THE UNIVERSITY OF MICHIGAN COLLEGE OF ENGINEERING of Chemical and Metallurgical Department Engineering Progress Report BUBBLE GROWTH AND DROP SIZES FOR FLASHING LIQUIDS Ralph. Brown J.. Louis ork *.;, *. UMR-I P roct.28l5 under contract with: DELAVAN MANUFACTURING COMPANY WEST DES MOINES, IOWA administered by: THE UNIVERSITY OF MICHIGAN RESEARCH INSTITUTE ANN ARBOR January 1960

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TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS v SUMMARY ix INTRODUCTION 1 PHOTOGRAPHIC STUDY OF THE BREAK-UP ANALYSIS OF THE BREAK-UP MECHANISM7 ANALYSIS OF A SPRAY FROM A FLASHING JET 15 Method of Measuring Drops 15 The Spray Analysis 15 Future Work 17 REFERENCES 19 iii

LIST OF ILLUSTRATIONS Table Page I Description of Experimental Nozzles 5 II Minimum Initial Radius for Bubble Growth in Water Under One Atmosphere 8 ITT Diffusivities in Liquids at Their Saturation Temperatures at One Atmosphere 13 Figure 1 Camera arrangement for high-speed photographs. 21 I. Photographs of Superheated Water Jets A. The Rough Orifices 2 Nozzle A, T = 148~C, P = 120 psig, negative no. 118. 22 3 Nozzle B, T = 130~C, P = 120 psig, negative no. 25, 22 4 Nozzle B, T = 145~C, P = 120 psig, negative no. 28. 2z 5 Nozzle B, T = 155~C, P = 120 psig, negative no, 29. 25 6 Nozzle B, T = 160~C, P = 120 psig, negative no. 34. 24 7 Nozzle B, T = 140~C, P = 120 psig, double-exposure, 14-fsec delay, negative no. 64 ' B. The Smooth Orifices 8 Nozzle C, 140~C, P - 120 psig, negative no. 51. 25 9 Nozzle C, 150~C, P 120 psig, negative n. 23. 25 10 Nozzle D, 155~C, P = 120 psig, negative no. 12. 26 11 Nozzle D, 145~C, P = 120 psig, negative no. 13o 26 v

LIST OF ILLUSTRATIONS (Continued) Figure Page 12 Nozzle 13 Nozzle 14 Nozzle 15 Nozzle 3-usec B. The Smooth Orifices (Concluded) D, 150~C, P = 120 psig, negative no. 14. D, 150~C, P = 120 psig, negative no. 17. D, 150~C, P = 120 psig, negative no. 90. D, 1500C, P = 120 psig, double-exposure, delay, negative no. 81. 27 27 28 28 II. Photographs of Supersaturated Water Jets A. The Rough Orifices 16 Nozzle B (with L = 0.1 in.), T = 18~C, P = 100 psig, 1.4 wt o C02, negative no. 48. 17 Nozzle B, T = 15~C, P = 75 psig, 1.25 wt % CO2, negative no. 128. B. The Smooth Orifices 18 Nozzle C, T = 18~C, P = 100 psig, 1.4 wt % C02, negative no. 42. 19 Calculated initial bubble radii. 20 Diameter versus time for bubbles on jet. 21 Camera arrangement for drop-size measurements. 22 Photograph of spray (1OX). 23 Drop-size distribution at location 1. 24 Drop-size distribution at location 2. 25 Drop-size distribution at location 3. 29 29 50 51 51 52 52 33 55 33 54

LIST OF ILLUSTRATIONS (Concluded) Figure Page 26 Drop-size distribution at location 4. 34 27 Estimated drop-size distribution curves at the four locations 35 28 Linear mean drop-sizes'at the four locations 35 29 Volume distribution across spray. 6 vii

SUMMARY This report presents data obtained on bubble growth in jets of superheated water emerging from both rough and smooth orifices. The data are examined and compared with existing theories of bubble growth and bubble nucleation. Rough orifices appear to give consistent results, and data are presented to show estimates of the size of bubble nuclei. Drop sizes from a typical spray formed by a flashing jet are presented, showing spatial distribution by size and number of drops. ix

