I
W. E. RANZ and CLARENCE HOFELT, Jr. Department o f Engineering Research, Pennsylvania State University, University Park, Pa.
Determining Drop Size Distribution of a Nozzle Spray
) A standard test method for determining the d r o p size distribution o f a nozzle spray uses the principle of inertial impaction in a special flow system to give a relative numerical measure of size distribution. The information obtained i s useful in d e velopment and utilization o f spray systems.
NOT
MUCH ATTENTION has been paid to a simplified engineering attack on the problem of measuring drop size distributions in sprays and the development of rapid and standardized test procedures to give reproducible data. indicative of drop size. The interpretation of the data may be difficult; the results may not be as pure as a scientist desires; but the information obtained is factual and useful and may overcome many of the barriers to development and utilization of spray systems. If a test method is rapid enough, it does not have to be too accurate, but there is a product of rapidity and accuracy which
Figure 7
288
Rectangular impaction jet
limits practicability. In the case of drop sizes, this product has never been exceeded to anyone's satisfaction. Rapid sizing methods depend upon some easily measured quantity which is a function of drop size-for example, settling or inertial velocities, light scattering, light absorption, and electric charge capacity. Because the functional relationship is always complex and practical difficulties must be surmounted, none of these methods has become standardized. A standard test method is proposed for determining the drop size distribution of a nozzle spray, using the principle of inertial impaction in a special flow system. Because of the absence of an accepted absolute measurement, the reliability of the absolute values of the sizes obtained was not evaluated. Inertial Impaction Principles
Rectangular Jet Impaction System. The varying impaction efficiency of drops of different sizes is a convenient principle on which to base a test method for measuring drop size. Because inertial separation is always a problem in spray sampling and tends to superimpose itself on nearly all other sizing methods, it is logical to take advantage of the phenomenon itself as a sizing method. Knowledge and use of inertial impaction are extensive. Albrecht ( 7 ) Sell (a), Taylor ( 9 ) , Langmuir and Blodgett (4), May ( 6 ) , Davies and Aylward ( 3 ) ,and Ranz and Wong (7) have made contributions of general interest to the subject of inertial impaction and inertial separation. The literature on mist and dust collection equipment and its operation ( 5 ) is closely related. Figure 1 is a schematic diagram of the two-dimensional impaction zone chosen for the test method. Gravity acts in a direction perpendicular to the plane of the figure, and any drops falling to lower
INDUSTRIAL A N D ENGINEERING CHEMISTRY
levels experience the same air flow. If spray drops of a particular size, D, are uniformly distributed across a horizontal jet stream of width W , if the drops are initially traveling with the stream at a uniform velocity, UO, when they enter the impaction zone, and if they are not so dense that their trajectories interfere with one another, the fraction, N,, of drops impacted on an infinitely wide plate at a distance, S, away from the mouth of the jet will be a function of: N D = ( p i ~ ? / 18 ~ B W ) ' ' a D an inertial size parameter
(1)
ivm
(2)
= (9P24UO W!PlP,)
"=
an inertial Darametcr which accounts for drop motion which does not follow Stokes's law
s/w (3) a geometrical parameter accounting for the spacing of the jet
Figure 2 is a plot of the fraction of drops impacted, UT, as a function of the inertial size parameter, No, for the impaction system of Figure 1 and for various values of nozzle outlet spacing, N s . The solid lines are theoretical curves calculated by Davies and Aylward ( 3 ) for ideal air flow and Stokes law particle behavior-that is, for N p v = 0. The dashed curves are experimental curves (6, 7) for small but finite values of N p , (of the order of lo1). I t is immediately apparent that the impactor acts as a separating device. With given operating conditions and a spray of many drop diameters, drops below a certain size all escape impaction, drops above a certain size all impact, and there is but a narrow range of sizes with partial impaction efficiencies. For example, if an impactor is operating at the conditions, N s = 0.64, N p , c 0, and iVD/D = IO2 cm.-', drops larger than 46 microns hit; drops smaller than 36 microns escape entirely and are car-
