WADC TECHNICAL REPORT 54-390 August 1954 THE EVAPORATION AND BURNING OF LIQUID FUEL DROPS Jay A. Bolt Thomas A. Boyle William Mirsky University of Michigan Engineering Research Institute Project No. 1988-6-F Power Plant Laboratory Contract No. AF33(600)-5057 Task No. 30236 Wright Air Development Center Air Research and Development Command United States Air Force Wright-Patterson Air Force Base, Ohio

Xj ipq3FORE FOREWORD This report was prepared by the Engineering Research Institute of the University of Michigan under USAF Contract AF 33(600)-5057, Supplemental Agreement No. S2(53-308). The contract was initiated under research and development project identified by Expenditure Order No. R-533-106C "Fuel Nozzles," and completed under Task No. 30236, "Fuel Nozzle Program." It was administered under the direction of the Power Plant Laboratory, Wright Air Development Center, with Mr. J. W. Fulton, acting as project coordinator. WADC TR 54-390

ABSTRACT This report is concerned with the evaporation and combustion of liquid fuel drops in the range of sizes used in aircraft gas turbine combustors. Clouds of uniform size fuel drops in the size range of 70 to 150 microns diameter were produced by means of a spinning disc. A photographic technique was used to obtain an indication of the rate of change of diameter and the velocity of the burning crops, while moving freely in air. The mass rate of burning was found to be proportional to the first power of the drop diameter. Equipment has been developed which permits a drop to be stabilized in space by means of air drag forces and an ultrasonic field. Data on drop evaporation taken with this equipment reveals that for drops of initial size of 800 to 1300 microns a linear relationship exists between droplet diameter and elapsed time of evaporation. It has been determined that the ultrasonic field increases the rate of evaporation, the rate increasing with increased field intensity. PUBLICATION REVIEW The publication of this report does not constitute approval by the Air Force of the findings or the conclusions contained herein. It is published only for the exchange and stimulation of ideas. FOR THE COMMANDER: NORMAN CAPPOLD Colonel, USAF Chief, Power Plant Laboratory WADC TR 54-390 iii

TABLE OF CONTENTS Page FOREWORD ABSTRACT LIST OF TABLES LIST OF FIGURES SUMMARY OF PREVIOUS WORK SUMMARY OF PREVIOUS WORK DONE UNDER THIS CONTRACT SECTION I: COMBUSTION OF GROUPS OF DROPS Experimental Work SECTION II: EVAPORATION OF INDIVIDUAL DROPS Introduction Description of Apparatus The Barium Titanate Piezoelectric Transducer Experimental Procedure Experimental Results Effect of the Ultrasonic Field on Evaporation ii iii v vi 1 1 11 11 13 13 13 19 23 28 31 BIBLIOGRAPHY APPENDIX A: APPENDIX B: APPENDIX C: BURNING DROPS - DATA SUMMARY FOR FOUR HYDROCARBON FUELS DEVELOPMENT OF THE EQUATION FOR THE STABILIZING ACTION OF THE ULTRASONIC FIELD ON DROP POSITION TEMPERATURES AT WHICH A STATIONARY SOUND FIELD IS ESTABLISHED IN THE PIEZOELECTRIC TUBE 33 55 42 WADC TR 54-390 iv

LIST OF TABLES Table No. I II III Title Rate of Combustion of Four Hydrocarbons Combustion Data from Photographs with Vertical Plane Evaporation Rates of Some Hydrocarbon Fuels Page 11 12 32 WADC TR 54-390 v

Figure No. 1 2 5 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 LIST OF FIGURES Title Equipment for Making, Burning, and Photographing Uniform Size Fuel-Drops Photograph of Drop Combustion Equipment Photograph of Drop Combustion Equipment, Showing Kerosene Spray Burning in Heated Air Photograph Showing Double Images of Burning Kerosene Drops in Combustion Zone - Initial Drop Diameter - 100 Microns Mean Diameter Squared vs Elapsed Time 80 Micron Benzene Drops Mean Diameter Squared vs Elapsed Time 100 Micron n-Heptane Drops Mean Diameter Squared vs Elapsed Time, 80 Micron Propanol Drops Mlean Diameter Squared vs Elapsed Time 100 Micron Cyclohexane Drops Photograph of Burning Drops with Axis of Camera Horizontal Photograph of Burning Drops with Axis of Camera Horizontal (Plane of Picture Vertical) - Heated Air Supply Schematic of Equipment Set-Up, Single Droplet Technique Photograph of Equipment Set-Up, Single Droplet Technique Nozzle Contour - Archimedes Spiral Schematic of Ultrasonic Frequency Amplifier Cut-Away View of Lens Extension Tube Close-Up View of Camera, Barium Titanate Tube, and Droplet Light Schematic of Switch Box Basic Piezoelectric Elements Action of the Piezoelectric Tube Under Changes in Polarity of Applied Voltage Generation of the Standing Sound Wave by the Piezoelectric Tube Section of 16-mm Film Showing Change from Stop-Watch to Droplet Image Sequence of Frames Taken from a Film of an Evaporating Droplet (Acetophenone)-Elapsed Time Given in Minutes and Seconds Page 2 3 3 4 5 6 7 8 9 10 14 14 15 15 16 18 18 20 20 22 22 24 WADC TR 54-390 vi

LIST OF FIGURES (Cont.) Figure No. 23 24 25 26 27 Title Evaporation Curves for Some Pure Hydrocarbons, Diameter vs Elapsed Time Evaporation Curves for Some Pure Hydrocarbons, Diameter vs Elapsed Time Evaporation Curves, Diameter vs Elapsed Time Boiling Point and Latent Heat of Vaporization as a Function of Evaporation Rate for Some Pure Hydrocarbons Effect of Ultrasonic Field Intensity on Evaporation Rates (Tert-Butylbenzene) Page 25 26 27 29 WADC TR 54-390 vii