INTRODUCTION Water is being injected through orifice nozzles to investigate the effect of flashing on the break-up of cylindrical liquid jets and the sprays subsequently formed. Flashing, defined as spontaneous vapor evolution, can occur if the liquid is injected at a temperature above the saturation temperature of the liquid at the pressure of the receiving medium. In this case the liquid is "superheated" with respect to the receiving pressure. Flashing may also occur if gas is dissolved in the injected liquid at a concentration higher than the solubility of the gas in the liquid at the pressure of the receiving medium. Here, the liquid jet is "supersaturated" with respect to the receiving pressure. In both these cases, flashing must occur within the body of the liquid jet to help disintegrate it effectively. The mechanism by which the flashing occurs is therefore critical in determining whether flashing will occur within the liquid jet and produce a fine spray under prescribed conditions. The results of previous experiments on superheated water jets as reported in the last progress report have shown that flashing occurs downstream of the orifice exit if short-length orifices are used.4 Therefore the break-up can be photographed and possibly be "stopped" by the use of high-speed techniques. These photographs, some of which were presented in the previous report, provide a basis for the theoretical work presented here on the break-up mechanisms of superheated liquid jets. The variable used to determine the effectiveness of a given method of spray formation is the drop size of the spray formed. In these studies a photographic technique is employed to obtain the average drop size and drop-size distributions of the sprays from the flashing water jets. 1

PHOTOGRAPHIC STUDY OF THE BREAK-UP To investigate the effect of the method of flashing, injection temperature, orifice diameter, and orifice roughness on the break-up mechanism, 130 highspeed photographs were taken of water jets. Some of these photographs, representing the important results, are presented here. The photographs represent a lOX magnification. The camera lens was an Argus with a focal length of 50 mm and a between-the-lens aperture setting of f-5. The lens was positioned so that the photographs show a 0.5-in. portion of the jet starting at the orifice. Lighting was from the rear of the jet facing into the camera as shown in Fig. 1. A General Electric Photolight Cat. No. 9364688G1, which provides a high-intensity flash for approximately 1.sec, was employed. This provided for a l-Lsec silouette photograph of the liquid jet. In some cases, a double exposure was taken using two photolights flashing a few microseconds apart. In this case, the photolights were positioned as shown in Fig. 1. Photographs were taken with Kodak Contrast Process Ortho Film. Photographs were taken of jets from 4 different nozzles described in the following table. TABLE I DESCRIPTION OF EXPERIMENTAL NOZZLES Nozzle Diameter, in. Length Type A 0. 02 0.02 in. rough orifice B 0.03 0.03 in. rough orifice C 0.02 round-edged Delavan 6:00 (no distributor) D 0.025 round-edged Delavan 12:00 (no distributor) Nozzles A and B were made by drilling holes in 3/8-in. pipe caps and milling down the ends to the desired orifice lengths. They represent the rough orifices and their roughness is estimated to be in the area of 20 irms. The other two nozzles are commercial oil-burner nozzles without their distributors. These are smoothly machined round-edged orifices. Figures 3-6 are a series of photographs from the larger-diameter rough orifice over a range of temperature. At 130~C the superheating has essentially no effect on the jet. Only one small bubble can be seen on the surface of the jet. At 145~C the superheating does partially disintegrate the jet, but the spray 3

