Sprays Formed by Flashing Liquid Jets
RALPH BROWN and J. LOUIS YORK
University of Michigan, Ann Arbor, Michigan Liquids forced from a high-pressure zone into a low-pressure zone often cross the equilibrium pressure for the liquid temperature and disintegrate into a spray by partial evolution of vapor. The ordinary aerosol dispenser is a common example of this operation, and flash boiling i s another. This paper reports on a study of the sprays formed by such a process and of the mechanism of spray formation. Sprays from water and Freon-11 jets were analyzed for drop sizes, drop velocities, and spray patterns. The breakup mechanism was analyzed and data presented to show some of the controlling factors. A critical superheat was found, above which the jet of liquid is shattered by rapid bubble growth within it. The bubble-growth rote was correlated with the Weber number, and a critical value of the Weber number was found to be 12.5 for low-viscosity liquids. The mean drop size was also correlated with Weber number and degree of superheat. The spray from rough orifices and sharp-edged orifices was compared with sprays produced from cold liquids by other techniques and was found to be comparable in all respects except temperature.
Liquids moving isothermally from a high-pressure zone to a low-pressure zone may cross the bubble-point curve, attaining final equilibrium wholly or in part as a vapor. This action has long been the basis for flash evaporation and for pressure dispensing of aerosols, such as insecticides, hair sprays, and many other household materials. Thermodynamic studies of the process have been made, but practically nothing appears in the literature regarding the physical process of disintegration of the liquid mass into drops and vapor. This paper reports on a study of the mechanism of spray formation by flashing of a cylindrical jet and on the spray formed by this process ( 1 ). Experimental techniques include highspeed photography of the breakup zone and of spray, with drop sizes and velocitid computed from a photographic analytical procedure. Most of the data are for superheated water injected into the room atmosphere, but some data on Freon-11 (trichloromonofluoromethane) are considered. The voluminous literature on sprays includes a reasonable number of articles on mechanism of spray formation, but all of these describe systems for which aerodynamic forces and surface tension are the key forces in disintegration. The range of flow rates, velocities, and stream sizes employed in this study provides poor spray formation with cold water as the liquid medium, but a satisfactory spray with superheated water. This indicates that the normal relationships of dimensionless groups and variables is not effective when bulk vaporization is a factor in the spray formation. Many of these
relationships were examined with the data from flashing jets in an attempt to organize and to explain the data, and some were helpful. Rayleigh ( 2 ) analyzed the instability of liquid jets which disintegrated by surface tension forces, and Weber ( 3 ) extended the analysis to include aerodynamic forces. Weber found that the magnitude of the disruption increases with a dimensionless number, now called the Weber number, one form of which is
The Weber number may be considered as the ratio of the impact stress of the gas phase on the interface to the normal stress caused by the interfacial tension acting on any cross section. For low-viscosity fluids the type of disintegration depends upon the Weber number (4).When N,, < 0.2, only the pinching-off action of interfacial tension applies; from 0.2 < N w a < 8, the action is a sinuous distortion which whips the jet into segments; and for Nw,> 8, the action is more violent with ligaments of fluid separating from the jet and atomization occurring. At even higher Weber

numbers the masses and drops of liquid formed originally from the main jet will themselves be broken up still further; that is secondary atomization will occur. Thermodynamically, flashing results from suddenly lowering the pressure on a liquid until the bubble point is reached. Further lowering of the pressure will leave the liquid superheated or at a temperature higher than the saturation temperature corresponding to the pressure, and the liquid tends to convert to a vapor to regain equilibrium. Under adiabatic conditions the vapor formed can obtain its latent heat of vaporization only at the expense of the sensible heat of the remaining liquid, Equilibrium will be reached when the fraction of liquid converted to vapor has extracted enough energy from the residual liquid to cool the two phases to the saturation or equilibrium temperature. Flashing can also occur when a solution of gas in liquid is suddenly reduced in pressure below the bubble point. As the gas comes out of solution, it will require heat which can come only from cooling of the residual liquid. When the phase change has restored equilibrium, the process ceases. The generation of vapor in either case is not restricted to the surface of
Fig. 1. Liquid injection system.
Ralph Brown is with Scott Paper Company, Philadelphia, Pennsylvania.