SUMMARY OF PREVIOUS WORK In an effort to learn about the combustion of fuel drops of approximately 100 microns diameter three somewhat interdependent schemes have been pursued: 1. Burn single drops of 1000-2000 microns or larger original diameter and extrapolate the results into the region of interest. In practically all of the work of this type the drops have been suspended on a filament or represented by porous spheres wetted with the fuel under study (Godsave2 and Spalding6). The method has several distinct advantages: The location of the drop is fixed and the drop is easily photographed. With sufficiently large initial diameter acceptable accuracy may be had either by photographing the suspended drop or measuring the fuel flowing to the porous quasi drop. In contrast to the advantages,the method introduces the possibility of complication arising from the presence of the filament used to support the drop; this also serves to limit the minimum diameters. Moreover, the possibilty exists that, although regularities are observed in the evaporation and combustion of drops 1000 microns and larger, these regularities are not reliable for purposes of extrapolation into the range of size of interest. The results of these experiments are also difficult to adapt to groups of drops. 2. A second method is, of course, to build acceptable theory to account for the behavior of the drops. Such theory will be implemented by experimentally determined property values, or by assumptions, in some cases based upon photographic studies carried out as above. The paucity of basic data is such that one usually finds many assumptions are necessary. 5. A third possible approach to studying the combustion of drops of the order of 100 microns original diameter is to apply established means of photographic spray analysis - to a sample of the spray as it proceeds to evaporate and burn. This is the general line of procedure followed in the work covered in this section of the report. SUMMARY OF PREVIOUS WORK DONE UNDER THIS CONTRACT Previous work carried out under this contract dealt with the producing, burning, and observing of groups of uniform size drops of 100-120 microns initial diameter. The work reported herein augments that reported previously in Reference (1). A brief resume of this work follows: The spinning disk sprayer was used as the drop source because it was determined that this device would yield spray from 60 to 140 microns diameter with acceptable uniformity. Acceptable uniformity was arbitrarily taken to be represented by a spray with standard mean deviation of 5 microns. The limits of sprayer operation satisfying the requirements of uniformity were determined by examining the spray by means of photographs. The spray delivered by the disk was burned in the form of a concentric ring about the disk, in a horizontal plane. The analysis of the burning spray was based upon a series of photographs taken vertically downward through the flame. See figures 1, 2, and 3, which are reproduced from Reference (1). These photographs revealed the successive reduction of diameter as the drops passed through the flame. They also revealed that the uniformity of size and velocity of the spray in the flamne zone was considerably diminished as burning proceeds. WADC TR 54-590 1

HINGE ALLOWS CAMERA TO SWING AWAY FROM FLAME ZONE / Ho TO -FLAH PHOTO- FLASH LAMP LAM DROP FOR_ FOR FIRST DROP LAMP FOR IMAGE SECOND DROP / M ---IMAGE Fig. 1. Equipment for Making, Burning, and Photographing Uniform Size Fuel-Drops. By taking a series of double flash pictures the velocity and diameter of a number of drops were determined, see Figure 4. Combining and averaging the results of a number of these photographs yielded the average time necessary for burning a fuel drop from 100 to 120 microns diameter, to 50 or 60 microns diameter. The time for combustion of the entire drop was determined by extrapolating to zero diameter. The time thus determined for the evaporation and combustion of a 100 micron drop of kerosene varied from 0.01 to 0.0267 second, for the conditions of the test. For one series of photographs air was supplied througn a tubular air heater. This procedure aided in burning somewhat larger drops (120-130 microns). Similar analysis of these photographs did not reveal any significant change in burning time. Practically all initial work was done using kerosene as the fuel. Some trials had been made with single component fuels; the continuation of this work is reported below. WADC TR 54-390 2

Fig. 2. Photograph of Drop Combustion Equipment. Fig. 3. Photograph of Drop Combustion Equipment, Showing Kerosene Spray Burning in Heated Air, IADC TR 54-390

Fig. 4. Photograph Showing Double Images of Burning Kerosene Drops in Combustion Zone - Initial Drop Diameter - 100 Microns. * WADC TR 54-590 4

I 0 N 7 2 X"^ C,) Z 0 r.6...5 w 0 TIME - SECONDS x 102 Fig. 5. Mean Diameter Squared vs Elapsed Time 80 Micron Benzene Drops. Fig. 5. Mean Diameter Squared vs Elapsed Time 80 Micron Benzene Drops. WADC TR 54 —590 5

C= 0 c 1.0 -- ----- 0.9 0 0.8 0.7 Cm 0.6 rlo\ w 0.5._ o 0.4 0.3 ---------------------- 0.2 0.1 0 ____I____I____I____ 0. 1.2.3.4.5.6.7.8.9 1.0 1.1 1.2 1.3 1.4 1.5 TIME-SECONDS x 102 Fig. 6. Mean Diameter Squared vs Elapsed Time 100 Micron n-Heptane Drops.

Cw 0.7.8.9 I.C TIME-SECONDS x 102 Fig. 7. Mean Diameter Squared vs Elapsed Time, 80 Micron Propanol Drops.

1.0 N ir w w 0.9 0.8 0.7 0.6 0.5 -- 0.4 0.3 0.2 0.1 0.1.2.3.4.5.6.7.8.9 1.0 1.1 I. TIME - SECONDS x 102 Fig. Mean Diameter Squared vs Elapsed Time 100 Micron Cyclohexane Drops. 2 WADC TR 54-390 8

Fig. 9. Photograph of Burning Drops with Axis of Camera Horizontal. iADC TR 54-390 9

Fig. 10. Photograph of Burning Drops with Axis of Camera Horizontal (Plane of Picture Vertical) - Heated Air Supply. WADC TR 54-390 10

SECTION I COMBUSTION OF GROUPS OF DROPS Experimental Work A detailed analysis was made for burning sprays of benzene, cyclohexane, n-propyl alcohol, and n-heptane. The photographic negatives were examined' on a comparator with a total magnification of 30. The negatives were divided into zones, and the zones were aligned as described in detail in Reference (1). Summaries of the resulting drop counts will be found in Appendix A. The data for this work was taken from 29 photographs, this number representing the productive group of some 250 photographs taken. The data is plotted showing the square of the mean drop diameter versus the elapsed time. As can be seen in Figures 5, 6, 7, and 8, the resulting plot closely follows a straight line down to a size of about 50 microns. The slope of this line is the constant X for the particular fuel, as defined below. Given the value of X for a particular fuel the time for evaporation and burning can be obtained readily from D2 = D2 - Xt where D = diameter at time t Do = original diameter t = elapsed time, seconds X = evaporation constant, cm2/sec Results for the four fuels tested are presented by meahs of the values of X taken from the plot as well as showing the corresponding life of a drop of 100 microns original diameter. The data for these burning tests are shown in Appendix A for these four fuels; the most significant items of interest are shown in Table I, which follows: TABLE I Rate of Combustion of Four Hydrocarbons 2F^I (cm/ sec)Time to Evaporate _______Fuel 2_________(cm2_/_sec) 100 p drop - seconds Benzene.0033.03 Cyclohexane.0066.015 n-Propyl alcohol.0046.0217 n-Heptane.0047.0213 In pursuing this method some question arose as to whether a significant proportion of the smaller drops drifted up with convection currents within the flame zone. The photographs serving as the basis for the foregoing work were taken with the axis of the camera vertical, the region of focus being about 0.6 mm in depth and located close to the bottom of the flame. Any drift of small drops up out of the zone of focus of the camera would result in an apparent increase of the mean drop diameter remaining in focus in each succeeding zone, and therefore a deceptively low value of X with a correspondingly long drop life. To check this a series of photographs were taken at right angles to those mentioned above. The drops coming from part of the spinning disk were shielded and the camera was located in the shielded space with its axis tangential to the group WADC TR 54-390 11