ried off in the outgoing air stream. The separation is even sharper than the minimum value indicates, as over 80% of all drops smaller than 41 microns also escape impaction. Because the difficulties associated with establishing the experimental curves introduced many unknown errors, it is impossible to know completely the validity of the theoretical curves. However, the Nn’s for 50% efficiency are about what would be expected of the theoretical curves (see Figure 3). The fact that the separation appears less sharp is to be expected, because the outer limits of the jet stream are subject to turbulent deterioration (verified by water table experiments). This condition will tend to move the higher efficiencies to values of N D higher than the theoretical curves indicate. I t is impossible, however, to say categorically that the experimental curves are “truer” than the theoretical curves. The reverse statement is likely to be as accurate. Figure 3 is a plot of hTD us. Ns for various values of hrz. The separating power of the impactor is again illustrated by interpreting the ordinate scale as drop diameter. Nozzle spray drops do not always experience drag coefficients in the Stokes law range. Thus, Npe is an important parameter to consider in establishing the impaction characteristics of a jet impactor. Figure 4 is a correction factor to be applied to the N D ( N 1 = 0.5) values of Figure 3. This correction is arbitrarily taken from a curve-fitting process on the calculated curves for two other two-dimensional flows, a ribbon (4) and a cylinder ( 2 ) . As the ND’s ( N z = 0.5) of these two systems are very different and the stagnation point flow field is similar, it is probable that the correction applies equally well to jet impaction systems. Indeed, for the test method, Figure 4 is assumed to be a necessary and approximately correct factor to be applied to the characteristic inertial size parameter. A qualitative picture of the actual curves which should appear on Figure 2 for various # p i s is not difficult to establish. For a given N s there will be a group of curves for various Npg)~. The curve shown is for A?,, = 0. All other curves join this curve at N z = 0 and fan out to the right of the curve for Npo = 0 toward Nz = 1.0, passing through points a t Nz = 0.5 which are given by Figure 4. Because of its superior separating ability, a jet impaction system was chosen as the test method described here. Its success in analyzing the size range of ordinary nozzle sprays (50 to 150 microns) depends, however, on special features (see Figure 6): Jet width of several inches and an air flow system with a capacity of the order
10
N, = 0 167
0 356
06-
r -
of several thousand cubic feet per minute (to have a “cut” diameter in the range of interest when operating a t practical air velocities) Horizontal air flow in the intake nozzle and impaction zone (to eliminate the effect of gravity in the impaction direction) Rectangular intake nozzle and jet with vertical length of several feet (to prevent larger droplets from dropping onto the floor of the intake nozzle before they experience the impaction zone) Intake nozzle with entrainment length of the order of 10 feet, into which the nozzle spray can be directed (to allow the spray drops to be accelerated or decelerated to air speed before entering the impaction zone) Single-stage operation (to make analysis easier and prevent cumulative errors) Practical provisions to assure that the theoretical impaction system is achieved and the proper measurements are made (to give meaning to the data)
sharply at a certain “impactor” drop size. This cut diameter is chosen to be the drop size at the K Dfor an impaction efficiency of 50% ( N z = 0.5). This characteristic N D is taken from Figure 3, which accounts for the effect of jet spacing, and corrected by the factor of Figure 4, which accounts for non-Stokes-law behavior. The drops impacting on the plate are run off and collected and their volume is measured. The drops escaping impaction are subsequently separated from the air stream, run off, and collected, and their volume is measured. The cumulative volume fraction of the spray that is in drops smaller than the calculated drop diameter is interpreted as the ratio of the volume collected in the separator to the sum of the volumes collected in the separator and on the plate. For example, a rectangular jet 6.0 inches wide is operated at a velocity of 12.1 feet per second; the specific gravity of the sprayed liquid is 0.83; the density of the air is 0.075 pound per cu. foot; the viscosity of the air is 1.80 X poise; and the plate spacing is 4.5 inches. In a 10-minute test run 325 ml. of liquid is collected from the plate and 225 ml. from the separator. For this case,
Interpretation of Test Data
Standard Method of Analysis. O n the basis of experience and with consideration for directness and simplicity, it is assumed that the impactor will operate as though it separates the spray 0.8 rd n .5
I
Theory
0 Experiment -,---0.8
-
/ / -
U
a .
N,= 0.5
__-----0.2
a
I---
1
N, = Frociion Impacted I
0.2
0.4
,
I
06
,
,
OS
,
,
I
2
I
4
6
8
Jet Spacing Ratio, Ns= S / W
Figure 3.
