THE UNIVERSITY OF MICHIGAN NDUSTRY PROGRAM OF THE COLTEGE OF ENGINEERING ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.. SPRAYS FORM:BY FLASHING LIQUD JETS Ralph Brown A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosopby in the University of Michigan 1960

r t il-I, 1 1 N -tt L - ~Jk

Doctoral Committee: Professor J. Louis Yorlk, Chairman Doctor RH Stephen Berry Professor Jay A. Bolt Assistant Professor M. Rasin Tek Professor Brymer Williams

ACKNOWLEDGEMENTS First and foremnost, the author wishes to express his sincere thanks to Professor J. Louis York for his able guiance, encouragement, and friendship during all phases of this work Sincere thanks are also due Professors Brymer Williams, J. A. Bolt, M. R. Tek, and Dr. Ro S. Berry, the remaining members of the octoral committee, for their helpful advice and suggestions. Many thanks also go to Gordon Ringrose, for his invaluable assistance in preparation and calibration of the electrical circuits o The author would also like to express his sincere appreciation to the Delavan Manufacturing Company, Des Moines Iowa for their financial assistance and research grants that helped support this research. The assistance of the Industry Program of the College of Engineering., in the final preparation and reproduction of the manuscr~ipt is greatly appreciated.

TABLE OF CONTENTS Page LIST OF TABLES........................................... V LIST OF FIGURES. o o.... o o. o o.,o. e n o e.o.o.o...... io o o o o o e o jS @@*o o, <o oo| e 0oo o oo e o ~ oe o o ~ o o o oe o o o o o o o eG e e e o o~ LIST OF APPENDICES...................................... viii CHRAFTER o e o e o),l @o oe oeo oo o oo e e e so@e o o o ~ e o o o o, o o o e ~ ~ ~ o e o G R ION........................................ 4 II. SURVEY OF LIQUID JET BREAK-UP.................. 5 III. EXPERIMENTAL. APPARATUS AND PROCEDURES............... 1 The Injection System........................ High-Speed Photography......................... 18 Orifice Nozzles................... 24.......... Range of Experimental Variables................ IV. TEE BREAK-UP MECHANISM.......................... 28 Photographic Study of the Break-Up......... 28 Analysis of the Break-Up Mechanism........., 31 The Effect of Physical and Dynamic Properties on the BekU....,..........,,....... 48 V. TEE SPRAYS FROM FLASHING JETS..................,...... 58 Drop-Size Distributions...,..............,.......... 58 Characteristics of the Sprays..................... 72 VII. REOMEDTON...,....,,....,,,,,,,,,,,. 86 High 86~~~~i

LIST OF TABLES Table Page I Break-Up Conditions for a Low Viscosity Cylindrical Liquid Jet.ooo.... o o..o..o o o o o o. o o o o II Description of Nozzles.......................... 25 III Minimum Initial Radius for Bubble Growth in Water Under One Atmosphere......................8 IV Mean Drop-Sizes................................. 59 V Typical Uniformity Parameters for Atomizers......... 69 VI Determination of Minimum Sample.................. o4

LIST OF FIGUIRES Figure Page 1 Break-Up of a Cylindrical Liquid Jet........... 6 2 Liquid Injection System................... 17. 3 Camera Arrangement for High-Speed Photographs.... 21 Sample Locations......................... 21. 5 Typical1 Drop-Size Photograph...................... 2 6 Experimental Nozzle Types....................... 26 7 Orifice of Nozzle Type C with Sand lOX.............. 26 8 Flashing Jet................................ 5.2 Flashing Jet......................... 3152. a ng Jet.................................... 11 Flashing Jet....................................... 3 13 Flashing Jet-......... 34 141 Flashing Jet..,......................... 35 15 Flashing Jet............................... 35 16 Flashing Jet,............................. 36 17 The Growth and Collapse of a Bubble in a Superheated 18 Bubble Growth Rate Constants for Superheated Systems at One Atmosphere.............,................. 45 19 Bubble Growth Rate Constants for Supersaturated Systems at One Atmosphere............... 46 20 Experimental Bubble Growth Rates for Bubbles on 0.031-in. Diameter Water Jet Injected at 268.F...... 49

LIST OF FIGURES (Continued) Figure Page 21 Effect of Weber Number on Water Jet Break-Up....... 52 22 Effect of Weber Number on Water and Freon-ll Jet Break-Up........................................ 54 23 Effect of Reynold's Number on Water and Freon-ll Jet Break-Up.................. o...... 56......... Typical Drop-Size Distribution................... 61 25 Effect of Weber Number on Drop-Size Distributions at Constant Injection Temperature.................. 6 26 Effect of Injection Temperature on Drop-Size Distributions at Similar Weber Numbers............. 64 27 Effect of Bubble Growth Rate and Weber Number on Drop-Sizes.......................................... 65 28 Typical Cumulative Distribution Function (Logarithmic-Probability Scales)................... 68 29 Uniformity of Sprays from Water Jets.... en.... 70 30 Variation in Drop Diameters Across Sprays from Flashing Water Jets............................ 75 31 Velocities of Drops in a Spray From a Flashing Water Jet Six Inches from the Orifice............... 76 32 Thermocouple Calibration......................... 95 33 Flowmeter Calibration for Saturated Water at 120 psig. 00........................................ 95 34 Effect of Filters on Optical Density............. 98 35 Determination of Minimum Sample................... 102 36 Comparison of Distributions from Two Photographs at a Sample Location.......................... 105O 37 Comparison of Spray Flow Rates and Injected Flow

LIST OF APPENDICES Page APPENDIX A. SUPPLEENTARY EXPERIMENTAL DETAILS...................... 1. Determination of the Maximum Orifice Length...... 2. Calibrations of Pressure Gauge, Thermocouple, Flowmeter, and Time-Delay Unit................ 3. Control of Exposure9....6............. 96.. 4. Developing Technique.......................... 99 5 Minimum Drop Sample........................... 100 6. Flow Rate Check............................... 105 7. Time-Delay Circuit............................. 107 B SUMARY OF DATA AND CALCULATED VALUES.........1..... Break-Up Data.............................. 110 2. Bubble-Size Data............................... e11 3. Drop-Size Data.................... 112 C. SAMPLE CALCULATIONS........................ 122... 1. Calculation of Jet Velocity...................... 122 2. Calculation of Weber Nubr................ 122 3. Calculation of Reynold's Number....,............... 1"i25 4. Calculation of Bubble-Growth-Rate Constant......... 125 5. Calculation of Bubble-Growth-Rate Constant for 6. Calculation for One Location in Spray...,.,,...,..00. 125 7. Calculation for the Whole Spray.....o............,, 126 D. LITERATURE CITATIONS,........,.,.................. _ 28

NOMENC LATULRE Alphabetic A area ft. t 2 C bubble-growth-rate constant in superheated ft./hr liquid id bubble-growth-rate constant in supersaturated ft./hri liquid Ld initial gas concentration weight fraction Cf final gas concentration weight fraction heat capacity of vapor b ot o C2 heat capacity of liquid b.to' D drop diameter microns D mean drop diameter, subscripts referring microns mn p to which mean, see Chapter V. Equation (1) Dvmd volume median drop diameter microns d jet diameter inches f(D) probability distribution. function F(D) cumulative distribution fuanction gc conversion factor., lb. and l'b. force ft.-1.bj/lb.force-sec. 2 hi ~enthalpy in initial state b.t.u./lb,, hf enthalpy in f inal state b.t.u./ lb. k thermal conductivity b tu ft/r -t2_-oF kg mass transfer coefficient molj/hr.-ft. 2_ m.f. L latent heat of vaporization b.t.u./lb. AUS percentage of drops in any given size range

NOMEhC LATTJRE Alphabetic (Continued) vapor pressure lb ft p~ difference in pressure inside and at great b1 ft distance froni bubble P0 external pressure on liquid lbft.2 injection pressure psig R gas constant (lbft.2)(ft3) (lb.mole) (OR) ~T temperature OF T0 liquid temperature t time mi-croseconds m: r bubble radius microns minimum initial radius for bubble growth microns ri ~ initial bubble radius microns V relative velocity between liquid jet or ft./sec.. drop and surrounding vapor v1 ~ specific volume of vapor ft 3/lb. V2 ~ specific volume of liquid ft)3/lb. X weight fraction flashing y mole fraction of gas being transferred in surrounding gas Yi ~mole fraction of gas at liquid-vapor interface Greek 6 ~~delta., uniformity parameter for logarithmicnormal distribution -,-~ "-