of drops that was burning. When viewed thus the flame presented a roughly triangular outline and revealed the drop images concentrated along the lower boundary of the flame (see Figure 9). It was noted that when heated air was supplied from below, through the tubular air heater, some small drops were observed rising through the flarie zone, certainly out of focus of the vertically oriented camera (see Figure 10). The proportion of drops rising in flames without heated air supply appeared much lower. A series of these photographs were analyzed for purposes of checking the values presented above. It should be pointed out that the numbers of drops appearing in focus are much smaller, therefore the resulting values would be more sensitive to anomalies and correspondingly less reliable. They are presented for two of the fuels in Table II. TABLE II Combustion Data from Photographs with Vertical Plane -............,.....,, Fuel Time to evaporate 100. drop-seconds Cyclohexane.00763.013 n-Heptane.0091.011 The results from the two methods are seen to agree in one instance, yet differ by roughly a factor of two in another. This irregularity may be attributed to the limited number of drops dealt with in one method, or to the apparent drop life being artificially lengthened by virtue of the small drops going out of focus in the other. In order to compare the burning times of different fuel drops it would be desirable that the individual burning times be measured more accurately. The burning times reported here may be artificially long because of the dearth of small size drops. Work has been done in an effort to improve the accuracy of the measurements of the rate of burning of the drops. One method consists of having a series of six flashes from a single flash lamp, during the life of the drops. In this manner a complete history can be obtained for a particular drop. This has been accomplished, and work is being done to improve this technique. WADC TR 54-390 12

SECTION II EVAPORATION OF INDIVIDUAL DROPS Introduction This investigation was originated to study the burning process of single droplets of various fuels. A subsequent evaporation study was initiated with the intention of adapting the techniques developed in the evaporation study to the study of the single droplet combustion process. Preliminary work led to the development of a technique whereby single droplets of fuel could be maintained in a fixed position by means of a vertical blast of air passing through a stationary ultrasonic field. This is the technique being used at the present time to study the evaporation of droplets. At the same time, the apparatus is being further developed to adapt the technique to the combustion study of single droplets. The original apparatus and technique have been described elsewherel) This report describes the apparatus as modified since the appearance of the original report. Changes which are being considered in the hope of increasing the versatility and scope of operation of this technique are also described. All results obtained up to the writing of this report are included, but a full evaluation of these results has been delayed because of the undetermined effect of the stationary ultrasonic field on the evaporation process. Inconclusive tests relating to the ultrasonic effects are described briefly, and their preliminary results are given. Description of Apparatus Principal components of the apparatus used for freely suspending droplets are shown schematically in Fig. 11, while an actual view is given in Figure 12. These components include a surge tank, wind tunnel and nozzle, barium titanate piezoelectric tube, oscillator, amplifier, and camera. A hot water tank, rated at 150 psig continuous duty, serves as the surge tank. No modifications were required to adapt the unit to the system since normal working pressure during operation of the apparatus is about 95 psia. The vertical wind tunnel is composed of three sections: diffuser, calming section, and nozzle. Both the diffuser and calming sections are constructed from one-half inch white pine boards, fastened together with cross members as seen in Figure 12. Overall dimensions of the diffuser section are 21 x 21 x 31 inches high, the divergent angle being 30 degrees. The calming section is 21 x 21 x 19 inches high and contains a series of screens as indicated in Figure 11. Screen mesh starts, at 20 x 20 at the lower part and increases in jumps of 20 x 20 up to 100 x 100, each screen being placed two inches above the next lower screen. The function of these screens is to progressively decrease the turbulence existing in the air flow before the air enters the nozzle. The nozzle at the top of the wind tunnel is cut from a large block made up of 1-1/2 x 6 inch boards glued and then bolted together with four through bolts, the dimensions of the finished block being 21 x 21 x 6 inches high. The bolts are located so as not to interfere with the contour cutting operation described below. Cutting was done with a large flycutter, in the form of the Archimedes spiral shown in Figure 13, mounted in a vertical drill press. Considerable chatter developed as the cutting progressed, but this was eliminated each time by changing the speed of the drill press. Small cracks were then filled in with body putty and the nozzle sanded and varnished. A one-half inch aluminum plate with a 1-5/8 inch WADC TR 54-390 13

VIEWING SCREEN LENSE SCREENS WIND TUNNEL POWER AMPLIFIER OSCILLATOR SUPPLY SURGE TANK CONTROL FILTER aL.VE Fig. 11. Schematic of Equipment Set-Up, Single Droplet Technique. Fig. 12. Photograph of Equipment Set-Up, Single Droplet Technique. WADC TR 54-390 14

I T, poER TR'ANSFORMER 150.- O.C. 150 ma. D.C. V, 6F6 V2,V3=6L6 V4 z5U4G R, 0.5MEG., 1/2W R3 = 1700, 1/2 W R3 5.1K, 30W R4 200, lOW R% 2250,25 Fig. 14. C, I Ommfd., MICA CoC5 =25mfd, 25V. C,,C4 s4mfd.,400V. Li 4H AT 130ma.,l00 Ohms Ti = DRVER TRANSFORMER, TURNS RATIO, PRI-I/2 SEC.4:1 T - OUTPUT TRANSFORMER 3800 OHM PRIMARY TO 500 OHM SECONDARY Schematic of Ultrasonic Schem~ ~ ' Frequency Amplifier. 15 WADC TR 54-390

l \O 0 VIEWING MIRROR VIEWING IMAGE SPLITTER EXTENSION LENSE SCREW MOUNTING BOARD D>= DROPLET IMAGE PATH - - STOP WATCH IMAGE PATH STOP WATCH ^ C= Fig. 15. Cut-Away View of Lens Extension Tube