still contains a core of large drops. Several bubbles can be observed on the surface of the jet and the jet is expanding slightly. At 155~C the jet is completely disintegrated into a spray of fine droplets. This disintegration can easily be noted in the photograph by the rapidly expanding jet a short distance from the nozzle. Visual observation of the sprays has indicated that the temperature difference from the value where the jet disintegrates to a spray with a core of large drops and the value where the jet completely disintegrates to a fine spray is small, about 2-3~C. The photograph of the jet at 160~C shows the reason relatively large drops can often be observed around the jets. Dribbling of the liquid just at the orifice exit causes this. The best temperatures for observation of the bubbles growing on the jet are in the 140-145~C range for this nozzle. There are few bubbles below that temperature range and above it the rapid disintegration clouds any that may be there. Figure 7 is a double exposure of the jet at 140~C. One can observe the expansion on the bubbles on the surface from the first exposure to the second. Figure 2 shows a jet from the smaller-diameter rough orifice at 1480C. Bubbles can be observed on the surface of the jet. The jet also appears less turbulent than those of the larger diameter as would be expected in view of the lower Reynolds number. The importance difference between this nozzle and the larger one is that, at this temperature, a jet from the larger orifice would be completely disintegrated. The appearance of the bubbles in this jet is similar to those in the larger diameter jet at about 140~C. The jet is only partially disintegrated by bubble growth, the final spray containing a core of large drops. The photographs of the jets from the smooth-orifice nozzles show some outstanding differences from those of the rough-orifice nozzles. Figures 8 and 9 show two jets from the smaller smooth orifice at 140~C and 150~C. The cooler jet is expanding slightly. The warmer jet appears to split into a sheet with bubbles growing in it. Figures 10-15 of the larger jets also show the slight expansion of the cooler jets. The jets at 150~C all break up completely but in different ways. About 20 photographs of jets from this nozzle at this temperature were taken and each one is entirely different. Observations from the photographs indicate that the jet disintegrates anywhere from 1/8-1/2 in. from the nozzle. Often a delicate network of bubbles appear on the surface and often the jet just seems to explode suddenly. An extremely loud noise is associated with this break-up above about 145~C. Visual observation of these jets suggests that the break-up point oscillates and the density of the spray formed by the jet fluctuates at any given point. The sprays seem to be very fine. The intact portion of the jets looks very smooth, which is also indicated by the photographs. Carbon dioxide was bubbled through water in a vented tank for several minutes. The tank was sealed and the gas bubbled through until the desired pressure was reached. The gas concentrations given in Figs. 16-18 are estimated from the solubility of carbon dioxide in water at the injection tank pressure and the water temperature. In all these cases about 1 wt % of the liquid jets should evolve as gas when the pressure is reduced to 1 atmosphere. In the photographs, the jets from the rough orifices appear very turbulent at the sur

faces but the jet from the smooth orifices is perfectly smooth. The jet from the longer rough orifice expands slightly, whereas the one from the shorter one does not. The important point of comparison here is that when a superheated water jet was injected through the longer rough orifice nozzle at a temperature such that 1 wt % flashed, vapor evolution was initiated inside the orifice and the jet was broken up.4 5

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ANALYSIS OF THE BREAK-UP MECHANISM The mechanism by which flashing occurs in the superheated jets from the rough orifice is bubble formation. This is apparent by the bubbles observed on the surface of the jets in the photographs. This is not the case, however, in the jets from the smooth orifices. The flashing of these jets is a more random, explosive type of mechanism. The situation here is analogous to boiling a liquid in a test tube. If some porous stones are in the tube, small bubbles will nucleate on the surface of these stones and the liquid will vaporize into these bubbles, causing them to grow and rise. If only pure liquid is in the test tube, vaporization will take place by a series of spontaneous small explosions referred to as "bumping." The reason for the two different vaporization mechanisms is the same in both the case of the water jet and the heated test tube: vapor bubbles will not grow in a superheated liquid unless bubble nucleii are already present. The surface tension of a liquid exerts a pressure on a spherical bubble in the liquid of a magnitude given by the following relation: = 2a (1) r where P = pressure inside minus pressure outside the bubble, a = surface tension of the liquid, and r = radius of the bubble. Considering the limiting case for water, if a bubble is the mean diameter of a water molecule, r = 1.9 A, the excess pressure inside the bubble would be 7500 atmospheres assuming the surface tension is constant down to atomic dimensions. For a bubble to grow in a superheated liquid, the vapor pressure of the liquid minus the pressure on the liquid must be greater than the pressure exerted on the bubble given by Eq. (1). A minimum initial radius for bubble growth can be found by equating these two pressures. r o = Pv(To) - P ro = Pv(2o)~a (2) 7