NOMENCLATURE Greek (Continued) epsilon, surface roughness - arithmetic average lambda, disturbance wavelength inches I mu,~ viscosity centipoie pi, a constant p> vapor density lbft p2 liquid density lb./ft3 p~ density of surrounding vapor lbft.3 sigma interfacial tension dyne/cm. AT tau superheat Dimensionless Groups Nwe Weber number, - p V2 d 2gcg R Reynold' s number, =Vopd W Weber constant, = \ d/g. & Subscripts 1 ~~refers to vapor 2 refers to liquid i refers to initial state f refers to final state

CHAPTER I INTRODUCTION Spraying is the process of breaking a mass of liquid into a zone of drops. Sprays are most often produced by the injection of a liquid under pressure through a device which forms an unstable jet or sheet or by the passage of a high velocity air stream over a liquid jet In both these methods the liquid is broken into drops by the action of the stresses at the liquid-vapor interface. The object of this investigation is a study of the characteristics of the sprays formed by flashing liquid jets. In a flashing liquid, the spray is formed partly by the internal gas evolution which rapidly expands the jet. The specific objectives can be divided into two major categories: 1) determination of the break-up mechanism and the controlling physical variables., and 2) finding the effects of operating variables on spray characteristics such as drop-sizes., drop-size distributions., drop-veloci-ties., spray patterns and vaporization rates. Flashing, defined as spontaneous vapor evolution, can occur if 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 Ttsuperheatedt! with respect to the receiving pressure. The liquid must attain its saturation temperature in order to-reach a condition of thermodynamic equilibrium. The sensible heat available from the liquid 1,, -1; 4 n V'-~'n+,- by tis tmpertur reut io(- +- n Y-, — provides — I'+ n1~'IC the latnt heat for- the,

spontaneous vaporinzation of a portion of ito Flashing may also occur if gas is dissolved in the liquid at a concentration greater than the solubility of the gas in the liquid at the pressure of the receiving medium. Here, the liquid is "supersaturated" with respect to the receiving pressure~ In this case, a portion of the dissolved gas must come out of solution in order to reduce the concentration to its equilibrium value. The most common application of flashing for the formation of sprays are the household "aerosol bombs" for the spraying of insecticides, perfumes, and deodorants, The material to be sprayed is stored in a pressure vessel with a portion of propellanto The propellant is commnonly an inert, non-toxic compound which is gaseous at room temperature, Typical propellants are Freon-12 or nitric oxide, When the mixture of the material and propellant is injected into the atmosphere, a fine spray results, Although flashing for the formation of sprays is not widely employed in other applications, there are several areas where it might be advantageous. In fuel c9nbustion, the fuel can be preheated before injection into the combustion chamber, Fine fuel sprays could be formed at low injection pressures if they are injected at a high enough temperature, Another possible application is spray drying. Injecting a superheated material has two advantages in this case, The spray is at a high temperature so that the liquid portion of the material sprayed vaporizes rapidly, and the spray zone is contained in a relatively small volume, reducing the necessity of very wide spray towers,

This method of spray formation. produces sprays having certain characteristics Whether this method or another of the various available methods of spray formation is desirable in a given application depends upon the reuirements of that particular application. A small drop-size is not always the most important factor, The applications suggested here utilize various spray characteristics peculiar to this method of spray formation A purpose of this research is to present the characteristics of the sprays from flashing liquids so that the information might be of value in considering it as a method of spray formation for any particular application. This investigation is restricted to the break-up of cylindrical liquid jets The break-up of a cylindrical liquid jet is probably considered the most fundamental means of making a spray and has wide application, The break-up of these jets has been both theoretically and experimentally studied by several investigators, Therefore, the results obtained with flashing can be compared with the information available concerning ordinary jet disintegration, To date,. there has been no investigation reported in the literature of the sprays formed by flashing liquids,, Another reason for studying cylindrical jets is that the nozzle design for producing them is very simple —a circular orifice, Simplicity of nozzle design is importan-t in any break-up study as the nozzle design often has a profound effect on the break-up mechanism. With an orifice

4The break-up mechanism is studied by taking high-speed silhouette photographsof the flashing jet to "stop" the break-up action The photographs are taken of water jets under various injection conditions The important variables are injection temperature and design of the orifice. Photographs arie taken of both superheated and supersaturated water jets A quantitative measure of the liquid break-up is made by dropsize analyses. There are several methods of obtaining drop-size data but the only one feasible in this case is a photographic technique in which high-speed photographs are taken across the spray zone0 This is necessary because of the high vaporization rates and velocities of the drops in the spray which do not permit physical sampling. Drop size analyses are made for sprays from water and Freon-ll jets0 The analyses are made for sprays formed over a wide range of operating variables including orifice diameter., orifice roughness., injection pressure, and injection temperature0,

CHAPTER II SURVEY OF LIQUID JET BREAK-UP This chapter will review some of the experimental and theoretical information available in the literature on the break-up of cylindrical liquid jets. This will enable us to compare the effectiveness of injecting a flashing jet to form a spray with injecting a thermodynamically stable liquid jet, The manner in which a liquid jet disintegrates into droplets varies considerably depending on the relative values of certain physical variables To describe the various physical processes, of the disintegra(17)* we can refer to a study by Lee and Spencer that speed photographs of liquid jets injected under various conditions Asse that liquid is flowing through a given size orifice into stagnant gas in the direction of the gravitational force and the velocity is slowly increased, At the lowest jet velocities, the jet breaks up as a result of the.pinching effect of surface tension, The jet first deforms in a symmetric., varicose manner and then breaks into droplets as shown in Figure la,. The jet velocity is increased so that the aerodynamic effects caused by the vapor flowing over the liquid become important, This produces faster disintegration as a result of vapor flow causing a decrease in pressure over the bumps in the jet and an increase in the wells as schematically presented in Figure lb. With further increase

-6-_ I- - - - - 1 0o O0 0 o (a) (b) (c) SURFACE TENSION BREAK-UP AERODYNAMIC FORCES FLAG-WAVING Figure 1. Break-Up of a Cylindrical Liquid Jet.

-7in velocity, the aerodynamic forces cause the jet to deform in an unsymmetrical, "flag-waving" manner illustrated in Figure lc, The whipping action at the end of the jet causes it to break into drops. At still higher velocities the almost immediate, chaotic mass disintegration of the jet can be observed High-speed photographs have shown that the liquid is actually caught up and drawn out by the vapor. The liquid is pulled into fine ligaments which further disintegrate by the surface-tension mechanism, The larger drops formed from the initial break-up of the jet may further be shattered This final disintegration process is called "atomization" In all the theoretical analyses of the break-up of liquid jets developed to describe the above processes, certain assumptions had to be made to solve the equations of fluid flow, The analyses are based upon the assumption that small random microdisturbances exist on the liquid surface, These may be caused by a number of factors includ-ing roughness on the orifice surface, impurities in the liquid or vapor, or turbulence, There are forces acting upon these disturbances causing them either to diminish or grow, An expression is obtained for the growth rate of these disturbances. The disturbances which are shown to have the maximum growth rate are assumed to ultimately lead to the jet break.-up, This type of analysis leads to two useful results. First, the size of the disturbance is generally characterized by its length in comparison to the jet diameter. The length of the disturbance that has the maximum growth rate

-8This gives an estimate of the size of drop that will result from the disturbance Second, the growth rate of the disturbance gives a measure of the break-up length of the liquid jet. This method of approach is valid if the disturbances are small compared to the size of the jet and randomly imposed If imperfect machining of an orifice produces a situation where a large disturbance is imposed in a non-random fashion, this analysis may not be of value. The first mathematical treatment of the instability of cylindrical liquid jets was made by Rayleigh(27) in 1878. He treated both the problem of injecting a jet of heavy liquid into a vapor, and injecting a gas into another gaso In his treatment of the liquid jet he assumed that the capillary force, or surface-tension force, was of major importance. A sinusoidal disturbance for the surface of the jet was assumed. Expressions for the potential and kinetic energies of the deformed jet were found, and from these the growth rate of the disturbance was found as a function of the jet diameter, surface tension., and disturbance wavelength. From this analysis the disturbance on an inviscid liqluid jet having the maximuim growth rate was found to be dependent only on the jet diameter and is given by x = 4,508 d (1) where,X = disturbance wavelength', and d = jet diameter, This solution is important in that it accurately predicts the drop-size from the size of the disturbance by assuming the drop is formed