Vol. 8, No. 2

A.1.Ch.E. Journal

Page 149

TYPE A

TYPE B ROUGH rlo

TYPE C EXTREMELY ROUGb el0
TABLE DESCRIPTION NOZZLES 1. OF

SHARP-EDGED

0 0004

Diameter, Tme

Length, in.

L/D 0.8 09. 09. 3

Roughness (Gin. RMS)
Fig. 2. Experimental nozzle types.
0.030 0.040 0.080 0.020 0.031 0.040 0.060 0.020
0.030 0.040 0.080 0.020 0.025 0.035 0.054 0.057

14-t & 1 3000

0.0004 (est.) 0.0004 (est.) 0.00035 0.00042 0.12
the liquid phase but can originate at any suitable nucleus in the liquid phase. After initial nucleation of the bubbles the gas will be more likely to form at the bubble surfaces, causing rapid growth of the bubble and a corresponding physical displacement of the adjacent liquid. The displacement can cause disintegration of unconfined liquid, analogous to that resulting from bumpin of superheated liquid in boiling flas s.
TABLE MINIMUM 2. INITIAL RADIUS BUBBLE FOR GROWTH WATER IN UNDER ATM. 1

T o ("F.)

2.90 220

0.605 266

0.470 275

0.378 284

0.300 293

0.245 302

0.201 311

EXPERIMENTAL EQUIPMENT

Flashing can occur in any configuration of liquid, either lying quiescent in a pressure tank or being ejected through some nozzle configuration into a low-pressure region. In an attempt to simplify the geometrical system this study was conducted on cylindrical jets issuing from simple circular openings, with no effort to induce swirl, twist, or internal turbulence in addition to that which is acquired by flow through ordinary tubing. Figure 1 shows the general piping diagram. The pressure tank could be operated with steam pressurization on hot water or air or gas pressurization on other fluids. The heat exchanger could be operated as a heater or cooler to control the liquid temperature fed to the nozzle. Maximum pressure on the system was about 300 lb./sq. in., but this was rarely employed, as the purpose of flash spraying is to reduce the pressures needed to produce a good spray. The three types of nozzles employed are shown in Figure 2 and described in Table 1. Type A was a sharp-edged orifice and gave a smooth-surface jet with cold water, which was stable for more than 100 jet diameters and then disintegrated by surface-tension action as discussed by Rayleigh (2). Type B was a drilled hole with a length-to-diameter ratio of about

1.0 and a roughness of about 20 L in. It flashing are in a narrow range of about , delivered a rough-surfaced jet with cold 5F. for each flow rate in each nozwater, appearing turbulent but being quite zle, although the limiting temperatures stable for several hundred diameters bs- shift in absolute value for each change fore eventually disintegrating by surfacetension action. Type C was a nozzle of in variable. The shuttering temperaType B with glass beads ( 170 to 200 mesh) ture is the name given to the mean cemented in the nozzle orifice to provide an value of the limits between no signifiextremely rough surface. With cold water cant effect on the jet and rather comType C gave a ragged stream with liga- plete disintegration of the jet. Data on ments torn from the main jet as it emerged the sprays produced showed little gain from the orifice. in breakup of the jet by further inThree liquids were sprayed: water, creases in the temperature; thus the Freon-11, and water through which carbon dioxide gas had been bubbled for 20 min. shattering temperature indicates a at 90 Ib./sq. in. Practically alI runs dis- unique action on the jet and is a distinct and reproducible effect. cussed here were with water. The breakup zone and the spray were A series of sample photographs studied by high-speed silhouette photog- shows best the effect of changing the raphy ( 5 ). Light flashes of about 1 EC. sec. nozzle type and size. Figure 3 shows duration were delivered. Photographs were a Type A nozzle with orifice diameter taken with a magnification of 10 X. Velocity measurements were made by double of 0.040 in., and Figure 4 shows a exposures with a time interval of 22.4 Type A nozzle with an orifice 0.030 in. in diameter. The smooth water jet p sec. between the two exposures. The distance between two images of a drop gave seems to explode suddenly and vioone component of its velocity. lently, and repeated photographs show Spray analyses were made on images of that the location of the disintegration the negatives projected onto a ground-glass varies rapidly and randomly from 0.1 screen at 10 X, a total magnification of to 0.5 in. downstream from the orifice 100 X. Then the drop images were counted into size classes from which the distribution for the larger jet. The smaller jet discould be shown and the average sizes cal- integrates further downstream and in d a t e d. The depth of field and the as- a manner which cuts the jet into dissociated degree of blur of the images in tinct sections which disintegrate more each size class was known; therefore the slowly. The center of Figure 4 is about count was for the drops in a known 1 in. from the nozzle. volume of spray. By multiplying the numFigure 5 shows a jet from a Type B ber of each size by the average velocity of nozzle 0.031 in. in diameter, and Figthat size a weighted average resulted which corresponded to the distribution of drops moving through the sample volume in a unit time.