hole in the center was bolted over the nozzle exit and serves as the mounting plate for the barium titanate tube. Generation of the stationary ultrasonic field by the barium titanate tube is by the piezoelectric effect. The tube, after installation of the windows and tuning as described in a later section, mounts directly into the aluminum plate and makes electrical contact at both the inner and outer surfaces with spring contactors, electrically insulated from the aluminum plate. The contactors connect directly to the output of the ultrasonic frequency amplifier which in turn obtains its signal from the variable frequency oscillator. A schematic diagram of the amplifier is given in Figure 14. Records of the evaporation runs, were taken with a 16 mm U. S. Army Air Force Type N-6 gun camera having speeds of 16, 32, and 64 frames per second. To increase the drop image sharpness, the projection box used in the original set-up was replaced by a lens extension.tube. The tube, made of one-half inch micarta, has an overall length of 11-1/4 inches, giving a magnification of 5X when used with a 50 mm focal length lens. The particular lens being used is a 50 mm, f/4.5 Wollensak Raptar in a Rapax shutter. The inside of the extension tube is lined with black velvet, and a black paper diaphragm is inserted in the tube to cut down light reflections from the tube wall. An image splitting block is mounted in the center of the tube at the camera end as shown in the cut-away view in Figure 15. The ground glass viewing screen and secondary lens are located directly above and below the block respectively. The focal length of the secondary lens was chosen so that the image of the stop watch just filled the frame of the 16 mm film. The image splitting block divides the images from both lenses; the transmitted image-passes directly through the block, the reflected image is reflected at 90 degrees. The transmitted drop image from the primary lens appears on the film while the reflected drop image appears on the viewing screen. The reverse is true for the stop watch image projected by the secondary lens. Using this arrangement, it is possible to view the droplet for position control purposes as it is being photographed. Figure 16 gives a close-up of the camera and piezoelectric tube in position on the wind tunnel. It shows the viewing hood, secondary lens, and two mirrors illustrated in Figure 15. The stop watch is located below the left mirror, out of view of the photograph. Two 90 degree prisms are used to make the image splitter. The hypotenuse of one, after being coated with a half-silvered surface, is cemented to the hypotenuse of the other, forming a rectangular block. A much cleaner drop image is produced than with the simple half-silvered mirror used in the original set-up since ghost reflections from the non-silvered surface of the plane mirror are eliminated. Figure 17 shows a schematic diagram of the switch box used for controlling the camera and selecting the subject to be photographed, i.. e. the droplet or stop watch. Changing from one subject to the other is accomplished by merely switching from one illuminating source to the other while the camera is in operation. By photographing the droplet and stop watch at certain specified time intervals only, relatively few feet of film are required to record evaporating droplets having even the slowest evaporation rates. This allows the recording of several different droplets on one reel of film and makes it possible to record droplets whose total time of evaporation is greater than 2-1/2 minutes, the approximate duration of a 50 ft length of film at 16 frames per second. WADC TR 54-390 17

Fig. 16. Close-Up View of Camera, Barium Titanate Tube, and Droplet Light. SI 115:26 115V 60Ofl~ 1 D XS3 II WATHLIGHT f) ( LIGHT.. _.. q LIGT, Fig. 17. Schematic of Switch Box. WADC TR 54-390

The Barium Titanate Piezoelectric Transducer The stationary ultrasonic field is generated by a piezoelectric tube manufactured by the Brush Electronics Company. These tubes come inavarious sizes and shapes, and the particular units being used, and tested for possible use, in this application are shown in Figure 18. Only the large tubular element was used to obtain the results given in this report, but the smaller tubular units are being considered for the study of smaller droplets since theoretical considerations given in Appendix B indicate that the stabilizing effect of the ultrasonic field is proportional to the square of the frequency and inversely proportional to the drop diameter. The higher resonant frequencies of the smaller tubular elements should therefore provide a greater stabilizing action onthe smaller droplets than has been obtained with the larger tube. -In all tests performed with the large unit, the stabilizing effect on droplets disappeared at about 100 microns. Dimensions of the large piezoelectric tube are 1-5/8 O.D. x 2 I.D. x 4 inches long, and it operates at a resonant frequency of about 33,000 cps. Maximum safe operating voltage specified by the manufacturer is 100 volts rms, but most test runs were made at about 12 volts. The voltage is applied between the inner and outer coated surfaces of the tube. Before the tube can be used for evaporation studies, it is necessary to fit the tube with two windows and then "tune" the tube by properly positioning these so as to cause the droplet to come to rest within the field of view of the windows. Cutting and tuning are done in the following manner. A cutting tool is made from a one-half inch brass rod, about 2 inches long. The diameter of half the rod is reduced, if necessary, to fit the chuck of a vertical drill press, and the large end is drilled out with a three-eighths inch drill to a depth of about threefourths inch, leaving a tubular wall thickness of one-sixteenth inch. The tool is completed by filing broad teeth in the tubular end. Window positions are then laid out on diametrically opposite sides of the tube, about one-third of the distance from one end of the tube. One of these positions is surrounded by a small putty dam slightly less than one inch in diameter, and the tube is supported horizontally on the bed plate of the drill press by a half-round wooden rod slightly smaller than the inside diameter of the tube. After locating —and lightly clamping the piezoelectric tube in position, the dam is partially filled with a diluted cutting compound. The cutting operation is carried out at a slow speed and with the drill handle weighted down to allow the operation to progress unattended. The cutting tool is lifted occasionally to allow the cutting compound to flow into the cut for better cutting and cooling. When both holes are cut, half inch window discs, cut and ground to shape, are cemented in place. Before the cement hardens, however, the piezoelectric tube is mounted on the wind tunnel and connected to the output of the ultrasonic amplifier. A droplet of liquid is then suspended as described in EXPERIMENTAL PROCEDURE. If, after coming to rest, the droplet cannot be positioned between the two windows by varying the air velocity, it will be necessary to tune the unit. Three windows adjustments are possible: a radial adjustment, a vertical angular adjustment, i.e. varying the angle between the window and the tube axis, and a horizontal angular adjustment, or varying the angle between the window and the tangent to the tube circumference. By varying the window positions and noting the effects on the drop position, it soon becomes possible to make the adjustments necessary to bring the droplet to rest between the two windows. The tube is then ready for use. When an alternating voltage is impressed across the transducer, the tube changes shape as shown in Figure 19. One polarity causes the tube wall to thicken, WADC TR 54-390 19

Fig. 18. Basic Piezoelectric Elements. + A B C Fig. 19. Action of the Piezoelectric Tube Under Polarity of Applied Voltage. Changes In WADC TR 54-390 20