-9This is only valid for the break-up of a low-velocity jet as shown in Figure la, as it neglects the aerodynamic forces that become important at the higher velocitieso Experimental measurements of the wave-length by Tyler agree very well with Eq. (1). In a subsequent paper, Rayleigh (26) extended his analysis of liquid jets to include liquids of high viscosity. This showed that as the viscosity was raised, the wavelength of the disturbance having the maximum growth rate was increased. A second theoretical study of jet break-up was made by Weber in 191 Weber first considered the same hydrodynamical equations and assumptions as did Rayleigh in solving the disturbance growth rate for low and high -viscosity jets. By making certain mathematical assumptions,, he obtained an explicit relation for the wavelength of the disturbance of maximum growth rate as a function of liqui'd properties. 2 __1)(2) where 4 = liquid viscosity,, p2= liqluid density., and cr= interfacial tension, This equation shows that for inviscid liqluids (Vt = ), the solution agrees very well with that found by Rayleigh. x 4.44 d (3)

-10Weber's analysis goes further than that of Rayleigh in that he then consid-'ers the effect of aerodynamic forces on the jet disintegration He first considers the effect of symmetrically-imposed forces as shown in Figure lb. This analysis shows that the disturbance growth rates increase with jet velocity. This results in the fact that the break-up time (time = 0 at the orifice) decreases with jet velocity. The length of the disturbance wth the maximum growth rate again increases with jet viscosity. Weber then considers the case where the jet is distorted in a sinuous manner which occurs at the higher velocities, In this case, the cross section of the jet is assumed constant, and the sinuous jet is considered as an elastic beam, subject to thrust and bending, The jet is assumed to be snusoidally distorted and an attempt'is made to obtain the size of the d'istortion with the highest growth rate. The size of the disturbance is found to decrease with a dimensionless constant., now referred to as the Web-er number. N pgV2d (4) we 2~ where pg = the density of the surrounding gas, V = the velocity of the jet, and = conversion factor,absolute to engineering units, High viscosity again has the effect of increasing the length of the disturbance with the highest growth rate and increasing the break-up time, The models of jet formation employed by Web-er in his analyses were based on an experimental study of the break-up made by Haenlein ) The results predicted b~ Weber agree in character with the experimental

-11results of Haenlein. The results of the previously mentioned photographic stdy of Lee and Spencer(17) also agree with Weber's theoretical results. Several investigators, particularly Castlemanpoint out that Weber's analyses do not apply to very high values of jet velocity where the jet disintegrates very close to the orifice. Photographic studies have indicated that many drops are created by the formation of ligaments on the surface of the jet. No mathematical analyses have been attempted for this regime of atomization as a result of its random nature. However, there are certain characteristics of the spray that may be drop in a high velocity air stream is uredicted. A large drop in a high velocity air stream is unstable and is subject to further disintegration. This shattering of drops that have been broken off the liqiuid jets is referred to as tisecondary atomization,1' The importance of this concept is that knowing the maxi-muni size of a stable drop as a function of the relative velocity between drop and vapor, we can predict the maximumn drop-size in a spray from a jet injected at a given velocity. The mechanism of secondary atomization has been studied by Baron 2)Litt aye(18 and Lane(16 The most useful re-sult of these studies has been the criterion for the onset of secondary atomization developed by Littaye 1a N =constant(5 we This says that if the Weber number is a higher value than a constant, the

-12Several empirical and semi-empirical relations have been presented to give the maximum drop-size for a liquid jet spray and its (13) break-up length Agood correlation for maximum drop size is Holroyds D/d = w-2/3f(R) (6) where D = maximum drop diameter, W = VIp2d/gc a and R = Reynold's number = Vp2d/ko It should be pointed out here that some confusion exists in the literature as to the definition of the Weber number. Some investigators define it as in Eq () and others call W, in Eq. (6) the Weber number. In this study, any reference to the Weber number will mean that defined by Eq. (4) This definition seems preferable since it is the ratio of the impact stress of the gas at the gas -liquid interf ace,, PgV2/2g c; and the normal. stress on any cross section caused by surface tension, a/d. This is a ratio of a stress tending to distort the jet to a stress tending to restore it to its original configuration and in this sense,, is a measure of the jet stability. There is a direct relation between the two definitions of Weber number and it is given by Nwe (P) Holroyd(13) says that the function of Reynold's number, f(R), in Eq~. (6) should be,obtained empirically for any particular application. Miesse(l9) has correlated the maximum drop-size data for the break-up of water and liquid nitrogen jets and applied Holroyd's equation to obtain

13the equation: D/d = w- 2/3(23.5 + o0.000395 R). (8) Both Eq. (6) and Eq. (8) are for jet velocities where secondary atomization does not occur. In cases where secondary atomization does take place, the maximum drop-size may be reduced considerably. 2) Baron suggests the function of dimensionless groups to correlate break-up length data be given by L/d = Wfl (R) (9) where L = the break-up length. Miesse() applied his data to this relation to obtain the correlation L/d = 1o7 W (0.0001 R) -/) This brief survey has been intended to point out the present state of the knowledge of liquid jet break-up., and is not intended as a complete literature survey, A complete literature survey of this subject is available (24),. The main purposes of this survey are: 1) to provide a basis for the choice of range and magnitudes of operating variables for the flashing study, and 2) to provide a basis for the comparison of the break-up of cold liquid jets and the break-up of flashing liquid jets, The choice of operating variables for the flashing study is in a range where the atomization of ordinary liquid jets to a spray is poor,Y that is, where the drop-sizes are the same order of magnitude as the jet diameter, The purpose of employing flashing would therefore be to obtain a fine

-14The atomization of the jets is poor in the regimes of the jet deformation and break-up shown in Figure 1. The onset of these various regimes of deformation can be characterized by the same criterion that is applied to the stability of droplets in a high-velocity vapor stream(116). The regimes are characterized by the Weber number The Weber numbers for the various break-up processes for low viscosity jets are tabulated in Table I.o TABLE I. BREAK-UP CONDITIONS FOR A LOW VISCOSITY CYLINDRICAL LIQUID JET pinching break-up when Nwe < 002 Figure la sinuous break-up when 0.2 < Nwe < 8 Figure lc atomization when Nw > 8 "Atomization" in Table I refers to the point where ligament formation is induced on the'jet surface and the original,jet drops are subject to secondary atomization. Note that this begins where the impact stress on the jet surface is about an order of magnitude greater than the surface normal- stress. It should be emphasized that the values given in Table I are very approximate as the transition between the regimes of jet deformation is very gradual and does not take place at a sharply cri'tical Weber number, The experiments with flashing are designed to cover a range of Weber numbers that cross the "critical" for the onset

jets is also subject to a change at the critical Weber number The Weber numbers in Table I are given for low viscosity liquid jets1 The effect of high-viscosity is to raise the value of the "critical" Weber number for the onset of atomization. Increased viscosity therefore has the effect of increasing the stability of a liquid jet or drop0 The critical Weber numbers for the onset of atomization of drops and jets as a function of viscosity are given by Hinze

CHAPTER III EXPERIMENTAL APPARATUS AND PROCEDURES The Injection System A diagram of the liquid injection system is presented in Figure 2. Injection is by gas pressure over the liquid in the storage tank This prevents pressure fluctuations which are inherent with injection by reciprocal or rotary pumps The system is designed so that liquid may be injected under the following conditions: 1) Hot water —The vented storage tank is filled with water and steam is bubbled through until the temperature is 212~Fo Steam is passed though the water for a few minutes to remove any air in the tank and the tank is then sealedo The steam can then be injected until the tank pressure reaches 135 Psig corresponding to a saturation temperature of 3580F. This hot water passes through the heat exchanger where it can be cooled to the desired temperature by varying the cold water flow in. the outer jacket. The injection pressure across the nozzle may be regulated either by the steam pressure in the tank or the gate valve downstream of the heat exchanger. 2) Hot or cold liquids —Any liquid can be put in the tank and injected under air or gas pressure through the heat exchanger where it is heated to the desired temperature by passing steam or hot water through the outer jacket.