JET BREAKUP

Fig. 3. Flashing jet 1OX. Type A, D = 0.040 in., P = 120 Ib./sq. in. T = 286OF.
Operation of the equipment at a constant flow rate and increasingly higher liquid temperatures shows that significant flashing does not occur at temperatures just above the saturation temperature, but that a substantial increase above saturation must be provided. The temperatures below which no effect is shown on the jet and above which the jet is shattered by
Fig. 4. Flashing jet 1OX. Type A, D = 0.030 P = 131 Ib./sq. in. T = 287F. One inch from orifice.

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May, 1962
A bubble is subject to three forces: the pressure on the liquid Po, the vapor pressure in the bubble P., and the pressure exerted by the interfacial tension. The interfacial tension causes a pressure of %/r. For a bubble to grow in a superheated liquid the pressure acting outward must exceed those acting inward, or

P, > Po + r

Fig. 5. Flashing jet 1OX. Type 8, D = 0.031 in., P = 120 Ib./sq. in. T = 295OF.
ure 6 shows a jet from a Type B nozzle 0.020 in. in diameter. The larger jet of Figure 5 is typical of the shattering occurring in the jet from such a rough nozzle, and Figure 6 shows the effect of a temperature just below the shattering temperature. The Type C nozzle is not shown because its extremely rough surface disintegrated even a cold jet, although irregularly, and the effect of flashing is not apparent in the photographs. The rough nozzles show disintegration beginning at the nozzle discharge, and the sharp-edged orifices give a delayed action, with disintegration setting in several diameters downstream. This difference is explained on the basis of nucleation. As the hot water passes through the nozzle and the pressure decreases until enough driving force is established to form a bubble, the molecular arrangement in the liquid controls the nucleation of the bubble. The rough orifice has sufficient length to permit the surface irregularities to form low-pressure eddies. These eddies are shed regularly, move downstream as part of the jet, and serve as low-pressure stagnation spots which may well nucleate bubbles. The sharp-edged orifice offers no such opportunity, and the bubble formation is much like that of a bumping liquid in a boiling flask, with a sudden violent eruption of the bubbles.
The smallest bubble capable of growth is that one whose radius r. just satisfies the equation P = P. 5
Since the vapor pressure is a function of the liquid temperature, then the minimum bubble radius can be calculated as a function of temperature and is shown in Table 2. Since the roughness in the Type B nozzles is of the order of 0.5 p, then a temperature of about 270F. would reduce the minimum radius to the order of the roughness in the orifice, and the eddies might be influential. The bubble must continue to grow if it is to disrupt the jet, and the growth rate will determine the shattering effect it will have. Plesset and Zwick (6) and Forster and Zuber (7) have studied the growth rate and solved the mathematical system by different techniques to arrive at the same results. The bubble grows initially at a very rapid rate because of the rapid relaxation of the surfacetension pressure and the slow decrease in temperature of the liquid surrounding the bubble. In a few microseconds the bubble is about ten times its initial radius, the amount of liquid vaporized to fill the bubble cools the remaining liquid at the surface, and

Fig. 7. Bubble growth-rate constants for superheated systems a t 1 atm.
heat conduction becomes dominant. The radius then follows the relation r = r, c f The bubble growth-rate constant was developed by Forster and Zuber to be
The first grouping in the parentheses
is the weight-fraction flashing at the
saturation temperature and lower pressure, the second parenthesis encloses the specific-volume ratio of gas to liquid, and their product is then the volumefric increase upon flashing. The last term is a measure of the rate of heat conduction from the liquid to the vapor. Larger values of the growthrate constant would indicate more rapid disintegration of the liquid mass. Calculated values of the growthrate constants are shown in Figure 7 for four different fluids. Water has a growth rate more than twice as large
WATER -SHARP-EDGEO ORIFICES WATER ROUGH SURFACE ORIFICES FREON-I1 -SHARP-EDGED ORIFICES
Fig. 6. Flashing jet lox, Type 8, D = 0.020 in., P = 120 IbJsq. in. T = 284OF.
Fig. 8. Effect of Weber number on water and Freon-11 jet breakup.

