, New Yolk, McGraw-Hi11 Book Co., 1941. (13) Tobias, M.,Ph.D. thesis, University of Minnesota, 1950. (14) Tsao, U., and Baker, E. h l . , 1xn. Exvo. CHmr., 32,1115 (1940). (15) Wald, A . , Ann. Math. Stat., 11, 284 (1940). (16) Weeks, J. R., S.B. the&, Massachusetts Institute of Technology, 1939. RECEIVED for review July 27, 1953.
ACCEPTEDFebruary 11, 1964.
Measuring Drop Sizes in Sprays E. H. TAYLOR
AND
D. B. HARMON,
JR.'
College o f Engineering, Universify o f California, 10s Angeles 2 4 , Calif.
V
ARIOUS methods of measuring drop sizes were considered in
detail before the instrument which is described in this paper was built. The frozen drop method of Longwell ( 4 ) held the greatest promise of providing the following desired characteristics: 1. The whole spray should be measured-no sampling technique was considered suitable. 2. Individual drops should be caught so that they could be examined. 3. The measuring technique should be devised so that the whole process of running the instrument and making all necessary measurements was almost automatic and very rapid. 4, The accuracy of most other systems should be equaled if not excelled.
I n addition, it was desired to construct the initial model of the 1 Present address, D. B. Harmon & Associates, 409 Nalle Bldg., Austin, Tex.
July 1954
instrument as cheaply as possible. This led to certain short cuts in the design which lowered the efficiency of the instrument. Water was chosen as the working or spraying fluid. Therefore, it was necessary to have a catching liquid into which the water could be sprayed that could be kept below the freezing temperature of water. The possibility that the larger drops might break on striking the surface of the catching liquid had to be accepted, though some tests were made with drops 2 mm. in diameter striking the catching liquid a t about the velocity expected from the spray and none of the test drops broke. The catching technique was designed to minimize the possibility of breakage of drops by spraying the water upward and catching the liquid a t the top of its travel. Instrument Combines Drop Freezing Technique and Stokes' l a w Separation
A cross section of the final design is shown in Figure 1.
INDUSTRIAL A N D ENGINEERING CHEMISTRY
1455
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT The water is sprayed over the edge of box a. The water lands in the catching liquid, b, which is hexane-cooled to about -20' C. with dry ice xhich is kept in the space within the boy and around the liquid pan. The drops freeze very quickly and fall to shutter e. When all the drops are resting on the shutter, the shutter pull, d, is opened, which allows the dro 8 to descend through the hexane to a scale pan, e. The drops falrapproximately according to Stokes' law (neglecting interaction effects) and the largest drops arrive first at the scale pan. The weight on the scale pan is transferred to a cord, ,f, which passes around an aluminum cylinder, g, and then to a spring, h, which balances the force on the scale pan. The slight movement of the disk, g, is amplified
I
Figure 1.
,%-
The weighing method used in this instrument could be adapted to the molten wax spraying system of the Shell Petroleum Co., Ltd. (W,3). A different catching liquid would be necessary. but cooling of the catching liquid n,ould be unnecessary. Of course, this inconvenience would be replaced by the nece3sity of heating the wax and the nozzle. The instrument as built has several flaws which are not inherent in the design. The shutter allows soine of the drops to fall through before the shutter is pulled. This allows a slow drift a t the scale pointer so that the proper zero point is difficult to mark. It is also hard to keep the hexane a t a uniform temperature, which is necessary so that calculated values of density and viscosity may be used. Since the top of the hexane bath is the warmest and the bottom the coldest, there are no apparent convection currents generated. The fumes from the hexane and dry ice are obnoxiouP and made an exhaust blower almost a neoessity. With the present shutter many of the drops are trapped and do not fall through the shutter. This means that a separate differential density measurement is necessary to use in Equation 1 for drop size measurments. If all the drops injected into the liquid catching medium went through the shutter a t the right time, an automatic differential density measurement could be
Cross Section of Drop Measuring Instrument
by the pointer, i, which moves over a measuring scale, j, calibrated to indicate the differential weight on the scale pan. The weight on the pan versus time relationship is determined by use of a stop watch, though in a more complex instrument this could easily be done electrically with greater accuracy. The weight falling on the pan can be transformed simply into equivalent drop diameters and total number of drops a t each diameter by use of a drag coefficient which depends upon the velocity or Stokes' law for the smallest drops. It is then necessary to convert the measured sizes to true drop sizes by allowing for the density difference between the ice and the water which was sprayed. The ratio of pointer tip movement to pan movement is 10 to 1. The pan moves approximately l/, inch. The total depth of fall of the drops is 12 inches, which gives a possible error of about 37, from pan movement. The exact relationship may be calculated a t any point if desired. Method Is Rapid and Requires N o Special Sampling cf Spray
The instrument fulfils the basic design criteria because the whole spray is caught in the upper pan, yet individual drops can be taken out a t this point and examined. During the various trials, examination of individual drops never showed that two or more had stuck together. The drops can be removed after weighing simply by removing the shutter and withdrawing the scale pan on which the drops remain. Repeated runs could be made in a short time if scale sheets were prepared in advance. The measurements are easily made. For a complete run, it took about 10 minutes to accumulate the desired data for the drop size range of the tests which m-ere made. This does not include set up or takedown time, which is extensive since the hexane is siphoned from the catching pan. It appears from the brief experience gained that a more advanced model 11o d d permit several runs under different conditions to be made in a single day. The data could then be reduced to the desired form a t a convenient time. No elaborate washing or sieving techniques are required. All the desired information appears on the marked scale sheet with total weight versus time recorded on it.