-17w~~o -JJ amz^~ xm_ J w~~~ - J M gn 0 w w I-~~~~~~~~~~~~~~~~~~~~~~~~0 Mu a ~~~~-H (i) C8P:C z 0~01 If)~ ~~I 0~~~~ -J ~ ~ ~ ~ U >~~~~~~~~~0> co cD~ 0 w~~~ C-)

Liquid with dissolved gas —Gas from cylinders may be bubbled through liquild in the tank in the same manner that steam is bubbled through the water Gas is bubbled through the vented tank for 20 minutes to assure it is dissolved to saturation and all the air is vented from the tank, The tank is then sealed and gas injected until the desired pressure is attained, In su ary9 the injection system will inject cold, superheated, and supersaturated liquids into the atmosphere at pressures up to 500 psig. Provision is made for metering the flow with a Fischer-Porter variable-area flowmeter capable of measuring flow rates from 0~026 galo/min to 0211 gal./min with an accuracy to the nearest 0~002 gal/min An iron-constantan thermocouple measures the temperature of the pipe just upstream of the nozzle. The pipe and thermocouple are heavily insulated and the temperature can be measured to the nearest 0.50F. Injection pressures are measured by a calibrated Jas, P. Marsh Corp. Mastergauge Type 105 which, measures pressures to the nearest 1 psig. The calibrations are discussed in detail in Appendix A,, High-Speed Photography Several methods of analyzing sprays are available,, Most of these,, however,, depend on the physical sampling of the spray or on the scattering.of light by the spray,, Physical sampling is usually accomplished by having drops impinge on cups or microscope slides or by sucking them out of the spray by a tube, Any physical sampling technique has the disadvantage that the impingement process discriminates against capturing the smaller drops

-19% and the larger drops are shattered. This is particularly aggravated in the case of the sprays from the superheated jets. The drops are at their saturation temperature as soon as they are formed and so vaporize at a very high rate. They must therefore be sampled near the orifice where their velocities are the highest. The higher velocities increase the tendency to shatter the large drops when making the sample. The light scattering techniques have the disadvantage that the data is extremely difficult to Lanalyze unless the drops are in a very narrow range of sizes Neither physical sampling or light scattering techniques yield any information concerning drop velocities. In the photographic technique of spray analysis, a photographic sample of the spray can be taken without disturbing the flow pattern. In general, photographic techniques rely on taking high-speed photographs in various locations of the spray. The photographic method employed here is that described by York and Stubbs(32) which uses double exposures to.obtain drop velocities. This method provides drop-size distributions and drop velocities for various locations in a spray and for the whole spray. High-speed photographic techniques are employed for another type of measurement. That is the photographic study of the break-up of the flashing jets. The equipment and techniques for taking the photographs for the break-up studies and the spray analyses are almost identical., the major difference being the location of the field of the spray photogrlaphed

-20The camera arrangement for the high-speed photographs is shown in Figure The camera lens is an Argus with a variable aperture setting from f-.5 to f-16 and a focal length of 50 mmo The geometry of the camera provides for a magnification of lOX of the image on the film0 This photographs a sample of the volume of the spray with a face 0,4-in, x 0,5-in. parallel to the face of the lens and a depth of field depending upon the aperture setting (about 2 mm.,at f-3o5). In a spray analysis, the aperture setting must remain constant in order to maintain a constant depth of field. Mylar filters are therefore used to control the intensity of illumination from the photolightso Lighting is provided by two GeneralElectric Photolights Cat. No 964688G1, which give a high-intensity flash for approximately 1 microsecond0 The lights can be positioned at right angles with a halfsilvered mirror between them as in Figure 5 and discharged with a definite time delay governed by the time-delay circuit, This produces a double exposure-of the diops with a known time delay for velocity measurements, The lights may also be employed singly for single-flash photographs. The light beamn is directed at the lens, producing a shadow photograph of the drops. Photographs are taken with Kodak Contrast Process Ortho film because it has high contrast and good resolution. In the spray analyses, the nozzle is placed on a movable stand so that the samples can be photographed at various locations in the spray. The nozzle is connected to the injection system by means of insulated

-21TIME I DELAY I CIRCUIT PHOTO- OBJECT PLANE LIGHT ~PHOTOLIGHT MYLAR HALF-SILVERED DPTH FILTERS MIRROR OF FIELD Figure 3. Camera Arrangement for High-Speed Photographs. 0.5 I1N. K OZZLE POO 0.4 IN 61N CMERA 30IN Figure 4. Sample Locations.

In a typical spray analysis, single-flash photographs are taken in a number of the sample locations depending on the width of the spray zone. Some double-flash photographs are also taken for velocity measure ments o The double-flash photographs are not used to obtain drop-size distributions because the double exposure reduces the resolu.tion of the smaller drops. After the photographs are developed, the drops are measured on an optical comparator which projects a lOX magnification of the negative. This provides a lOOX magnification of the original dropso Since photographs of the spray show both drops in sharp focus and blurred drops, as in Figure 5, a standard technique has to be employed to determine which of the drops should be considered as part of the sample, This is done by taking several photographs.of drops of various size suspended on glass fibers, The lens is 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 is established as the limit of focus and any drops as sharp or sharper than. these are accepted. Drops are 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 drops in each sample that lies within each size range. This gives a spatial dropsize distribution. in a sample. The distribution desired, however, is that in a given period of time or temporal distribution, This is found from the spatial distribution by multiplying it by the velocities of the drops in each size range which have been measured from. the double-flash

-23F r..... i....D Figure~~. Tyia. rpSz Poorp~1X

photographs. The drop-size distribution for the entire spray is calculated frol the distributions in each location. The mean drop diameters may be calculated from tiese distributions~ A sample calculation for a spray is presented in Appendix C,O The break-up photographs are taken with the same equpment as the spray analyses except that the photograph is usually taken at the orifice exit. No filters are used to reduce the light intensity but the aperture is reduced to f-5. Both single and double-flash photographs of the jets are taken. Orifice Nozzles Although the design of an orifice nozzle'is rather simple, there are still a number of design variables that may,be considered, The obvious ones are the geometric variables of orifice diameter and orifice length. Othexas are orifice shape and metal surface roughness., Experiments are made over a range of orifice diameters that are given in Table II. The orifice length must be small enough so that vapor evolution is not initiated inside the orifice as this causes a severe reduction in mass flow rate at high injection temperatures or concentrations, The results of preliminary experiments (see Appendix A) indicate that orifices with L/D (length to diameter) ratios of 1 are sufficiently short to prevent vapor evolution in the ori fices for the conditions of the.se experiments,

-25The three main types of nozzles are illustrated in Figure 6o Nozzles of type A are sharp-edged orifices which produce extremely smooth, undisturbed liquid jets. The nozzles of type B are tap-drilled and the edges rounded. The surface roughnesses are measured with a Micrometrical Manufacturing Co. Profilometer with a type QC Amplimeter and a type AE Pilotoro These nozzles produce jets whose surface is slightly disturbed by the metal surface. A nozzle of this type with a sharp downstream edge was tried but the dribbling greatly increased the mean drop-sizes. The nozzle of type C was designed to provide an extremely rough surface. This was made by cementing 170/200 mesh glass beads on the inside surface of a 00060-ino-diameter nozzle with epoxy resin0 The surface roughness is estimated from a photograph of the nozzle shown in Figure 7. This roughness is severe enough to tear portions of the liquid jet off at the orifice. TABLE II DESCRIPTION OF NOZZLES Type Diameter Length L/D Roughness e_D (inches) (inches) (microinches ARS) A 0o3Q o0.o00 1 - A o.o4q ooo4o 1 - A OO8o oo80o 1 - B 0.020 0.020 1 - Ooo0004 (esto) B 0.031 0,025 o08 - 0o.0004 (est.) B o~ 4o 0.035 0.o9 14+1 0. o0035 B oo60 0o.o054 0.9 25+1 0.0o0042 C 0.0020 0.0057 3 3000 0o12

-26~TYPE A TYPE B TYPE C SHARP-EDGED ROUGH EXTREMELY ROUGH c/D 0.0004 /D 0 Figure 6. Experimental Nozzle Types. Figure 7. Orifice of Nozzle~~~~~~~~~~ Type.. wit Sad.lx

-27Range of Exerimental Variables The liquids that are injected are water and Freon- Cold water saturated with carbon dioxide at 90 psig is also injected. Injection pressures for the water and Freon-il range from 60 psig to 130 Psig. Water jets are injected with temperatures up to 300~F corresponding to 9.2 wt percent flashing when the liquid is reduced to 212~F. The Freon- is injected with temperatures to 152~F. corresponding to 21.0 wt percent flashing when the liquid is reduced to 748~Fo., its saturation temperature at one atmosphere. With the range of injection pressures and orifice diameters employed,, the variation in vol,umetric flow rate went from 0.925 cubic feet/hour to 11-70 cubic feet/hour. Freon-ll was chosen because of its convenient boiling point, nonflammability, and difference in physical properties as cQmpared to water. The liquid density df Freon-ll is about 50 percent greater than that of water and the gas density is about 10 times that of water vapor, Furthermore, the surface tension of Freon-ll is about 1/5 the surface tension of water.