where ro = the minimum initial radius for bubble growth, pv = the vapor pressure of the liquid which is a function of its temperature, To, and PO = the pressure on the liquid. Several values for this initial radius for water are given in Table II. TABLE II MINIMUM INITIAL RADIUS FOR BUBBLE GROWTH IN WATER UNDER ONE ATMOSPHERE ro (0) 5.90 0.605. 470 0.378 0.300 0.245 0.201 To (~C) 105 130 135 140 145 150 155 There are a number of different means that provide small nuclei for bubble formation in a superheated liquid. These nuclei may be provided by vapor spaces in the small cavities of boiling stones, free vortex motion in a highly turbulent situation, or by small gas bubbles held in the liquid. Whatever the means, bubble formation in a pure continuous phase of superheated liquid cannot take place without some original bubble nucleii. In the case of the rough orifice, the nucleii are probably provided by lowpressure eddies behind the sharp micro-roughnesses on the orifice surface. With a smooth orifice, the superheated liquid passes by the orifice undisturbed into the atmosphere. There is no provision for continuous nucleation of bubbles on the orifice surface. Rather, the spontaneous evaporation of a portion of the superheated jet is initiated by some random disturbance. Such a disturbance might be an aerodynamic distortion of the jet or a small vibration of the nozzle. The resulting spray, although fine, oscillates in flow pattern and density. It appears that a better spray pattern is obtained when the break-up is a result of bubble nucleation. The theoretical and drop-size studies therefore concentrate on this case. The effectiveness of bubble formation in breaking up the jet will involve the rate at which the bubbles grow and increase the volume of the jet. It would therefore be of considerable value if one could predict the bubble growth rates. The growth of a vapor bubble in a superheated liquid is controlled by the inertia of the liquid, surface tension, and the vapor pressure. As the bubble grows, evaporation takes place at the bubble boundary, thereby decreasing the temperature and vapor pressure inside the bubble. The heat inflow requirement for evaporation is dependent on the rate of bubble growth, so that the dynamic problem is linked with a heat-diffusion problem. 8

Solutions for this problem have been presented by Plesset and Zwick,3 and by Forster and Zuber.2 The detailed mathematics of these solutions is omitted here as it is available in the references. The mathematical analysis indicates that there are two regions of bubble growth. In the first region, the bubble radius is of the same order of magnitude as its initial radius, ro. Here the growth rate is quite rapid because the increasing radius is relaxing the surface tension pressure on the bubble. There also has not been enough evaporation to cool the liquid on the bubble surface and severely reduce the vapor pressure. The growth rate of the bubble in this range is given by:3 r ro (1 +AeBt) () where t = time, and A, B = constants dependent on the physical parameters of the system. This rapid expansion rate is shortly slowed down by the cooling of the liquid around the bubble and subsequent reduction of the vapor pressure inside it. The rate is then governed by the balance between heat transfer and evaporation and is approximately given by: r = r + roCt1/2 (4) where C = a constant dependent on the physical parameters of the system, ro = minimum initial radius for bubble growth, and rl = initial bubble radius. This growth-rate relation describes the bubble as soon as the radius is about 10 times the minimum radius, which is the case within a few microseconds. This secondary growth-rate function agrees very well with experimental data. The problem in applying these growth-rate relations to this situation is that we do not know the initial radii of the bubbles. Bubbles formed by lowpressure eddies behind micro-roughnesses on the orifice surface probably have initial radii considerably greater than the minimum for bubble growth when they leave the orifice surface. Therefore, since surface tension forces are inconsequential in this range, Eq. (4) describes the bubble growth. The average initial size of these bubbles would be dependent on both the surface roughness and the turbulence in the orifice. The constants A in Eq. (3) and rl in Eq. (4) are functions of the roughness and the Reynolds number. 9

One can, however, make rough experimental estimates of these initial radii from photographs such as Fig. 4. Bubbles can be measured at distances from the orifice. The distance from the orifice is proportional to the time for a steadyflow condition. The radii of these bubbles inside the orifice can then be calculated by Eq. (4). The constant in this equation is given by: C = 1T($D) 1/2c (5) roLP 1 where AT = the superheat (liquid temperature - saturation temperature Ts at external pressure), D = thermal diffusivity of the liquid, PI = density of the vapor at external pressure and Ts, P2 = density of the liquid at Ts, cl = specific heat of the vapor at Ts, ro = minimum initial bubble radius, and L = latent heat of vaporization at Ts. This estimate of the initial radius by Eq. (4) is quite approximate because this equation is the solution for a vapor bubble in an infinite extent of liquid. The bubbles on the liquid jet, however, break through the surface and are exposed to the atmosphere. The jet also cools quite rapidly by evaporation on the surface. Therefore the bubbles are not surrounded by a uniform temperature field. To check Eq. (4) for the case of bubbles on a jet, several photographs were taken of a jet from the 0.03-in.diameter nozzle when water at 120 psig and 140~C was injected through it. The sizes and distances from the orifice of a total of 18 bubbles from 10 photographs were measured. There was a distribution of bubble sizes, and only the largest ones are reported here. Initial radii for each bubble were calculated and the range was 0.001-0.007 in. The plot in Fig. 19 of the calculated initial radius versus time shows a definite increase in the initial radius with time. If Eq. (4) correctly described the growth, the calculated initial radii would have been constant with time, but these results indicate that the bubbles actually expand at a rate somewhat greater than proportionally to the square root of time. The plot of the measured diameter versus time in Fig. 20 shows that the bubbles on the jet more likely expand at a rate directly proportional to time in this range. This result may be predicted by considering the simplified case of a hemispherical bubble on a flat liquid surface. Neglecting surface tension forces and assuming a constant temperature, the liquid evaporates from the surface into the bubble at a rate proportional to the area covered by the bubble. V = Akt (6) 10