Figure 19-B, thereby gnerating a radial compression wave within the tube, while the opposite polarity causes the tube wall to become thin, resulting in a radial rarefaction wave. Waves originating at a given position on the, inner surface of the tube travel along a diameter to the opposite side of the tube; a similar wave travels in exactly the opposite direction at precisely the same time. When the tube diameter (d) and wavelength (l) are properly related, (d = n!, n = 1,2,...) there results a stationary sound field as shown in Figure 20. The figure shows that two identical waves, traveling in opposite directions, combine to form a standing wave, i.e. a wave with stationary nodes. The droplet position in the field is indicated. When using the large tube in a horizontal position, droplets of liquid of approximately 600 microns have been suspended against gravity solely by the action of the ultrasonic field. The droplets did exhibit some axial motion, possibly due to harmonics caused by the slightly distorted tube shape. The condition required for a standing wave is that the tube diameter and wavelength have the relationship given above, i.e. the tube diameter be a whole multiple of the wavelength. A change in either the diameter or wavelength will upset the relationship and destroy the standing field. Since the tube diameter is fixed, only wavelength changes will affect the field, that is, either a change in frequency or velocity of the wave in air. Since the tube must operate within a very narrow frequency band around the resonant frequency, the field is essentially controlled by the sonic velocity in air. From the well known relationship for sonic velocity, a = vT = 49.1 where a = sonic velocity in ft/sec y = ratio of specific heats Cp/Cv =1.4 for air R = gas constant = 1715 ft-lb/slug ~R T = degrees Rankine, the fact is established that the ultrasonic field is dependent upon air temperature only and that any change in temperature will destroy the stationary field and, therefore, the stabilizing action on the droplet. However, the possibility remains that the temperature can be changed by an amount such that the required relationship between wavelength and tube diameter be re-established. This has been done in Appendix C which shows that the required temperature changes are large and that at most, only two points are possible within what might be classed as a reasonable temperature range. The tube, therefore, is not adaptable to studies involving changes in temperature. To overcome this effect, attention has been directed to the possibility of maintaining the proper wavelength - diameter (distance) relationship by changing the distance between the wave generating surfaces as the wavelength changes. Although impossible with the tube, this might be accomplished with flat parallel plates. Using four plates to form a square duct, it may be possible to create a standing field in which the stationary nodes form a square grid. Changing the distance between opposite plates by the proper amount would thus compensate for changes in wavelength due to changes in temperature, thereby maintaining the required wavelength - distance relationship and also the stabilizing effect on the droplet. During the evaporation runs it was noted that as the droplets decreased in size the stability of the droplets decreased and finally disappeared when the WADC TR 54-390 21

DROPLET - 7 / / / / / / / / / ^ Vlr /,-/ e%..- \ o% 4-7N 0-% #411% "/, % 0 \ / \ / \ %.0 \ v - A. B /I ~ /\/VW/\ A / \./ 1.. %.4f -." -. - / / / PIP_, --- WAVE GENERATED AT THE RIGHT SURFACE -- WAVE GENERATED AT THE LEFT SURFACE - RESULTANT PRESSURE WAVE Fig. 20. Generation of the Standing Sound Wave by the Piezoelectric Tube. Fig. 21. Section of 16-mm Film Showing Change from Stop-Watch to Droplet Image. WADC TR 54-390 22

diameter decreased to about 100 microns. This follows from the result derived in Appendix B which shows that the maximum droplet displacement is inversely proportional to the droplet diameter. It can be assumed, therefore, that when the displacement increases to a sufficient portion of the wavelength the stabilizing effect is permanently lost, and the droplet wanders about within the tube. The equation also shows the displacement to be inversely proportional to the square of the frequency, indicating that an increase in frequency should result in greater stability, so that tests with droplets smaller than 100 microns seem feasible. The flat plate element shown in Figure 18 operates at a resonant frequency of 200,000. cps, a considerable increase over the 33KC operating frequency of the tube being used at present. This indicates that evaporation studies can be extended to much smaller drop sizes than are possible with the present apparatus. Work is in progress to adapt the flat plate elements to the present investigation in order to overcome the temperature effectsmentioned earlier and to investigate droplets below 100 microns. Exerimental Procedure Before the equipment is used, the field of view of the camera should be marked on the viewing screen. A focusing screen is first made from a discarded film magazine and a piece of fine-grained ground glass and is inserted into the film magazine compartment. By focusing on a stationary flat object and noting the limits of the image appearing on the focusing screen, it becomes possible to mask the same image on the viewing screen with transparent scotch tape. A straight piece of fine wire glued to the end of a very fine thread is also required for focusing and size determination, as explained later. The equipment, set up and connected as shown in Figures 11 and 12, is ready for its initial run. Several minutes before the run is to be made, the ultrasonic amplifier, oscillator, and variable D.C. supply are turned on and allowed to warm up. During this time the camera lens is opened, set to about f/4.5, and the focusing screen is inserted into the film magazine compartment. The power to the switch box is turned on and the control switch, S3 in Figure 17,set to position 1. This turns on the background light for the droplet. The lamp is positioned to give the best field of illumination when viewed on the viewing screen in the lens extension tube. With the air turned on at a relatively low velocity and the ultrasonic supply warmed up, the oscillator is tuned to the resonant frequency of the tube (approximately 33,000 cps for the large tubular element). The voltage across the tube is then adjusted to about 20 volts by varying the D.C. supply. The wire is then suspended in the tube, close to the position originally occupied by the droplet during the window tuning operation. At the same time the oscillator frequency is varied until the wire is suddenly "grasped" by the sound field and held in a fixed position. The voltage is again adjusted to about 20 - 30/volts and a fine frequency adjustment is made to increase the "grasp" if possible. When the adjustment is correct, it is possible to slightly shift the upper end of the thread holding the wire without causing the wire to shift. A glass eye-dropper, drawn to a fine tip, is next filled with a liquid of relatively low volatility, such as kerosene, and droplets are shaken from the dropper into the tube directly above the node previously occupied by the wire in the frequency adjustment operation. If the majority of the droplets fall, the air velocity should be increased. If they rise, the air velocity should be decreased. It will be found that eventually some droplets will be held suspended in the air stream. The air velocity should then be adjusted until the droplet occupies a WADC TR 54-590 23

Fig. 22. Sequence of Frames Taken from a Film of an Evaporating Droplet (Acetophenone)-Elapsed Time Given in Minutes and Seconds. WADC TR 54- 390 24

3 \J1 40 0 1300 1200 1100 1000 900 800 700 CU z 0 wr 2 1: L I -J 0 0. 0 600 500 400 300 200 0 I I I I I 1. 1 I I I _ 1 I 0 tO 20 30 40 50 I 10 20 30 40 50 2 ELAPSED TIME-MINUTES 8 SECONDS Fig. 23. Evaporation Curves for Some Pure Hydrocarbons, Diameter vs Elapsed Time.

\3 I Vr 1200 t 0 1100 1000' 900 V) z o 800 nr o 1 700 aR) J- 600 2r o 500 ILI 5 400 0 cr 300 300 200 100 0 1 2 3 4 5 6 7 ELAPSED TIME - MINUTES Fig. 24. Evaporation Curves for Some Pure Hydrocarbons, Diameter vs Elapsed Time.