Characteristic size parameters VOL. 49, NO. 2
FEBRUARY 1957
289
I
100, x Ribbon 4
I
1
I
90
Cylinder
80
70 60
50
30 40 50 60 70 Volume, Per Cent
80
Drop size distribution from impactor data
Delavan P-30 nozzle; cone angle, 8 0 ' ; flow rate, 294 Ib. mars Diesel oil per hour at 200 Ib. per aq. inch gage; orifice diameter, 0.075 inch; swirl chamber diameter, 0.1 50 inch; 6 swirl slots, each 0.024 inch wide by 0.030 inch deep
= 4.516 = 0.75
for a cumulative volume fraction of 225/(225 325) = 0.41. If the air velocitv is decreased. a smaller fraction of spray liquid is collected on the plate for a n impactor drop diameter of larger size. If the air velocity is increased, a larger fraction of spray liquid is collected on the plate for an impactor this drop diameter of smaller size. way points can be established on a size
9 X 0.07Y X 12.1 X (6/12) X 0.672 (0.83 X 62.4) (1.8 X X 1O-I) = 490 From Figure 3 N o ( N r = 0.5:. N o.~n = 0 ) = 0.46
+
=
for Using the correction of Figure Npo = 490, Nn(characteristic) = 0,46 X 1.25 = 0.575 But also by definition (Equation 1)
4
(0.83 X 62.4) X 12.1 iVD(characteristic) = ( 1 8 X(1.8 X 10-4X0.672X10-1)X(6/12!i1'2 =
78.8D(cm.)
Entrainment Channel and
Figure 6.
(12
x
2.54)
w
D(impactor drop diameter) = (0.575178.8) cm. = 73 X 10-4cm. = 73 microns
I
D(cm.)
distribution curve such as Figure 5 . Another way of varying the impactor diameter is to vary the jet width. For represents the Same velocity a larger a larger D.
Whence
290
10 20 Cumulative
Figure 5.
Figure 4. Correction factor to be applied to characteristic size parameter to account for non-Stokes-law behavior of drop motion
it's
5
\
Separator
Impactor
Plate
Plate
\
Spray Sector
Spray Nozzle
Channel
Floor
Diagram of apparatus used for development tests
INDUSTRIAL AND ENGINEERING CHEMISTRY
Presumably, if the practical variations in W a n d v g are wide enough, the cumulative volume (or mass) distribution curve can be drawn over its full range. It is evident from Figure 5 that at the very least the test method can indicate a volume median diameter and the relative spread of sizes (slope of line). Equipment Used for Development Tests
Figure 6 is a diagram of the apparatus used for development tests. It consisted of a liquid flow circuit, slot system for sectioning and sampling the spray, horizontal entrainment channel and nozzle, impact plate, case, separator, orifice meter, air exhaust system, and various drainage channels and tubes for collecting spray liquid. A schematic diagram of the liquid flow system is shown in Figure 7.8. Diesel fuel was the fluid used in all tests. (To prevent drop size change by evaporation, it is important that the test liquid have a very low vapor pressure, less than about one tenth thar: of water.) This oil had a specific gravity of 0.83, a kinematic viscosity of 2.79 centistokes (100' F.), and a surface tension of 24 dynes per cm. (70' F,). The oil was transferred from the sump under the slot box to the nozzle via a small gear pump, filter, bank of Fischer and Porter Flowrators with capacities of 68, 515, and 2000 pound mass per hour of Diesel oil, Bendix-Stromberg multiple plunger, variable-flow pump driven by a 3-hp., 870 r.p.m. motor, designed originally for gasoline injection, and accumulator. The nozzle pressure was measured by Bourdon-type gages connected into a tee about 6 feet from the spray nozzle. Copper tubing 1/4-inch was used for all high pressure lines.