C.HAPTER IV THE BREAK-UP MECHANISM Photographic Study of the Break-Up To investigate the method of flashing, injection temperature orifice diameter, and orifice roughness on the break-up mechanism, about 10 high-speed photographs were taken of water jets. Some of these photographs, representing the important restilts, are presented here n most cases, the lens was positioned so that the photographs show a lOX magnification of a 0.5-in portion of the jet starting at the orifice. Figures 8-10 are a series of photographs of jets from the. - in.-diameter, rough-surface (type B) nozzle over a range of temperature. At 251F. the superheating has essentially no effect on the jet. Only one small bubble can be seen on the surface. At 2680F. the superheating does partially disintegrate the jet., but the spray 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 295'F. the jet is Completely disintegrated into a spray of fine droplets. This disintegrati-on can easily be noted in the photograph by the rapidly expanding jet a short distance from the nozzle. Visual observation of the spray has indicated that the temperature difference from the value where the jet disintegrates to a spray with a core of large drops to the value where the jet completely disintegrates to a fine spray is small, about 50F- Figuire 11 shIows a jlet at'5c40F. from

-29downstream edge Dribbling on the edge causes relatively large drops to form Rounding the outer edge prevents most Of this dribbling. The best temperatures for observation of the bubbles growing on the jets are in the 2650-2700F. range for this nozzle. There are few bubbles below that range and above itthe rapid disintegration clouds any that may be there. Figure 12 is a double-exposure of the jet at 268~Fo One can observe the expansion of the bubbles on the surface of the jet from the first exposure to the second, Figure 13 shows a jet from the 00020-ino-diameter type B nozzle at 28F 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 Reynold's number, The important difference between this nozzle and the larger one is that, at this temperature,, a jet from the larger orifice would be completely d'isintograted. The appearance of the bubbles -in. t'his jet is similar to those in the larger diameter jet at about 2680F. The jet is only partially disintegrated by bubble growth., the final spray containing a core of large drops. The phot,ographs,of.the jets from the sharp-edged orifice nozzles show some outstanding differences from those of the roUigh-orifice nozzles, Photographs of jets from the 0.040[-in.-diameter-orifices do not indicate any effect of the flashing until the temperature reaches about 2750F. F'igures 14 and 15 show jets at 2860F. The jets at this temperature all

-30from this nozzle at this temperature and injection pressure were taken and each one is entirely different. Observations from the photographs indicate that the jet disintegrates anywhere from 1/8-1/2 ino from the orifice. 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 275~Fo Visual observation of the jets suggest that the break-up point oscillates and the density of the spray formed by the jet fluctuates at any given point. A Strobotac, which is a variablefrequency flash unit, was di.rected on the jets but the point of break-up could not be made stationary indicating that this point did not oscillate at a regular frequency. The intact portion of the jets appeared smooth, which is indicated by the photographs0 Note that the jets from the 0o031ino., type B nozzle and the O.o040-ino, type A nozzle are about the same diameter. This results from the fact that a jet formed from a sharp-edged orifice contracts more than one from a round-edged, rough orifice~ When injecting water at 130 psig through a 0.030-in, diameter sharp-edged orifice at 287'F., the jet was to all appearances completely disintegrated to fine spray. Photographs at the orifice,, however, showed smooth and undisturbed jets. Therefore, several photographs were taken of the jet at various distances from the orifice. Figure 16, which is taken 1-ino from the orifice shows that the break-up does take place in this case, but further from the orifice. Apparently, bubbles are nucleated inside the body of the jet and grow until they break the jet. In this

- 31photograph the bubble that has broken has cut the jet, leaving intact portions on either side of the bubble. The bubble following the one that has broken is about to repeat this same action. The intact portions of the jet will be further atomized by aerodynamic forces. A crackling noise is associated with this break-up, not quite as loud and intense as with the larger sharp-edged orifices. Photographs of water jets that had dissolved carbon dioxide in them appeared identical to pure water jets at the same temperature. The water was saturated with the gas at 90 psig which would cause about 1 wt percent of the liquid to flash when the liquid is injected into the atmosphere. These jets were also produced by a long orifice nozzle (L/D = 6) that had been used in preliminary experilments0 The dissolved gas still had no effect upon the jet break-up. The important point of comparison here is that when a superheated water jet was injected through this same nozzle at a temperature such that 1 wt. percent flashed, vapor evolution was initiated inside the orifice throat and the jet was broken up. Analysis,of the Break-Up Mechanism The mechanism by which flashing causes the break-up of superheated liquid jets is bubble formation. This is apparent by the observation of the bubbles on the suirfaces and inside of the superheated jets in

-32Figure 8. Flashing Jet 1OX. Type B, D 0.051-in., P 120 psig, T = 251~F.: -.. -............. ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~............,,.,.,... __ _w_,'. %.;'.' _. = = =!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...... Figure 9. FLashing Jet lOX. Type B3, B, 0.031-in. P= 120 psig, T = 251~F.

- 33-,,.., s *......... S UE d.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...... il~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~, X Figure 10. Flashing Jet lOX. Type B, B = O.D120 sig~ = 29~F.......... P~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ =. 12 pi, T =;95F Figure 11 Flshn Je lOX Typ B::, with: Sharp Dontra Ede P 0.3-i. P,, 12 psig,::: O-K

-34Figure 12. Flashing Jet 1oX. Type B, D 0.031-in., P 120 psig, T 268~F, Double Exposure (14 Microsecond Delay) P, 12 psig, T_ 8F

- 35I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~: c~Zl........ k s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~'iiiiili..,!! }~.'. I?_~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...._!8i'i......iiiii _.....~ -i!?? Figure 15. Flashing Jet 10lX. Type A, D = 0.040- in., P = 120 psig, T = 286~F.

36-.................... ~i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x...~~~:<.. A.. l~_ 11l.......... i ii:,,,.D...... Figure 16. Flashing Jet 1OX. Type A,~ D 0.030-in., P -131 ps ig, T = 287 ~F. One inch from Orif.ice.

-37jets, Some explanation must be rrmade, however, for the striking differences between the photographs of the break-up of the jets from the rough-surface orifices and the sharp-edged orifices. The rough-orifice jets, when injected at a sufficiently high temperature, simply expand a short distance from the orifice to form a fine spray. The superheatGed jets from the sharp-edged orifices, however, disintegrate in a random, explosive manner. 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 qtube, vaporization will take place by a series of small explosions referred to as "bumping," The reason for the two different vaporization mechanisms is the same in the case of the water jets and the heated test tube; vapor bubbles Will not. grow in a superheated liquid unless bubble nuclei 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 expression: p 2a (1) r where P = pressure inside minus pressure outside the bubble, a = surface tension of the liqu.id, and r = radius of the bubble. Considering the limiting case for water, if a bubble is the mean diameter 0 of a water molecule, r = 1,9 A, the excess pressure inside the bubble would be 7500 atmospheres assuming.surface tension is constant down to

-38atomic 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. -= P(To) Po ro (2) 2a pv(To) - Po where r0 = the minimum initial radius for bubble growths pv = the vapor pressure of the liquid which is a function of its temperature, To, and Po = the pressure on the liquid. Several values of this initial radius for water are given in Table III. TABLE III MINIMUM INITIAL RADIUS FOR BUBBLE GROWTH IN WATER UNDER ONE ATMOSPHERE ro (microns) 5.90 o.605 0~470 0.378 0.300 0.245 0.201 To (~F.) 220 266 275 284 293 302 311 There are a number of different means by which small nuclei for bubble formation may be provided to a superheated liquid. These nuclei may be initiated 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 continuous phase of superheated liquid cannot take place without some original bubble nuclei,