Page 151

0 I 18 GROWTH RATE CONSTANT (FT/HR I/Dl
260 zro 300 INJECTION TEMPERATURE 'F (WATER POINTS ONLY)
Fig. 9. Effect of bubble growth rate and Weber number on drop sizes.
as the organic compounds, when compared at the same superheat. The analogy between thermal diffusivity and molecular dsusivity immediately brings forth the parallel concept of flashing from super-saturated liquids as well as super-heated liquids. The values of molecular diffusivity are an order of magnitude lower however, and the corresponding growth-rate constants are about one tenth as large as for superheated liquids. One experiment was attempted on cold water through which carbon dioxide was bubbled for 20 min. at 90 Ib./sq. in. gauge. If saturation was attained, about 1% of the liquid volume would be flashed off. This system showed breakup almost identical with that of water containing no dissolved gas, which would be expected if the growth-rate constant was too low to influence breakup. Water at a superheat sufficient to cause flashing of 1% of the volume easily shattered a jet. Observation and the data bring out the fact that a jet of large diameter may shatter at a superheat for which a smaller jet does not shatter. This brings in the possibility that jet stability may be an important factor; therefore the Weber number was determined for each system studied. The temperature at which each jet shattered permitted calculation of the Weber number and the growth-rate constant for each fluid system, with the result shown in Figure 8. Higher values of the Weber number permit shattering to occur with less superheat at the same flow velocity, giving smaller growth-rate constants. A Weber number of 12.5 is critical, with lower values of the Weber number requiring a significantly higher growth rate for shattering. This usually requires higher superheat. The two straight lines representing the data best have the equations

Page 752

OZZLE TYPE 1 267.F
1.DISTANCE FROM SPRAY AXIS (INCHES)
Fig. 10. Variation in drop diameters across sprays from flashing water jets.
19.7 - 0.58 N,, for N w , < 12.5
c = 11.5 - 0.42 N~~ for Nwe> 12.5
An interesting aspect of Figure 8 is the lack of influence of roughness on the relationship, with close agreement for data for both kinds of orifice. This is in contrast to the marked difference breakup Seen in the photographs*

SPRAY CHARACTERISTICS

given in Table 3. The four different mean drop sizes were computed from
Dma = __ ' :h ; ; ; ; A *

I"'

D,,the
The drop sizes in the spray at a distance of 6 in. from the nozzle are
is the linear mean diameter, surface mean diameter, D,the volume mean diameter, and the volume-surface mean diameter. The corresponding dimensions of the orifice and the jet itself are given in Table 3, along with temperatures,

TABLE MEANDROP 3. SIZES

0 1132

I LO I20

,I 0 14

"

0 1131

11 Oh6

287 1n4

59 K 186

" " " "

336 82.2

1.22 I 43 I 49

2n7 287

0 1125

0 ill,

17 ? 13 h

L9R 15 b

in7 254

Liil 270 I

I 3 (1 I 3 f,

iJ 3 7

44 ,1n

17 I 32 4

I 95 I 60

i - 1 1

bubble growth-rate constants, and Weber numbers. The uniformity parameter, also shown in Table 3, is derived from a log-normal probability plot of the data for each analysis and is defined as
other devices. High pressures and high velocities are not necessary for the process, although superheating must be provided.