\J I ~o To 10004 900 4 \A (n 2 0 0 LJ ILLJ -J 0 01..]. 800 70C 60C 50C 40C 30C o KEROSENE * ACETOPHENONE ) 1 I - a__I_________I__I__II__II__I — k I ) ) ) r) 200 100 0 I %k 0 20 40 60 80 100 120 ELAPSED TIME -MINUTES Fig. 25. Evaporation Curves, Diameter vs Elapsed Time.

position directly between the two windows and becomes visible on both the focusing and viewing screens. Using a pencil type microscope, about 20X, to view the image on the focusing screen, the camera is adjusted to bring the image into sharp focus. The control switch S3 on the switch box is then turned to position 2 with switch S2 in the off position, turning on the stop watch light source and turning off the droplet light. The stop watch is then taped to a movable platform directly below the camera and in full view of the secondary lens as indicated in Figure 15. The light source is adjusted to get maximum illumination, and then the stop watch is brought into sharp focus by raising or lowering the platform. When making a run, the equipment is allowed to warm up for about half an hour. During this time the eye-dropper is thoroughly cleaned and filled with the fuel to be checked. If the equipment has not been used for some time it may be necessary to retune the oscillator and to focus the camera. After selecting the correct lens opening and shutter speed, and setting the footage indicator, a "shot" is taken of the test number and another of the wire suspended in the ultrasonic field. By measuring the actual size of the wire and the size of the image on the developed film, a magnification factor is obtained. Droplets are then shaken into the cylinder until one becomes suspended, and a photographic record is immediately started. This is done with both switches S1 and S2, see Figure 17, in the "on" position and the control switch S1 started in position 1. A shot is taken by turning the control switch to positions 2,3,2, and 1 in the given order. In position 2 the camera is turned on and the stop watch illuminated, thereby recording the time. In position 3 the camera is kept running while only the droplet is illuminated so that the droplet image is recorded. In going to positions 2 and 1 again, the time is recorded a second time, and the final position stops the camera and illuminates only the droplet so that its position can be controlled by manually varying the aii flow. Shots are taken at about one-half or one minute intervals until it is no longer possible to control the drop position. Figure 21 shows the conversion from stop watch to droplet image during a typical shot. The developed film is then projected on a screen to get an additional magnification. Here the wire image is accurately measured to obtain the overall magnification factor. The sharpest image from each shot of a droplet is then measured in two directions at right angles to each other to get average droplet diameter, and the time is computed from the closest stop watch image. The result gives average droplet diameter vs elapsed time of evaporation. Experimental Results The experimental data were obtained with the large tubular element shown in Figure 17, and all tests were carried out at room temperature and pressure. In all cases the droplet was falling at its terminal velocity, a characteristic feature of the technique used. A typical film record is shown in Figure 22. All results are plotted in Figures 23, 24, and 25 and are summarized in Table I where the negative inverse slopes of the evaporation curves, in seconds/micron, are given for each pure hydrocarbon tested. The table also gives the boiling points and latent heats of vaporization, and these are plotted against the negative inverse slope in Figure 26. The results show a linear relationship between droplet diameter and elapsed time of evaporation for the pure hydrocarbons. Slight deviations, however, from this linear relationship are noted at the start and finish of some of the runs. It is presently believed that these effects can be attributed to one or more of the following factors: WADC TR 54-390 28

220 3 0 201 18' 1 o N 0 -- 12( O z 10 ~ 004 ro 0 H 61 z Ld t 4 J 0 0 0 0 0 0 I\ 13 2 oi0 0,0 /,12 8 o 7 9 2 0 / A 05 *5 07.12 so" 9 I n J10 ~ ~ *9 i 0 3 A 6T 0 2 8 1 14 15 II o BOILING POINT C~0 ~* LATENT HEAT NUMBERS REFER TO FUEL IN TABLE (3) O) _ D I III I 2 (.01.02.04.06.08 0.1 0.2 0.4 0.6 0.8 1.0 2.0 NEGATIVE INVERSE SLOPE- SECONDS MICRONS Fig. 26. Boiling Point and Latent Heat of Vaporization as a Function of Evaporation Rate for Some Pure Hydrocarbons.

1200 1000 V) z 0 cr CD w LiJ J UJ Q 0 cr 0 800 600 400 o 0 VOLTS ~ 5 VOLTS o 0 VOI LTS * 20 VOLTS V "^tL-Ni. --- ----- ----- ----- ----- ----- ---- ----- v^'^^~~~~~~~~~ *^v^ --- —~~~~~~~~~~~~~~~~~~~~ I~ ~ ~ I I VOLTSI I I. 200 0 0 2 4 6 8 10 ELAPSED TIME-MINUTES Fig. 27. Effect of Ultrasonic Field Intensity on Evaporation Rates (Tert-Butylbenzene) WADC TR 54-590

a. Initial cooling of the droplet upong entering the air stream. b. Impurities present in the fuels. The purity of the fuels tested ranged from 99 mol % to unspecified values. For the present developmental stages of the technique and apparatus this is considered adequate, but these will have to be replaced eventually with fuels of a uniform high purity. c. Changes in intensity of the ultrasonic field. During some of the runs, the intensity of the field was increased towards the end of the evaporation run to improve droplet stability. In view of recent tests discussed in a later section, the increased evaporation rate with an increased field intensity should be expected. Figure 25 indicates that the evaporation process is influenced to a greater degree by the boiling point than by the latent heat since, in general, the rate increases with an increase in boiling point while the latent heat remains about constant. This is indicated by the solid lines drawn through the widely dispersed points. These lines are meant to show only the genral trend of each property with rate of evaporation. Effect of the Ultrasonic Field on Evaporation Tests to investigate the effects of the ultrasonic field on evaporation have been initiated only a short time ago, so the results at this time are meager and inconclusive to some extent. However, it has been determined that some influence exists and that the effect increases with the intensity of the field, becoming quite pronounced at the higher intensities. Some results are shown in Figure 27, indicating the increase in evaporation rate with increasing sound intensity. Tests were made in still air with droplets suspended in the sound field on a fine glass filament. At zero and 5 volts across the piezoelectric tube, the filament was clamped firmly to a support, while at the higher voltages the glass filament was suspended from a fine thread, allowing the droplet to find its equilibrium position in the sound field. The fuel used was tert-butylbenzene. The test carried out at zero volts represents, essentially, the technique used by Godsave, except that no burning took place. An interesting factor to note is that the character of the evaporation curve changes when the evaporation takes place in still air, for under this condition the curves are no longer linear, as was true for all other tests in this investigation, but exhibit a definite curvature. It is felt that additional tests will have to be made before definite conclusions can be reached on the ultrasonic effects. The results given are based on a single test run, and whether or not they can be repeated is not known. Additional work along these lines is being pursued. WADC TR 54-390 31