Details of the slot system for sectoring and sampling the spray are shown in Figure 7,B. The spray nozzle was SUSpended in a box 18 inches square by 8 feet high from a steel rod mounted above the entrainment channel. A combination of two blocks, a rod, and a pivot permitted alignment of the nozzle in any direction. The slot system was made of two movable 12 X 8 inch aluminum plates with 2-inch-wide, sharp-edged plates mounted with piano hinges on the slot edge and aimed into the spray. Both the width of the open slot and the angle of the side plates could be varied. The depth of the slot was set by another plate, and all plates had vertical drain grooves. Sprayed liquid not escaping through the slot impacted on the plates and box and drained to the sump. The entrainment channel and nozzle was 6 inches wide, 29l/2 inches deep, and 6 feet long. I t had a flared inlet, and the nozzle extended 6 inches into the impactor case. For test controls spray liquid collecting on the right and left walls and on the floor of the channel was drained and measured separately. An impact plate, 24 inches wide by 36 inches long was mounted 4.5 inches from the channel outlet. V-shaped gutters, 3 / 4 inch wide, mounted on each side of the plate, directed run-off liquid to a floor gutter and two drains. Spray drops escaping collection on the plate impacted on the walls of the case, settled onto the floor of the case, or were removed in the separator. The case was a rectangular box, 3 X 3 X 4 feet, with a sloping floor and a drain trough underneath. The separator was essentially a second impact stage and occupied the rear end of the case. Velocities in the separator jet were three to six times that of the nozzle and the width was 1 inch or one sixth that of the nozzle. Thus, the separator could remove all droplets remaining in the air stream having diameters larger than about one sixth the cut diameter of the first stage. Under these conditions the fraction of spray liquid escaping through the exhaust system was usually less than 1% and negligible for test purposes. The impact plate for the separator was 20 inches wide, with large enclosed gutters to prevent re-entrainment at the high air velocities. The cross-sectional area of the separator nozzle could be set at two values by a damper which could be turned to cover half the available area. Air from the case was exhausted via a 10-inch duct through a standard 6.25inch ASME orifice meter with radius taps and an exhaust fan (Buffalo Forge exhauster, size 25, rated a t 12 inches of water, 1500 cu. feet per minute, 5 hp.). The air flow was controlled by means of a damper a t the fan inlet. The largest pressure loss occurred across the separator nozzle and across the orifice (several
Spray Sector
ui’ /’,! &a
Adjusting Screws
rn Qi 9 0 -psig. IO0
Bypass
Reservoir
Filter Filter
Pump
B
A
Figure 7. A.
liquid flow system.
6.
Schematic diagram
Slot system for sectoring and sampling hollow cone sprays
inches of water a t the highest velocities). The pressure difference across the separator made it necessary to seal the separator collection bottle and vent it to the case behind the separator plate.
Experimental Procedure T h e alignment of the nozzle and the setting of the slots can influence the test results. The procedure followed was to set the nozzle orifice 4 to 6 inches behind the slot edges and to open the slots to the geometric slot width where a point orifice could “see” the sides of the entrainment channel a t its exit. Eighteen inches was selected as the distance between the slot box and channel inlet. The nozzle was aligned so that the axis of the spray sheet passed horizontally through the slot and so that the center line of the sector paralleled the center of the channel about 3 inches below the channel ceiling. To check alignment, a trace pattern of the spray at the entrainment channel inlet was obtained by momentarily exposing a paper target in the inlet. The type of setting used for pressure swirl nozzles is shown in Figure
7,B. The slot setting and nozzle alignment were given a final check during stabilization and test runs by noting the quantities of liquid collected on right and left walls and on the floor of the channel. For reliable data points two important criteria were established : 1. The wall drains should drain more than 1% of the total sample flow (to assure that the channel is filled from wall to wall) and less than 8% (to prevent the walls from acting too much as a prior impaction stage), 2. Less than 2% of the total sample