NOTATION

6 = 0.394/logl0 (D,/D,)
where D, and D, are the diameters read from the plot for cumulative percentages of 90 and 50, respectively. The size distribution fits the log-norma1 probability function as well as any other spray data. The two lines in Table 3 for water below its boiling point show the poor breakup to be expected from such Fig. 11. Velocity of drops in a spray from low-pressure orifice injection, even flashing water jet 6 in. from the orifice. with the artificially roughened Type C nozzle, which tends to tear the stream into irregular masses because of its value. The line through the band for roughness alone. water can be described by the equaComparison of the mean drop sizes tion with those for other types of spray 1,840 - 5.18 T ( O F. ) __ devices is only approximate, since inDIOP = NW. jection conditions are quite significant for many devices. In general the Aash- The standard deviation is 6.1 %. ing of water through these orifices An attempt to correlate the uniproduced a spray roughly similar to formity parameter with the bubble that from a swirl-chamber nozzle, growth-rate constant failed to show somewhat larger in mean drop size any significant relationship. than for gas atomized sprays, and Drop-size analyses at different locasomewhat smaller than the spray pro- tions across the spray showed a trend duced by most spinning-disk units. of increasing drop size with distance The mass fraction of the liquid flashed from the spray axis. This is shown in upon emerging from the nozzle can Figure 10, in which the effect of be computed from the first term of the Weber number is indicated for each bubble growth-rate constant and ranges nozzle type at various temperatures. up to a maximum of 7.8% (at 287F.) The larger drops apparently migrate for water. This compares favorably away from the center because of their with the need for 0.5 to 1.0 lb. of air inertia and the radial component added needed per pound of water in many to the drops by the explosive flashing gas-atomizing nozzles. This effect is less evident when the The uniformity parameters averaged Weber number is below the critical. 1.55 for a range of 1.21 to 1.95. This The velocities of the drops at the may be compared with typical values 6-in. distance are shown in Figure 11 for other devices ( 8 ) : for the different drop sizes at different locations across the spray. The smaller Gas atomizer: 6 = 0.93 drops appear to have reached the Spill-controlled swirl multiphase flow velocity at that dis6 = 1.29 tance, and the decreasing velocities nozzle: Vaned-disk sprayer: S = 1.54 with increasing distance from the spray axis represents the velocity Study of the data in Table 3 shows gradient to be expected in such a that the mean drop sizes decrease multiphase system. slightly with increasing Weber numThe spray pattern was one of rapid ber at a given temperature and there- expansion to a diameter of 3 to 4 in., fore at the same bubble growth-rate with no significant expansion evident constant. A slight decrease is also in- beyond the 6-in. distance chosen for dicated with increasing temperature our analytical point. Evaporation is and bubble growth-rate constant when rapid beyond the 6-in. distance howthe Weber number is approximately ever, with practically all of the drops constant. These two trends suggested disappearing within 4 to 5 ft. from the the best generalized correlation of drop nozzle. sizes found, a plot of ( % * N w e ) VS. C, as shown in Figure 9. All water CONCLUSIONS data for Type A and Type B nozzles Flashing is an effective technique fall in a reasonable band, but the Type C nozzle shows a smaller drop for producing sprays with a drop-size size and Freon-11 shows a smaller pattern similar to that produced by

C C, D,

= bubble growth-rate constant
= heat capacity of liquid
= average drop size in each
size class in an analysis
= mean drop size corresponding to chosen values of m
= thermal diffusivity of liquid = diameter of liquid jet = conversion factor (poundals

per pound force)

= latent heat of. vaporization = integer constants such that

m>n

= Weber number = pressure on system at free

liquid surface

= vapor pressure of liquid at

its temperature T

= radius of bubble at any time
of smallest bubble capable of growth = radius of bubble when heat conduction begins to control (rl = 10 ro) = time from bubble radius r, = velocity of jet relative to gas medium of drops in each size class in an analysis superheat uniformity parameter in drop size distribution height of roughness projection density of gas phase surrounding jet density of vapor density of liquid surface tension

= radius

Greek Letters AN& = number

LITERATURE CITED

Ralph, Ph.D. thesis, Univ. Michigan, Ann Arbor, Michigan ( 1960). 2. Rayleigh, Lord, PTOC. London Math.
SOC., 10, 4 ( 1878). 3. Weber, C., Zeit. fur Angew. Math., 11,

1 Brown,.

106 ( 1931). 4. Hinze, 1. O., A.1.Ch.E. Journal, 1, 289 ( 1955): 5. York, J. L., and H. E. Stubbs, Trans. Am. SOC. Mech. Engrs., 74, 1157

(1952).

6. Plesset, M. S., and S. A. Zwick, J. Appl. Phys., 25, 492 ( 1954). 7. Forster, H. K., and N. Zuber, ibid., p.
474. 8. Ranz, W. E., Dept. Eng. Res., Bull No. 65, The Pennsylvania State Univ., State
College, Pennsylvania ( 1956).
Manuscript received December 29, 1960; revision received July 31 1961; paper accepted Aueupt 14, 1961. Paperpresented at A.1.Ch.E. N e w Orleans- meeting.

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