where V = volume of the bubble, k = a constant, and A = area covered by the bubble. Substituting the expressions for volume and area as a finction of radius into Eq. (6), the radius is shown to be directly proportional to the time. r 3 kt (7) 2 Bubbles in the liquid jets therefore have two regions of growth. In the first, the bubbles:are inside the jet and expand in proportion to the square root of time as governed by Eq. (4). They are then thrown to the surface of jet and expand in direct proportion to time as in Eq. (6). Only bubbles on the surface can be measured on the photographs. Therefore to obtain accurate predictions of the initial radius by Eq. (4), it is necessary to choose a bubble just as it appears on the surface near the orifice. Most of its growth up to this point can be described by Eq. (4). The initial bubble radii can be estimated in the preceding manner from nozzles of various size and having a given roughness at temperatures such that bubbles appear on the surface. This would yield an empirical relation between the Reynolds number and the initial bubble diameter for a given surface roughness. The calculated initial radius from the bubbles near the orifice in photographs measured here is about 0.003 in. and the Reynolds number is 206 000. The experimental results have indicated that the transition from a partial break-up of the liquid jet and a complete disintegration takes place within a small temperature range. If we hypothesize that this "critical" temperature corresponds to a critical value of the bubble growth rate constant C, we have a method of predicting the temperature at which a superheated liquid jet disintegrates. Such a critical constant, however, would be valid only for a given initial bubble radius. We could measure the disintegration temperatures for a number of jets having various initial radii and obtain an empirical relation beveern the initial bubble radii and value of the growth rate constant at the critical temperature. Then suppose we were given a liquid jet of a given size and velocity being injected through an orifice having a given surface roughness. We could first estimate the initial radius from the initial radius-Reynolds number correlation, then obtain the critical rate constant from the relation between the initial radius and critical rate constant, and finally calculate the required superheat by Eq. (5). Such a procedure may be of dubious value for predicting temperatures for disintegration since such a large quantity of experi.mental data must be gathered in order to employ it. However, this approach wil.l be taken in further experiments to determine whether the growth rate constant is the critical factor in the disintegration of a superheated liquid jet. 11

The hypothesis that the rate constant is the determining factor in breaking up the liquid jet is based upon the fact that the break-up of the jet is caused by the mechanical action of the expanding bubbles. The rate at which these bubbles expand and the size they become with respect to the jet diameter will directly affect the break-up. For example, it was noted that when a carbon dioxide solution was injected through a particular long orifice at a concentration such that 1 wt % of the jet vaporized, the jet was relatively undisturbed (see Fig. 16). When hot water was injected through this same orifice at a temperature such that 1 wt % vaporized, the jet was disintegrated.4 The same relations governing the growth of a bubble in a superheated liquid hold for a bubble in a supersaturated liquid since both heat transfer and mass transfer obey the same differential equations. To apply the relations given here to the supersaturated system, the thermal diffusivity in Eq. (5) is simply replaced by the molecular diffusivity for the mass transfer case. The reason the superheated jet disintegrated and the supersaturated jet did not was that the thermal diffusivity for the above case is 6.68 x 10-3 ft2/hr and the molecular diffusivity of the gas in water is 6.60 x 10o5 ft2/hr. So the bubble-growth-rate constant in the superheated case is (Ds/Dmn) /2, or 10 times the growth-rate constant in the supersaturated case. In view of the low molecular diffusivities of gases in liquid, much higher degrees of supersaturation are necessary for jet disintegration. From this example, it is clear that the diffusivity can be used as a preliminary test to compare bubble growth rates in liquids and thus the effectiveness of superheat or supersaturation in disintegration of liquid jets. Physical parameters other than diffusivity affect the growth rate, but this parameter has the greatest variability from liquid to liquid. It is very important because it represents the rateat which heat or dissolved gas flows to the bubble. Table III is a comparison of several thermal and molecular diffusivities for liquids at their saturation temperature at one atmosphere. The square roots of the thermal diffusivity ratios in the table show that the growth rates are about the same for water and these organic liquids. There is a more severe reduction in the growth rate with dissolved gas. This improves, however, at higher temperatures. 12