Evaporation Fuel - -- -- -- 1 2 3 4 5 6 8 9 10 11 12 13 14 15 2, 4-Dimethylpentane n-Octane Ethyl Alcohol Tert-Amyl Alcohol Pyridine Ethyl n-Valerate n-Butyl Alcohol Isopropylbenzene 2-Heptanone Tert -Butylbenzene n-Decane Furfural n-Butylbenzene Methyl n-Hexyl Ketone Ac etophenone TABLE III Rates of Some Hydrocarbon Fuels Negative Inverse Boiling Slope Point (Seconds\ (~C) Micron / 0.015 80.8 0.044 125.7 0.057 78.5 0.059 102.0 0.066 115.0 0.101 145.5 0.117 117.7 0.117 152.5 0.148 150.0 0.208 168.7 0.295 174.0 0.385 161.7 0.418 180.0 0.454 173.0 1.237 202.3 - Heat of Vaporization AHv (Calories\ \ Gram / 70.9 73.19 204.0 105.83 107.36 77.16 141.26 74.6 82.66 60.2 107.51 74.06 77.16 WADC TR 54-390 32

BIBLIOGRAPHY 1. Bolt, J. A., Boyle, T. A., Mirsky, W., "The Generation and Burning of Uniform-Size Liquid Fuel Drops," Project 1988, University of Michigan Engineering Research Institute Report, May, 1953. 2. Godsave, G. A. E., "The Burning of Single Drops of Fuel," National Gas Turbine Establishment, England, Report R87, 1951. 3. Gohbrandt, W. "Evaporation of Spheres in a Hot Air Stream," National Gas Turbine Establishment, England, Memo No. M10O, 1951. 4. Kinzer, G. D., and Gunn, R., "The Evaporation, Temperature and Thermal Relaxation - Time of Freely Falling Waterdrops," Journal of Meteorology April, 1951. 5. Namekawa and Takahashi, "Note on the Evaporation of Small Water Drops," Physico-Mathematical Society of Japan, 1932. 6. Spalding, D. B., "Combustion of Liquid Fuel in a Gas Stream," Fuel, 29, 2-7 and 25-32 (1950). 7. Spalding, D. B., "Combustion of Fuel Particles," Fuel, 30, 121-130 (1951). 8..Topps, J. E. C., "An Experimental Study of the Evaporation and Combustion of Falling Droplets," National Gas Turbine Establishment, Memorandum No. M105, February, 1951. WADC TR 54-390 33

APPENDIX A WADC TR 54-590

DATA FOR COMBUSTION OF BENZENE DROPS Original Drop Size 80 Microns P o Picture No. Zone 6 1 2 3 4 5 7 8 9 10 11 v - -- -- 1128 1153 1154 1155 1172 80 702 80 803 703 80 805 70 802 70 80 802 704 70 804 704 702 60 70 80 704 60 80 805 7013 60 80 70 60 70 80 704 60 70 802 7013 605 702 60 60 802 702 602 60 80 708 606 70 602 60 7o3 602 50 70 702 607 50 40 61.4 702 60 60 604 50 40 60 605 502 40 57.2 602 50 502 40 60 70 502 40 52.5 0-\ Mean Drop Diameter - 76.0 Microns 74.5 71.4 69.0 66.8 57.5 46.7 Mean Velocity - Fr/Sec 6.85 5.12 5.4 5.02 4.91 4.75 4.20 6.42 1.43 1.59 Mean Time to Traverse Width fo.101.134 Elapsed Time - Seconds x 102 Zone - Seconds x 102.131.235.138.366.141.504.165.108.514.436 0.101.645.791.956 1.578 1. Values tabulated are drop diameters in microns 2. Superscript indicates numbers of given size appearing in zone

DATA FOR COMBUSTION OF n-HEPTANE DROPS ziune Picture No. 1 2 3 k" 5 6 7 8 9 10 11 1211 1223 1227 1228 1229 1233 1234 1236 1245 110 100 100 90 110 100 100 110 100 110 1003 1002 90 110 110 100 100 90 1102 1002 100 100 110 90 90 90 100 100 1002 90 80 1102 100 902 1003 90 100 902 803 80 902 100 100 100 90 80 100 80 90 80 90 1102 903 70 80 70 100 90 90 80 902 802 702 904 90 902 902 80 70 902 80 903 802 100 903 90 805 702 902 802 90 90 90 80 80 80 80 50 902 70 802 702 60 80 70 802 90 90 80 40 80 50 80 90 80 60 70 70 50 70 4o3 80 80 70 40 70 50 40 702 50 70 1247 Mean Drop Diameter - Microns 102 102 98 92 87.3 87.8 81 75 69 70 50 Mean Drop Velocity - Ft/Sec 6.25 5.33 4.85 4.65 3.85 5.24 3.74 3.02 1.40 4.57 1.51 Mean Time to Traverse Zone - Seconds x.111.130.143 102.149.180.214.185.229.155.457 Elapsed Time - Seconds x 102 0.111.241.384.5533 713.927 1.112 1.34 1.99

\0 0 DATA FOR COMBUSTION OF PROPANOL DROPS Zone Picture No. 1 2 4 56 7 8 9 10 11 1532 804 804 802 702 80 703 80 703 703 60 603 30 1533 1536 1526 1518 m, 1519 1506 1492 806 805 802 804 806 806 804 805 50 80 70 602 50 802 60 70 803 802 702 706 70 602 502 70 80 70 80 704 60 50 702 802 70 602 705 60 702 603 70 703 703 603 703 603 603 502 70 70 50 40 603 503 603 503 602 502 40 602 50 30 602 503 40 60 502 40 30 60 602 40 70 605 502 604 502 502 40 30 50 403 807 80 703 803 806 802 80 702 802 802 707 602 706 602 Mean Drop Diameter - Microns 80 78.7 74.9 Mean Velocity - Ft/Sec 6.74 69.2 4.38 66.5 35.78 5.59 4.95 61.2 5.45.202 53.8 1.72.404 51.4.736.943 49.3 1.22.565 Mean Time to Traverse Zone - Seconds x 102.103.124.140 Elapsed Time - Seconds x 102 0.103.227.158.183.367.525 -7o8.910 1.314 2.257