-39In the case of the rough orifice, the nuclei are probably provided by low pressure eddies behind the sharp micro-roughnesses on the.orifice surface. These first produce bubbles on the surface of the jet. When the temperature is high enough, these bubbles are also produced throughout the body of the jet and lead to its eventual break-up. With the sharpedged orifice, the superheated liquid passes by the orifice undisturbed into the atmosphere. There is no provision for the continuous nucleation of the bubbles on the orifice surface. Rather, the spontaneous nucleation of bubbles in these jets 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 reason for the differences in the photographs can therefore be summarized by saying that surface roughness provides for bubble nucleation in a stable continuous manner, but without roughness, bubble nucleation is subject to random effects. Consider a superheated jet being injected into the atmosphere, The temperature of the jet right near the orifice is its injection temperatureo Traveling away from the orifice, the jet cools down to well below its saturation temperature by vaporization and convection from the surface, If a bubble is nucleated at the orifice, it will grow until it reaches the point in the jet where the temperature:.is below the saturation temperature, Then it will start to collapse. This growth-collapse phenomenom is commonly observed in surface boiling systems and is mathematically described by (1) Bankoff and Mikesell. Figure 17 is a diagrim of what a multiple exposure photograph of such a bubble might look like,

-40o o C C' K C( Figure 17. The Growth and Collapse of a Bubble in a Superheated Jet. If the -bubble does not grow to a large size, it will not affect the jet. If it does grow large enough, however, it can either break the jet or shatter it before it has an opportunity to collapse. From this model, we can see that the growth rate of the bubble is a critical factor~ Since the break-up takes place near the orifice, it is the growth rate at the injection temperature that is of interesto Means are available to predict the growth rate of a bubble in a superheated or supersaturated liquid given some of its physical and thermodynamic properities. Solutions for the problem of the growth of a vapor bubble in a superheated liquid have been presented by Plesset and Zwick(23), and by Forster and Zubr(7). These solutions take the Rayleigh equation(l5) for the motion of a bubble in a nonviscous, incompressible liquid, r d2r + 3(dr)2 = Ap (3) dt2 2 dt P2 where r = the bubble radius, t = the time, Zp = the pressure difference inside and at great distance from the bubble, and P2 = the liquid density

-41and extend it to include the pressure on the bubble by the surface tension. r d2r + 3 (dr)2 = (Ap 2) 1 (4) dt2 2 dt r P2 The pressure difference, Ap, can be connected to the temperature difference, AT, between the saturation temperature inside and at great distance from the bubble by the Clausius-Clapyron equation, Ap _ T Lvt AT (5) T(vl V2) where L = the latent heat of vaporization of the liquid, T = an average value of the temperature between the initial liquid temperature and the saturation temperature at the external pressure, and vl,v2 = the specific volumes of the vapor and liquid, respectively. The value of the temperature inside the bubble is assumed to be the temperature of the bubble wall, which is a good assumption since the temperature gradients within the bubbles are negligible in view of the small bubble sizes and the high thermal diffusivity of the vapor, The temperature at the bubble wall must be determined by the solution of the heat conduction problem across a spherical moving boundary where vaporization is takingplace. The Forster and Zuber solution assumes the bubble wall constitutes a spherically-distributed heat sink and uses the Green's function for the domain(30 integrated over the space that the vaporization takes place. The Plesset and Zwick solution uses an approximate solution to the heat conduction problem across a spherical

-42moving boundary that assumes the thickness of the layer of the liquid in which the temperature reduction takes place is small compared to the radius (22) of the bubble at any time (22) Both solutions proceed from these assumptions and employ different mathematical techniques to find an approximate solution to the integro-differential equation involved. The mathematical details are omitted here as they are available in the references. Both solutions arrive at the same results, The solutions indicate that there are two regions of bubble growth. In the first region, the bubble radius is of the same order of magnitude as its original 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 vaporization to cool the liquid on the bubble surface and severely reduce the vapor pressure. This rapid expantion rate is shortly slowed down by the cooling of the liquid around the bubble and the subsequent reduction of the vapor pressure inside ito The rate is then governed by the balance between heat transfer and vaporization and is approximately given by: r = r + C t (6) where C = a constant dependent on the physical properties of the system, and rl = the initial bubble radius (r1 - ro). This growth-rate relation describes the bubble as soon as the radius is about 10 times the minimum initial radius, which is the case within a few microseconds, This secondary-growth-rate function agrees very

-43well with data obtained by Deragabedian(6) for growth rates of bubbles in superheated water. The importance of this solution as applied to the study of the jet break-up is that Forster and Zuber give the growth-rate constant, C, in terms of the physical properties of the liquid and its thermodynamic condition, where T = the superheat (7) where AT = the superheat, Dth = thermal diffusivity of the liquid, p1 = density of the vapor at the external pressure and the saturation temperature, P2 = density of the liquid C2 = specific heat of the liquid, and L = latent heat;of vaporization of the liquid. The same solution can be applied to the formation of gas bubbles in a supersaturated liquid. The difference is that mass is being transferred through the liquid rather than heat. c,l i- of, Dm) (8) where ci = the initial gas concentration, cf = the gas solubility at the external pressure, and Dm = molecular diffusivity of the gas through the liquid. The expressions for the growth-rate constants given in Eqs. (7) and (8) are grouped in three terms. The first is the weight-fraction flashing when the liquid pressure is reduced and the temperature drops to the saturation temperature at the lower pressure, The second term is the

liquid to gas density ratio which is equivalent to the gas to liquid specific volume ratio. The product of the first two terms therefore are proportional to the volume increase of the material in the flashing process. The third term is a measure of the rate at which heat or molecules are transferred from the body of the superheated or supersaturated liquid into the bubbles. The importance of these growth-rate constants as applied to a flashing jet is that we can compare the growth rates of bubbles in various superheated and supersaturated systems to estimate the relative effectiveness of flashing in shattering a liquid jet. This growth-rate constant is calculated at various.superheats for a few pure liquids and plotted in Figure 18, In all cases the external pressure is atmospheric, The constant is also calculated for some supersaturated systems and plotted in Figure 19o In this case the constants are plotted versus injection pressure, and calculated assuming the liquid is saturated with the gas at the injection pressure. These calculations show that the growth-rate constants for the dissolved gas systems are considerably lower than for the superheated systems. This explains why injecting carbon aioxide in water had no effect on the jet break-up. The main reason for these low growth-rate constants is that the values of thermal diffusivities in liquids are about 100 times those for the molecular diffusivities of a dissolved gas in a liquid, The values of the corresponding growth rates for superheated and supersaturated systems differ by a factor which is

-4518 17 16 15 14 13 12 cm II cr 10 9 8 5 = - i' Dth 10 20 30 340 50 60 70 80 90 100 110 120 2 CC (C2M )(2t)(r Dth) 10 20 30 40 50 60 70 80 90 100 110 120 lr, SUPERHEAT ~F Figure 18. Bubble-Growth-Rate Constants for Superheated Systems at One Atmosphere.

-46C (C ) ()rDm) Ci = SOLUBILITY AT INJECTION PRESSURE Cf = SOLUBILITY AT ONE ATMOSPHERE GAS - SOLVENT TEMPERATURE "F I H2 H20 86 2 C02 H2 0 32 3 CO2 H20 68 4 N2 H20 86 5 CH4 C5He2 86 6 CH4 C6Hi4 86 1.0 7 CH4 CH1t6 86 8 H2 Cs H 14 100 0.9 OJ % 0.8 0.7 0.6 0.5 0.4 I 0.3 0.2 0.1 100 200 300 INJECTION PRESSURE (psig) Figure 19. Bubble-Growth-Rate Constants for Supersaturated Systems at One Atmosphere.