TABLE III DIFFUSIVITIES IN LIQUTDS AT THEIR SATURATION TEMPERATURES AT ONE AITMOSPHERE Saturation Diffusivity, DiffusivL /2 Liquid Temperature, (ft2/hr) \iffusivity H2C Cl Thermal Dlffusivities Water 100 6.7 x 10-3 1 n-hexane 69 3.2 x 10-3 0o70 Benzene 80 3.6 x 10-3 0,74 Molecular Diffusivities C02 in water 100 6.6 x 10-5 0.10 CH4 in benzene 69 4.0 x 10-4 0.25 CH4 in 30* 1o5 x 10-4 0.14 kerosene 60 2.1 x 10-4 0o18 C3H8 in 30 0o4 x 10o4 o.08 kerosene 60 o.0 x 10-4 0.12 *Not saturation temperatures in the case of kerosene. 15

ANALYSIS OF A SPRAY FROM A FLASHING JET METHOD OF MEASURING DROPS A photographic technique for obtaining drop sizes was employed. The camera and lighting arrangement is shown in Fig. 19. The same camera, lens, and lighting was employed as in the break-up mechanism studies. The lens aperture was set at f-3.5 for all photographs and Cellophane filters in front of the photolight were used to control the illumination. The aperture must be the same in all analyses to maintain a constant depth of field. A photograph of the spray gives a 10X magnification of the drops in the range of the camera. This photographs a sample of the volume of the spray with a face 0.4 in. x 0.5 in. parallel to the spray axis and a depth equal to the depth of field at f-3.5 which is about 1 mm. The nozzle was on a movable stand so that the samples can be photographed at various locations in the spray. The samples in these experiments were photographed side by side at the spray axis, at distances of 0.4., 0.8, and 1.2 in. The numbered sample locations are shown in the diagram. Each photograph represents a sample of the drops in a cylindrical annulus around the axis of the spray. Photographs were taken with Kodak Contrast Process Ortho film with an open shutter on the camera. The l-Psec flash of the photolight was sufficient to "st~op! the motion of the drops. After the photographs were developed, the drops were measured on an optical comparator which projects a 10X magnification of the negative. This provided a 10OX magnification of the original drops. Since photographs of the spray show both drops in sharp focus and blurred drops, as in Fig. 20, a standard technique had to be employed to determine which of the drops should be considered as part of the sample. This was done by taking several photographs of drops of various size suspended on glass fibers. The lens was advanced a known distance before taking each picture to obtain photographs of the drops at known distances from the point of focus. One of these photographs was established as the limit of focus and any drops as sharp as or sharper than those were accepted. Drops were counted and measured by adding the number of drops in a photograph found to lie within given size ranges. This analysis gives the percentage of the total drops in each sample that lie within each size range. The drop-size distribution curve can then be estimated from these percentages. THE SPRAY ANALYSIS A drop-size analysis was made on a spray from nozzle A (rough orifice D= 0.03 in., L/D 1) when water at 120 psig and 150~C was injected through it. Several photographs were taken at the four locations in the spray described in 15