1456
l n r Aftrr St
Figure 2.
Weight on Scale Time versus Pan mental Run
for Experi-
Measured differential density = 0.1 15 gram/gram HzO
made from knowledge of the flow rate from the nozzle under the experimental conditions. The shutter is of thin metal and when it is pulled it does not appear to agitate the hexane sufficiently to change the test results appreciably. The scale pan in the hexane appears to provide about critical damping. Theoretical and Experimental Test Results Show Reasonable Agreement
Only one useful run and differential density measurement have been made. Even in this case, only a small amount of water was sprayed into the apparatus since a higher differential density was expected than actually was found. The results are shown in Figures 2 and 3. Figure 2 shows the total actual water weight on the scale pan versus time; Figure 3 illustrates the total water weight versus the computed drop diameters for the run. Preliminary calculations indicated that the Reynolds number range was from 1 to 25, I n this region, the average drag coefficient is about 1.3 times that given by Stokes' law. The drop diameters, d d , of Figure 3 were, therefore, found by equating the
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
Vol. 46,No. 7
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT differential weight of the drops in the liquid to the drag on the drops, using the average drag coefficient. The equation is
and the supporting liquid, the liquid viscosity, the depth of fall, and the square of the diameter of the drops. For the instrument described, times of fall would range from about 4 minutes for drops 100 microns in diameter to about 27 hours for drops 5 microns in diameter. These times could be decreased by altering
where pd and p t are densities of the drop and the liquid (hexane), respectively, v d is the average velocity of fall, and g is the gravitational constant, all in consistent metric units. The drag coefficient, C,, is given by
where
Y
is the viscosity of the liquid.
The computed mean diameters from the data of Figure 3 are Sauter mean diameter = 0.0828 em. STolumetricmean diameter = 0.0516 ciii.
2
These figures should be compared viith the calculated theoretical value which is obtained by the following series of equations (1): diet
=
ddrops
fi dnomle 2
(3)
1.89djet
(4)
=
I-
I
0
ddrope
= 0.866 (1.89) (0.03048) = 0.0499 em.
(5)
which are valid for an inviscid liquid issuing from a nozzle of sufficient length to establish steady laminar flow in the nozzle. For an actual liquid the theoretical drop size would be slightly larger. The various possible sources of difference or error have led to a mean drop diameter error of approximately 6%. The possible errors or differences are in the choice of average drag coefficient, which is probably the largest single error, the variation in scale pan distance, calculated hexane viscosity'and density, variation of theoretical value from Equation 5 due to viscosity effects, and marking errors on the scale. A larger total weight on the scale would considerably reduce the last possibility for error. For smaller drop sizes than those measured in this experiment, the error would be reduced as the drag coefficient more closely approaches the Stokes' law value, allowing a better estimate of its value from drag coefficient graphs, Step by step calculations using exact drag coefficients were not undertaken because the uncertainty of the theoretical result may approach the total error due to use of an average drag coefficient. It is expected, however, that such calculations might result in calculated experimental results several per cent closer to the theoretical value, The time required for the frozen drops to fall through the liquid is a function of the density difference between the drop
Figure 3. Calculated Drop Diameters for Experimental Run Nozzle diameter = 0.03048 cm. Nozzle length = 2.03 cm.
the depth of fall of the drops. For drops of this sixe range a 6inch depth might be appropriate. This aepth of fall would give times from 2 minutes to 13.5 hours. It is not believed that it would be practical to test for smaller size drops, since at any point the total remaining weight of drops falling is known and the curve of drop number versus size can be easily extrapolated to obtain this information. Drops in this smallest size range rarely constitute an appreciable fraction of a spray. Literature Cited (1) Harmon, D. B., Jr., Ph.D. thesis, University of California, Los
Angeles, 1953. (2) Hopkins, J. L., Shell Petroleum Co., Ltd., Tech. Rept. I.C.T./6
(1946).
(3) Joyce, J. R., Ibid., I.C.T./7 (1946). (4) Longwell, J. P., D.Sc. thesis, Massachusetts Institute of Technology, 1943. RECEIVED for review September 8, 1853.
ACCEPTEDMay 3, 1954.
END OF ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT SECTION
July 1954
INDUSTRIAL AND ENGINEERING CHEMISTRY
1457