-47the square root of this, or aprroximately 10, The growth-rate constants for supersaturated systems could be increased by increasing the initial solubilities, but this would require raising the injection pressures. This would defeat the purpQse of employing flashing, however, which is to promote effective break-up at low injection pressures, Minimum injection pressures are required to inject jets in the superheated condition but these are relatively low. For example, all the superheats in Figure 18 may be attained with injection pressures no greater than 60 psig, It should be pointed out that this predicted growth-rate constant refers to bubbles.submerged in large extents of liquid at a uniform temperature. The bubble-growth rates required in the liquid jets are for bubbles near the orifice and within the body of the jet, These are the bubbles that contribute to the break-up, The liquid jet is at a fairly uniform temperature near the orifice, The growth-rate relation given in Eq. (6) does not refer to bubbles on the surface of the jets. This is of no matter as these durface bubbles do not greatly contribute to the break-up, The bubbles that are observed on the jets in Figures 9 and 12 have been formed at a temperature below that where the jet is effectively shattered. Several photographs.were taken of the jet from the 0.031-in.-diameter rough-surface nozzle when water at 120 psig and 268~Fo was injected through it. The sizes and distances from the orifice of a total of 18 bubbles from 10 photpgraphs were measured. There was a distribution of bubble sizes, and only the largest Ones were

measured, The sizes are plotted versus time (time = 0 at the orifice) in Figure 20. Note that the surface bubbles do not grow as large as predicted for a submerged bubble, and appear to grow linearly with time, rather than proportional to the square root of time. 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 liquid surface temperature, the liquid evaporates into the bubble at a rate proportional to the area covered by the bubble. Vol = Ak't (9) where Vol. = volume of the bubble, k' = a constant, and A = area covered by the bubble. Substituting the expressions for volume and area as a function of diameter into Eqo (9), the diameter is shown to be directly proportional to time. D = 3k't (10) The surface bubbles appear to be caused by the roughness of the orifice and are not to be confused with the bubbles that grow inside the body of the jets and shatter them. The Effect of Physical and Dynamic Properties on the Break-Up The bubble-growth rate, although important, is not the only criterion for shattering a jet. Some properties of the jet are also involved. The photographs of the water jets clearly demonstrate this, Figures 14, 15 and 16 are of water jets injected through sharp-edged

-490 LaW ccOD U- w a -i 0 N 4 0 w in wO~~~N o ~~LLJW~ L~0 N * 0 N t) aD~~~~~~~~~~~~~~~~~t W 0H o w w~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~01 00 ea: I I I II I I I d~~~~~~~~~~- cC\o 0 o z 0) ~'~ WD0 - B9 w H o.~O 10 C\j 0 O~ 0 4, p40 - CD C 0 0) -- 0 9 0 0 0 0 0 0 6d d 6d (S3HDNI):13.1.3 I~dVI

orifices at about the same injection temperatures and pressures. The bubblegrowth rates are the same in all the jets because of the equal temperatures. The larger jets (Figures 14 and 15) are completely shattered by the gas evolution. The smaller jet, however, is only broken up as a result of the bubbles cutting it into sections. Cylindrical portions of the jet are still intact after the bubbles have burnt. This same type of difference was noted in the discussion of Figure 13, which pointed out that a jet injected under the same conditions from a 0.031-in.-diameter rough orifice would have been shattered while this smaller one was not. These photographs indicate that the degree to which the growing bubbles affect the jet are influenced by some properties of the jet. The fact that at a given bubble-growth rate, one jet is shattered and another is cut into intact portions, suggest that the jet stability is probably an important factor. As we have seen in Chapter II, the Weber number is a measure of this Jet stability. To measure the effect of Weber number on the shattering temperature, water was injected through the experimental nozzles at pressures ranging from 60-130 psig and temperatures ranging from room to 300'F. In a typical run, water was injected through a nozzle at a constant pressure and the temperature was allowed to rise slowly. As the temperature was raised, a fine spray could sometimes be observed around the jet starting between one and two inches from the orifice. This spray was more prominent with the rough-surface orifices. The Jets,;.as has already been mentioned, were completely shattered within about a 5~F. temperature range, These shattering

temperatures are plotted versus Weber number in Figure 21, The Weber numbers are based upon the jet diameters obtained from photographs of the jet, not the orifice diameters, The velocities are calculated from the injection pressures and liquid density. A sample calculation is presented in Appendix C, Shattexing temperatures could not be obtained for the jets from the orifices with sand (e = 0ol) because the roughness was severe enough to disintegrate the jets within 1-inch from the orifice with cold water. The shattering temperature is very definitely a function of Weber number, the jet disintegrating at lower temperatures for the higher Weber numbers. There appears to be a break in the function of temperature versus Weber number at Nwe 12o5o The shattering temperatures are considerably lower at Weber numbers above this, This coincides with the existence of a "tcritical" Weber number for cold jets given for the point where the jet starts to become atomized, The accuracy of the shattering temperature is less at the Weber numbers above 12,5 because the cold jets break. fairly close to the orifice, It is therefore difficult to estimate at what point the flashing is making the major contribution to t,he jet disintegration, The shattering temperatures appear to be independent of which of t;he two types of nozzles formed the jets, If we hypothesize that at a given Weber number, a liquid jet must have a minimum bubble-growth rate to be shattered by vapor evolution; a shattering temperature - Weber number relation may be predicted for any liquid~ The bubble-growth rate in a liquid corresponds to its temperature

K%) C,) ~~~w ~~~~~~o~~o o LL a~ o 0 OrL cr 0~~~~~~~~ 0 w ( U.) a cc ~ ~ ~ ~ ~ ~ ~ ~ ~~~a e~~~~~~~~~~~~~~~~~~~~o 4-) 1(3~~~~~~~~~~ 30 > U k 39 c z K) Qf e0 4' C.)' od CH o a - c'J U) 0~~~ 0 0 0 0 0 0 0 0 0 0 0 0) U) f C- SC a) K) N'd4.-~ 3~IflJ.LV~idlN3.L 9NI~3.1.LVHS

or gas concentration as given by Eqso (7) and (8)~ This hypothesis may be tested by plotting the bubble-growth-rate constant at the shattering temperatures of water and Freon-ll versus the Weber number. This plot is presented in Figure 22 and shows that the points for the two liquids follow thepsame functional relation~ A least-squares correlation for the bubblegrowth rate at the shattering temperature was made and is given by C = 19a7 - 0o581 Nwe for Nwe < 125 (11) c = 11o5 - 0o419 Nwe for Nwe > 12 5 Although this test is experimentally made with only two liquids, it covers a wide range of physical variables. For example, consider injecting water and Freon-ll through a 0004-ino-diameter sharp-edged orifice at 100 psig. The break-up temperature for the water jet is 272~Fo and for the Freon-ll jet is 1180~F These break-up temperatures correspond 1 1 to bubble-growth-rate constants of 14 ftq,/hro2 for water and 2.8 fto/hro2 for Freon-11 The reason the bubble-growth rate for the Freon-l1 is so much smaller than that for water is that Freon-11 has such a high vapor density. The Weber number for the Freon-ll jet is much greater than that for the water jet even though they are the same diameter and nearly the.same velocity0 This is because the interfacial tension of Freon-ll is so much lower than that of water, being 19 dyne/cm. compared to 59 dyne/cmo for water0 The water and Freon-ll jets have Weber numbers of 9.3 and 24, respect ielyo

U) w 0 U mr'r 0c 0 O0 a i:: W m - O L,U- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 4, ~~~~~~~~~o Wt I w cnP 0~~~ Z t~ 0~~~~~~~~~~~ G) i 7 W W oQ.F~ rOrr -. 0 x~~~~~~~~~ c.) (1) c-i Id 0 ~) 6 (3OO 0 _o (0 ~I N 0 0 (O N ~ C~ m m ~ m m~ ~ ~ ~ ~ ~' N~~~~~~~~~~~~~~~~~~~~ (all 8 H/J.LI) fln~vuidV~3.L 9NIW3.LJ.LVHS iV.LNVJ.$NOD 3.LV8f-HJ.L0:19- 3'IGfn ~~~~O, o~~~~~~~~O