the preceding section, 12 in. from the orifice. The total number of drops counted in locations 1, 2, 3, and 4 were 299, 124, 106, and 98, respectively. The percentage of drops in each size range of the total drops in a location was calculated and divided by the magnitude of the size interval. This provided the average percentage of drops per unit size over each size range. This average percentage of drops per unit size for each size range was plotted versus the drop size, giving the experimental size distribution function. The continuous distribution function for the average percentages per unit size for infinitely small size ranges was estimated by drawing an equal-area curve through the experimentally determined discontinuous distribution function. The plots of the experimental distribution functions for each location with their corresponding estimated continuous distribution curves are given in Figs. 21-24. The distribution curves show that the highest percentage of drops were in the 20-404 range for each location. The curves indicate that the smaller drops are closer to the spray axis. The estimated continuous distribution curves for all four locations are given in Fig. 25 to provide a direct comparison. The linear mean drop diameters were calculated for each location. These mean diameters for each location are plotted versus the position of the sample with respect to the spray axis in Fig. 26. This plot shows that the mean drop size increases when going away from the spray axis. There were considerably more drops in the photographs of the locations close to the spray axis than in the further ones. The average number of drops per photograph for each location was determined. Considering each photograph as a sample, the average volume of drops in a sample could then be calculated from the number of drops per photograph and the drop distribution. This was calculated for each location and is plotted versus the distance from the spray axis in Fig. 27. The curve drawn through the lines representing the average volume in each location is an estimate of the distribution of the spray volume in a plane parallel to the spray axis. Samples were photographed only on one side of the spray axis. The plot in Fig. 27 is shown assuming samples taken on the other side of the spray axis would have given the same results, that is, assuming the spray is axisymmetrical. The curve shows that the spray volume is highest at the spray axis and decreases with distance from the axis. When a cold liquid jet is injected through an orifice at a sufficiently high velocity so that the aerodynamic forces disintegrate it to a spray, the spray volume is highest at the spray axis as in this case of the flashing jet. The drop sizes of the spray from the cold jet, however, decrease with distance from the spray axis. This is because the aerodynamic forces act at the surface of the jet. This break-up action on the surface produces smaller drops from the liquid at the surface. The result is that, downstream of the break-up point, the smallest drops are the furthest from the spray axis, and the largest in the center. In the -eae of the flashing jet, however, the break-up action is a result of expanding bubbles in the body of the jet. The more severe breakup action takes place inside the jet and subsequently produces smaller drops in the central portion of the spray. 16

The fact that a spray from a flashing jet has its smallest drops near the center of the spray axis should be differentiated from the case of the hollowcone nozzle. In the hollow-cone nozzle, aerodynamic forces act on the inside and outside surfaces of a conical liquid sheet. The smallest drops are therefore close to the axis of the conical sheet. The spray volume at the axis, however, is also much smaller than along the sides of the cone. The spray volume of the flashing jet is the highest at the axis although the drops are smallest there. FUTURE WORK The drop-size analysis presented here is part of a preliminary study designed to determine the number of photographs that must be taken of each location in a spray to obtain reproducible results. The higher the number of drops sampled, the more accurate the estimate of the actual drop-size distribution. The number of photographs necessary is therefore dependent on the number of drops in focus per photograph. This drop density per photograph has been determined and the required number of samples established. The drop-size analyses in the locations described here can be used to obtain a spatial drop-size distribution in a plane perpendicular to the axis of the spray. The distribution function desired, however, is the drop-size distribution in a given time or temporal distribution. This can be obtained from the spatial distribution if the velocity of the drops with respect to location in the spray can be determined. These velocities will be measured by taking doubleflash photographs of the spray with the lighting arrangement as shown in Fig. 1. The mean drop sizes for the whole spray can then be determined from the temporal drop-size distributions. Drop-size analyses of sprays from flashing jets will be made over a range of variables to determine their effect on the drop-sizes and spray patterns. The variables to be studied are injection pressure, injection temperature, jet diameter, and liquid physical properties. 17

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REFERENCES 1. P. Dergarabedian, Paper No. 53-SA-10, Heat Transfer and Fluid Mechanics Institute, June, 1953, Los Angeles, California. 2. H. K. Forster and N. Zuber, "Growth of a Vapor Bubble in a Superheated Liquid," J. Appl. Phys., 25, No. 4, 474-478 (1954). 3. M. S. Pesset and S. A. Zwick, "The Growth of Vapor Bubbles in Superheated Liquids," J. Appl. Phys., 25, No. 4, 493-500 (1954). 4. J. L. York, M. R. Tek, R. Brown, and E. Y. Weissman, The Influence of Flashing and Cavitation on Spray Formation, Univ. of Mich. Res. Inst. Report 2815-6-P,Ann Arbor, October, 1959. 19

L HALF-SILVERED I-JET MIRROR Fig. 1. Camera arrangement for high-speed photographs. 21

_jj Fig. 2. Nozzle A, T = 48~C, P 120 psig, negative ro. 118. Fig. 5. Nozzle B, T = 10~C, P - 120 psig, rnei;ative 2o. 2. 22

Fig. 4. Nozzle B, T = 145~C, P = 120 psig, negative no. 28. Fig. 5. Nozzle B, T = 155~C, P = 120 psig, negative no. 29.