flow should be collected from the channel floor (larger percentages indicate excessive settling and occurred below a limiting air velocity or, equivalently, above a limiting cut diameter), Apparently, any combination of alignment and slot settings (between about one half and two times the geometric slot width) which gave test data meeting these criteria also gave distribution curves which appeared well behaved, reproducible, and comparable. The geometric slot width was selected as the most convenient setting. After a nozzle had been flow-calibrated, mounted, and aligned, a routine procedure was followed. The air flow was set by the control damper to give a particular cut diameter, and the nozzle pressure was fixed a t a particular pressure. All sampling valves were positioned to return samples to the reservoir. Because equilibrium had to be achieved in liquid holdup, runoff, and collection, the apparatus was allowed to run a t constant settings for a stabilization period of from 10 to 30 minutes. During this period, the nozzle alignment was checked. The sampling valves were now turned to run the liquid into graduated cylinders for a timed test period. Ten minutes were found to be satisfactory for nozzles spraying in excess of 100 pounds per hour. The test period was then repeated. If the data were reproducible, the test was complete. Deviations were an indication that the run-off process had not yet stabilized, and the test period was repeated until the data were reproduced. The air flow was reset for the next cut diameter and the test procedure VOL. 49, NO. 2
FEBRUARY 1957
291
repeated for another point on the distribution curve. At the same sample flow rate the stabilization time could usually be reduced for subsequent points. Running time for establishing each point varied from 20 minutes to one hour. An example of the reduction of test data to give cumulative drop size has been given. However, liquid collected from the wall and floor drains is added to that collected by the plate when the cumulative volume is calculated. This action is equivalent to assuming that the channel acts like a prior impaction stage with a cut diameter very much larger than that of the jet impactor. Limitations of Test Apparatus
Figure 5 is an example of the type of information obtained from impactor data. The center portions of three cumulative size distribution curves are shown for the same nozzle operating a t three different pressures. The volume median diameters can be read directly from the curves. These are found to be inversely proportional to the 0.3 power of the nozzle pressure. The slopes of the lines indicate the relative spread of sizes, and it appears that the size distribution becomes slightly less uniform as the pressure increases. Figure 5 also illustrates the limitations of the apparatus used for development tests. Points below 60 microns could not be obtained because jet velocities higher than about 20 feet per second were beyond the capacity of the exhaust system. Attempts to obtain points above 90 microns (00 = 7 feet per second) gave excessive settling on the channel floor. Presumably, to extend the curves to 150 microns, the test channel would need to be a t least 6 feet deep (to satisfy the limitations of settling) and at least 12 inches wide (to obtain the proper cut diameter with velocities no lower than 5 feet per second). The capacity of the exhaust system required to reach a certain maximum cut diameter is roughly proportional to the fourth power of that diameter. Sectoring Nozzle Sprays
Entrainment Conditions. The problem of obtaining and analyzing a representative sample of a nozzle spray is in many ways less difficult with the impactor method than with most other methods of drop size analysis. A portion of the spray pattern is cut out of the total spray, and all of that sample is made to enter the entrainment channel. The cumulative volume must be collected from the walls and floor of the channel, from the plate, and from the separator. There is little chance for biased sampling, and the number of drops sampled is effectively infinite.
292
The flux distribution of the sectored spray at the outlet end of the entrainment channel appears at first glance to be a practical problem in impactor operation. If a representative sample can be made to issue through a slot system and fill the end of the channel from wall to wall, so that the flux density of a given size drop is nearly uniform across the channel, the results of impactor analysis should have the quantitative meaning of the theory. But how can this condition be met? Fortunately, the problem is not a serious one. Two factors alleviate the errors which may arise when the channel is not completely filled and when it is overfilled in the lateral direction. Impaction efficiencies of that portion of the spray traveling down the center of the channel will show much the same characteristics as that of the total spray. The cut diameter at the center line can be no less then that given by the mini= 0. Furthermore, mum 1VD at theory (3) indicates that the apparent cut diameter of the test impactor would have been decreased by no more than 3% if the channel were only 60% filled. If the spray sector is spreading laterally and some of it is able to strike the walls of the channel-that is, the channel is overfilled-the walls act like a prior impaction stage with a cut diameter very much larger than the jet impactor. Drops which escape the wall and plate are included in the separator fraction as the proper cumulative volume fraction for the cut diameter of the impactor plate. These two factors are apparently the reason why the slot system of Figure 7,B, could be varied over a relatively wide range and give nearly the same size distribution curve for hollow cone sprays. Applicability of the spray impactor to different spray patterns must be decided on the basis of flux measurements with a Patternator and the ability to design a sectoring system which will allow the spray sample to be distributed across the intake nozzle. Although the test impactor has been used with various types of spray nozzles, only applications involving hollow cone sprays are discussed here. Proper entrainment of the spray sample is another operational problem on which rests the success of impactor analysis. All drops should be traveling