DATA FOR COMBUSTION OF CYCLOHEXANE DROPS FI \O 0 Zone Picture No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 -- 1263 1264 1266 1305 1307 1102 03 904 903 100 1002 90 80 90 802 1002 100 1002 902 902 90 803 80 703 70 703 60 50 802 80 40 602 902 70 60 702 40 30 80 60 70 40 50 502 602 40 30 80 90 50 60 50 40 30 80 50 70 70 60 1002 1002 902 902 902 80 80 70 70 1002 1002 100 90 80 70 80 90 90 80 60 60 100 1004 1003 1002 100 907 904 903 909 9015 8011 804 802 806 804 70 702 70 60 90 70 80 70 902 802 702 60 80 80 80 70 80 80 70 60 602 Mean Drop Diameter 102 - Microns 98.5 92.3 88.1 87.5 80.4 76.2 71.4 69.0 63.2 62.0 53.4 51.6 50.0 Mean Drop Velocity - Ft/Sec 8.5 7.51 6.08 6.03 6.19 5.58 4.20 4.38 3.48 2.84 2.31 2.72 3.37 2.04 Mean Time to Traverse Width or Zone - Sec x 102.0825.092.114.115.112 Elapsed Time - Seconds x 102.124.165.158.199.244.288.255.206.340 0.o825.1745.2885.4o35.52.692.850 1.049 1.293 1.537 1.825 2.080 2.286

APPENDIX B WADC TR 54-390

APPENDIX B Development of the Equation for the Stabilizing Action of the Ultrasonic Field on Drop Position A B / g.Fig. A. Figure A illustrates the position of a droplet in tohe node of a standing sound wave. At a given instant, let the pressure distribution be represented by the solid curve A. Under these conditions, air will flow past the droplet from left to right as designated by the solid arrows.; Half a period later, the pressure can be represented by the dotted curve B and the air velocity by the dotted arrows from right to left. The air velocity relative to the drop can then be represented by the following equation: V = Vm sin wt. m (1) where V = relative velocity at time t Vm = maximum relative velocity w = frequency of the ultrasonic sound t = time This relative velocity givs r ise to a drag force on the drop, where the drag force is related to a drag coefficient by the following expression. D C = D D (l/2)paV2S (2) where CD = drag coefficient (dimensionless) D = drag force (pounds) p = mass density of air (slug/ft3) V = relative velocity of the air past the drop (ft/sec) S = projected area of the drop (ft2) From this, the drag force is given by, D = (1/2) PaV2S CD Substituting for V from equation (1) we get the drag force as a function of time, i.e., D(t) = (1/2) paVm2SCD sin wt where = D sin wt (3) D(t) = drag force as a function of time Dm = maximum drag force Since the motion of the droplet is subject to Newton's equation of motion, the equation becomes Drop mass x acceleration = forces causing the acceleration or M d2x dt2 = Dm sin wt (4) WADC TR 54-390 42

Integrating with respect to t, d (dx) dt dt dt Dmn sin wt wdt wM (5) (6) dx -D cos wt + CD dt -wMHere we substitute the initial condition: t = 0 dx dt o so that Dm v0 = ___+ C1 0 wM C1 = v + Dm wM (7) (8) (9) (10) Equation (6) becomes, dx / f Dm\ t -= VO + ) dt W Dm - - cos wt wM Integrating a second time with respect to t, we obtain, dt -~~.~mS mdt dt w2M cos wt w dt (11) which becomes, X = Dm\ x = 0~ + M t - m sin wt + C2 w2M Substituting the initial condition: lt = ~ equation (12) becomes, 0 = C2 The general equation of motion is then given as, (12) (13) (13) (14) x = (v + m t - D-M sin wt 1 Wm~ w-/ 2M Equation (14) shows that the displacement is made up of a continuously increasing term (vo + Dm/wM) t plus a sinusoidally varying term - (Dm/w2M) sin wt. Experimental results show, however, that x does not increase or decrease continuously with t. Since all the terms in the parentheses are constants, the following must be true to uphold the observed experimental result: vo + = 0 (t o) wM (15) so that Dm V = -_ M 0 wM (16) WADC TR 54-390

The equation of motion for the droplet therefore reduces to Dm x = sin wt (17) w2M from which we obtain the maximum displacement Xmax ^w2M (18) Xmax -w2M Substituting the following relations, Dm = (1/2) Pav S CD (19) M = (4/5) t r3Pl (20) S = i r2 (21) and w = 2x f (22) equation (18) becomes, 1PaVm fr2CDX xmax = (2f)2(4) r3 pt 3 C ^ - -162 9)P-f (24) Xmax = — 2 C *or -2 C D12 e/ 2 =1.9 x O2 ( )() ( ) (25) where x = droplet displacement (ft) CD = drag coefficient (dimensionless) d = drop diameter (ft) Pa = mass density of the air (slugs/ft3) p! = mass density of the droplet (slugs/ft3) Vm = maximum relative velocity of air and droplet (ft/sec) f = ultrasonic frequency (cps) and 1 ft = 30.48 x 104 micron~ Pa = 0.002578 slugs/ft3 Pwater = 1.94 slugs/ft3 Assuming: fixed droplet diameter (solid sphere) d = 500 microns V = 500 ft/sec standard atmosphere we get 3.719 x 10-7 P 278 1.567 x 10-4 ft2/sec Rv 500 1 \ 500 e ~ v - 304.8 x l03 1.567 x 10-4 Re = 5230 WADC TR 54-590 44

For this value of Reynolds number, Goldstein gives the value of CD = 0.4 for solid spheres. Substituting in equation (25), -2/ 0.4 ____ \ /.002378 500 \2 masx 1= x000 1 1.94 533,00 Xmax = 0.398 microns It must be remembered that this value is based on the following assumed conditions: V = 500 ft/sec CD = constant The result indicates that the maximum displacements of droplets in the node of an ultrasonic field are very small, an experimentally observed fact. WADC TR 54-390 45

APPENDIX C WADC TR 54-390

IIIIlIllll IltII[III1111 LjI!APPENlDIX C 3 9015 02229 1135 Temperatures at Which a Stationary Sound Field is Established in the Piezoelectric Tube The sonic velocity is given by a = y- HRT where 7 = 1.4 R = 1715 T = 460 + ~F so that a = 49.1 +460 + ~F ft/sec For a given sound frequency, the wavelength, I is given by, a (49.1 460 + F 12inches! = - = inches f 33,000 The number of wavelengths per tube diameter then becomes, d, 1.625 (33,000) T 12(49.1) 5/460 + ~F d _ 91 7 = /460 + ~F For the indicated number of wavelengths, the required temperature becomes, d: F = = — 3 - 460 = 454~F = 4: ~F = 9 - 460 = 58~F These results are based on an assumed resonant frequency of 33,000 cps. Actual resonance was established at 80~F, requiring a resonant frequency of 33,700 cps, while the manufacturers gives a general resonant frequency of 36,000 cps for this type of tube. WADC TR 54-390 48