I a *: Fig. 6. Nozzle B, T = 160~C, P = 120 psig, negative no. 34. Fig. 7. Nozzle B, T = 140~C, P = 120 psig, doubleexposure, 14-isec delay, negative no. 64. 24

Fig. 8. Nozzle C, 140~C, P = 120 psig, negative rlo. )1. Fig. 9. Nozzle C, 150CC, P = 120 psig, negative no. 25. 25

~1::.;. i: u..... ~:....w: t V::::~:: D: A:E,.:>.>~y:::,: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.::........ >.:: An: And::::::f::: 7::::::::::::: ~:,. / i;,// i~' '*.*' y *" i:B:.....: ii~iii,~/::~';~i1::;/:,~:i~i!. Nozzle 135~C' 120 psig egative no. 12. pBBBBB BBBBBBI^ —.;,::^:, \...'.*IHes 1 g.ozze, p = 120 psi, negative no. 26 13.

Fig. 12. Nozzle D, 150~C, P = 120 psig, negative no. 14. Fig. 13. Nozzle D, 150C, P = 120 psig, negative no. 17. 27

9AG l:? 'oui arTIau:: a:p o Earl-; 'aJInsodxa saLQ; - sdT OQ:T - d 'o3,0T ' alTzzON 51T * TF I- -, -- ci I-::::::::::::::I:i:i:::-:l:i: i:i::::::i::-s:iii:iisisili: 'Q6 (Tc^ AT4U:-'raou oU sdo OcHs - d 'OoO^T 'C OTZZOM '*+T 'STEA x

'*8I 'ou 9ATB3au ZEO o,;T T6.I 'BTsd Qt = d '3oIT = L 'i aTzzoM L'T * -9T 1_-r i:j -::: i:r -::~::::::: ' isd 001 = d 0o8T = *9( 'OU 'ATPSG8U '0.0 ~ ' 'I T L '( *U TOo = r TF^T) a TZZOM 91[ *OOI::::'::":: I

Fig. 18. Nlozzle C, T = 18~C, P = 100 psig, 1.4,t C02,. e;ative no. 42. 130

0.009 w I 0.008 O e z1-, 0.007 D * < 0.006 -J < 0.005 z * 0.004 ~ < 0.003 o 0 < 0.002 o 0.001 - 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 TIME (MILLISECONDS) Fig. 19. Calculated initial bubble radii. 0.030 2 0.026 I z 0.022 F 0.018- S ar. 0.01 4 0.010 I I I I I I I I I I I 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 TIME (MILLISECONDS) Fig. 20. Diameter versus time for bubbles on jet.

PHOTOLIGHT SAMPLE LOCATIONS FILTERS 50 mm CAMERA Fig. 21. Camera arrangement for drop-size measurements. Fig. 22. Photograph of spray (10X). 32

W N Qo 2 cr a. bn QJ 0 U 0 w (3 QI z W LJ uO N LI Q. n3 a. LJi 0 0 n 2 U0 (_ 0 z w LJ DIAMETER - MICRONS Fig. 23. Drop-size distribution at location 1. 20 40 60 80 100 DIAMETER MICRONS Fig. 24. Drop-size distribution at location 2. 33

w N cr Z z o. o. 0 0 U0 (D z 0 li 0W 20 40 60 80 DIAMETER-MICRONS 100 Fig. 25. Drop-size distribution at location 3. w N z D C) 2 a_ 0 cr U0 Li 0 LU 0 O r — Li 0 - 31 2 20 40 60 80 100 120 DIAMETER-MICRONS Fig. 26. Drop-size distribution at location 4. 34

Z N al. 0 2 0 z U 0 a20 40 60 80 100 120 DIAMETER-MICRONS 48 - 0 w 42 - I 38- 2 36 z -J 34 34 U/ / 2 3 4 0 0.4 0.8 1.2 DISTANCE FROM SPRAY AXIS (INCHES) Fig. 28. Linear mean drop-sizes at the four locations. 35

I _Ll L 0.08 x 0.07 LLU < 0.06 (I) L 00- 0.05 E w E 0.04 - - 0 > 0.03 LLU | LA0.02 LU < LOCA TIONS 0.01 / 2 3 4, lI I, I I I I I 1I 1.4 1.2 0.8 0.4 0 0.4 0.8 1.2 1.4 DISTANCE FROM SPRAY AXIS (INCHES) Fig. 29. Volume distribution across spray.

UNIVERSITY OF MICHIGAN 3 9015 02526 1390