a t the air velocity when they enter the impaction zone. If the operator had an independent means of judging the spray velocity a t various distances from the spray nozzle, he could use a short inlet jet and adjust the distance between the spray nozzle and the impactor plate to equalize air and spray velocities. Because little is known about spray velocities and because they vary considerably through the spray, an entrainment channel was employed as a practical means of eliminating the distance between the spray nozzle and the impactor plate as a factor in the analysis. The channel length chosen was the result of compromises based on calculations of the deceleration of individual drops from initial spray nozzle velocities. The time required to decelerate a single drop less than 100 microns to within 1% of the air channel velocity (which was of the order of 10 feet per second) is never more than 0.2 second. The relative stopping distance traveled during this time is never more than 4 feet. This adds up to an entrainment channel length of 6 feet. The spray stream acts like a density current, and these calculations may be deceptive. There is, however, an operational check. If the impactor air velocity is changed and the volume fraction collected in the separator remains unchanged, it is probable that the velocity of the spray stream itself is controlling the impaction velocity, and the entrainment conditions have not been met. Another theoretical condition for analysis is that the air stream must have a nearly uniform velocity as it issues from the entrainment channel into the impaction zone. The flared inlet opening was found to be essential to prevent flow separation at the entrance and large eddies in the channel. Such an inlet flow is initially uniform and remains so until the boundary layer on the walls grows thick enough to destroy that uniformity. The theoretical impaction system specifies an infinitely wide plate, but simplified calculations show that an impactor plate with a width greater than 3T.t’ is infinite for all practical purposes. Deterioration of the edges of the jet after it leaves the nozzle is a far more serious limitation to the obtaining of the minimum size for complete impaction.
6 A = 1.5
ing magnitude of error caused by i m p e r f e c t size separation in impactor
INDUSTRIAL AND ENGINEERING CHEMISTRY
6 :1.0
2E 5
.E
=e
0.9 I lo
I
I.5
Dcf Dwnd
210
2.5
The apparatus described here employs only one configuration and space setting to obtain a particular size range of practical interest. An Nsof 0.75 was chosen arbitrarily, because it provides a large cut diameter for a small channel width and an operating point a t a compromise position midway between experimental and theoretical points. An Ns of 0.3 would appear to give a sharper cut of the size distribution but a t a smaller characteristic drop diameter. Future development tests, where both Ns and W are varied, are desirable, but such tests should be preceded by a lengthly numerical calculation which determines accurately the effect of N p g on N z for various values of Ns and N D . Validity of Characteristic Diameter Concept
If the impactor is used on a spray with a uniform drop size, the tests will show a distribution of sizes instead of one size. Although uniform sprays are nearly impossible to obtain, it is never the less important to investigate the magnitude of the error introduced by the fact that the separation of sizes is not a completely sharp separation and that there is a range of sizes with varying impaction efficiencies. As a generalization of the correction cannot be made, an approximation to the correction is developed for a particular situation as a guide to the development of such corrections. Consider again the impactor conditions used to establish the size distributions shown in Figure 5 and in particular the conditions for the example point at 73 microns and a cumulative volume of 41%. The corrected characteristic N D for this test was found to be approximately 0.57 at N z = 0.5. The full efficiency curve for the particular test conditions would begin at No = 0.38 and NZ = 0 (see Figure 3) and pass through N D = 0.57 a t NI = 0.5. Accidentally, the experimental curve for N , = 2.7 appears to be something like that to be expected for the test conditions (which are far different from those of the experimental curve). As a linear approximation of the Sshaped impaction efficiency curve for the test example, let NO = 0.40 at NI = 0, N D = 0.57 a t N z = 0.50, and ND = 0.74 at NI = 1.0, such that N I = 0 for D
‘
J (8/+)exp(
+ ln(0 74/0.57) [l
-
1 Tr
0.57 exp(y - yc) - 0.40 0.34
6
exp( - V ) d Y
ln(0.40/0 5 7 )
I
< (0.40/0.57)D0
Nz = L 57(D/Dc) - 0’40 for (0.40/O.57)Dc< 0.34 N I = 1.0 for (0.74/0 .57)D,