One of the assumptions applied in the formulation of the bubblegrowth-rate problem was that the liquid was low viscosity. This is true for the liquids injected in these experiments. Also, the literature on cold jet break-up has not indicated that a strong effect of viscosity on jet stability exists with the range of viscosities covered in these experiments. We should therefore not expect viscosity to affect the jet break-Up for this study. A plot of the bubble-growth-rate constant at the shattering temperature versus Reynolds number given in Figure 23 shows that no correlation can be made. Some of the water points seem to follow a trend, but this is because the Reynold's number, like the Weber number are relations involving jet velocity and diameter. At several points where the water temperatures are similar, and thus the viscosities approximately the same value, we should expect a function bearing a certain relation to the Weber number to act similarly when plotted versus the Reynold's number. This breaks down, however, when widely different injection temperatures are involved and the viscosity varies considerably. The water and Freon-ll points do not coincide at all when plotted versus Reynold's number~ Another possible influence of turbulence is on the bubble-growth rate. The bubble-growth-rate relations are solved by obtaining the bubble wall temperature through a solution of the heat; conduction problem and ignoring convection from the bubble wallo When bubbles shatter a jet, they do so within a 1-ino section0 The characteristic diffusion length (2Dtht)2 for heat diffusion in a 1-ino section of a jet traveling 100 fto/seco is

-56-. ~~~~w~~~o 0 w N O 00 0 QSW a - 0. <J LI)- 0I -Q 0 0~~~~ a) wO * O 0 0 V) Q~ - X~0 o o~~~~~~~~o 0W ~ ~ ~~~~~~~0 0 W w 0 S 0 x 0 o 0 ~~0 8 CD~~~~~~~~Co 0 ~~~~~~o' > — ~~F 0~~ O~~~~~~~~~~~ U 0 a 0 ~~~0 cY I 0 o 0 O 0 o 08 N 0 ~~~~~~~~ ~~~ N 0 ~~~~~~~~~ (D ~~~~~~~ N \ -r4 o,m Co D QD ~ o o* CD qD W0 Nd Nd -- -- -- -- --'dlN31. 9NI83J..LVHS J.V.LNV.I.SNOO =m.VBi-HJ./OBig-3-1BB8f

about 0,0005-in. This is about 1/100 of the film thickness for heat transfer at these levels of turbulence. The thickness of the liquid layer around the bubble wall where the significant temperature reduction takes place is therefore well within the laminar region around the bubble wall. The exclusive consideration of the heat conduction problem is valid in this case and turbulence should have no effect. The difficulty in injecting superheated liquids into the atmosphere over a wide range of viscosity is that pure liquids have approximately the same viscosity at their boiling points. The viscosity data for a number of liquids, including straight chain hydrocarbons, esters, alcohols, aromatics, and halogen-substituted hydrocarbons were investigated and this seems to apply to all liquids.. Mixtures must therefore be injected in order to obtain a wide range of viscosity. This complicates the problem because not only will high viscosities affect the jet stability, the bubble-growth-rate relations may not apply, There may be a large variation in the viscosity at the bubble wall and in the body of the jet because of the temperature differences, In view of the large scope of the problem required to find the effect of high viscosity on the break-up of flashing jets, it is not included as part of this study,

CHAPTER V. THE SPRAYS FROM FLASHING JETS Drop-Size Distributions Drop-size analyses were made for the sprays from water and Freon11 jets over a wide range of injection conditions, The conditions and mean drop-size results are presented in Table IV. About 35,000 drops were counted and measured to make the 18 analyses, between 1500 and 2000 drops per analysis. The details of photographing the sprays, analyzing the data, and accuracy of the analyses are presented in Chapter III and Appendix A. In all but three cases, the analyses were made at injection temperatures above the value where the jet was shattered by flashing. Cold jets were usually not completely broken up at the sample location (6 inches from the orifice), just sinously deformed. The only cold jets which were disintegrated sufficiently to make an analysis were from the largest diameter nozzle and the nozzle with with sand on the orifice surface, A drop-size analysis is designed to give an estimate to the probability distribution function, f(D), which is defined in such a way that f(D)dD is the percent of the total number of drops that have diameters between D and D + dD. The results of an actual analysis give the percentages, ANN, of the drops found to lie within each of the experimental size ranges, AD. These percentages can be divided by the magnitude of the size intervals to provide the average percentage of drops per unit size over

-59TABLE IV MENAN DROP-SIZES Run No. Nozzles Jet Conditions Mean Drop-Sizes (microns) Type D Jet D T~F AP Nwe C 1 Liquid 5 D 0 D30 D- 2 in. in. ft/hr2 1 A 0.040 0.032 287 120 11.3 17.9 HDO 1.39 34.7 43.2 48.9 62.9 2 B* 0.031 0.031 287 120 11.0 17.9 H20 1.39 54.4 59.8 64.3 74.> 3 A 0.0o0 0.066 204 80 14.9 H,0 0.88 142 186 227 336 A 0.o80 o0.0o66 236 80 15.2 5.0 H20 1.22 43.0 50.9 59.6 82.2 5 A 0.080 o.o66 236 120 22.7 5.0 H20 1.43 33.9 39.4 44.9 -,8.3 6 A 0.030 0.025, 287 130 9.57 17.9 H20 1.49 3,.7 45.6 62.6 8..1 7 B 0.031 0.031 287 90 8.21 17.9 H20 1.71 34.3 40.0 48.7 71.9 8 B 0.040 0.035 270 130 13.3 13.6 H2O 1.77 30.7 34.9 39.4 50.0 9 B 0.040 0.035 287 90 9.27 17.9 H20 1.62 35.0 38.4 41.9 49.6 10 B o.o40 0.035 287 130 13.4 17.9 H20 1.69 29.8 33.9 35.7 39.4 11 B 0.060 0.053 254 120 18.4 9.9 H20 1.21 35.6 42.9 52.0 76.3 12 B 0.060 0.053 270 80 12.4 13.6 H20 1.67 32.7 37.4 44.1 61.2 13 B 0.060 0.053 270 120 18.5 13.6 H20 1.53 29.6 33.6 38.0 48.5 14 C 0.020 0.020 80 94 5.14.14 H20 0.73 82.3 118 197 280 15 C 0.020 0.020 270 130 7.56 13.6 H20 1.95 25.1 27.4 30.4 38.9 16 C 0.020 0.020 278 120 7.03 15.4 H20 1.60 24.2 27.1 30.0 36.6 17 A 0.030 0.025 152 94 18.1.0o F-11 1.66 28.5 32.4 36.0 44.4:8 C 0.020 0.020 129 95 14.1 3.2 F-ll 1.16 36.1 43.4 5.0 84.5

each experimental size range. This average percentage of drops per unit size range for each size range can be plotted versus the drop size, giving the experimental. distribution function. This is defined in the same way as the probability distribution function, except that average values of f(D) are given between the finite intervals D + AD, rather than point values at each D. The probability distribution function can be estimated from the experimental distribution function. An example of an experimental distribution function and its corresponding estimated probability function is shown in Figure 24o The mean diameters for a drop-size probability distribution are given by = D f(D)dD (1) Dnf (D)dD These may be estimated from the experimental distributions by Dm L ZDT j m-n (2) mn m-n The mean diameters that were calculated for these analyses were the linear mean diameter, D10; surface mean diameter, D20; volume mean diameter, D30, and volume-surface mean diameter, D32o These are given in Table IV, One notable observation of the drop-size results is that although water was injected at temperatures such that between 2,50 wt, percent and 7~85 wt, percent flashed, and the experimental Weber numbers ranged from

a. 0 (I) a0 W Oc cr-~~~~~~~~~I Ia. ~~o0 0 i 0. 0 z 2 cr 0~~ OQL -3 O o wI — n HZ ~., I-' a z ~~~~~o~~z,,,, ~ N-4W w OD CH -)~ z z cD 0 cn =) C0 W *o~~~~~~~~~~~~~~~~~~~~~~/ EH z:z - m 0'2 w~~~~~~~~~~~~~~ co a.~ 0 ~~~~~~~~o v.r-I C4 C3 0ZSiN 0 ~ C) 0 () Z Nt- 3 ~ ~ Z - 6 3ZISJJ. Nn ~13c.LN=IOJ3dl (G)~

-627 0 to 22,7, the range in the linear mean diamet.ers of the sprays from the flashing jets was only from 24,2 microns to 43,0 microns~ Apparently, once the Weber number and bubble-growth rate are high enough to shatter the jet, more intense conditions do not have a great effect on the drop-size. Observation of the data for the flashing water jets seemed to indicate that at a given injection temperature, the drop-sizes decrease with increasing Weber number. This may be seen in Figure 25 which presents three distribution functions for sprays from jets injected at 2700F,, where C is 13.6 ftb/hr2o The drop-sizes also appeared to decrease at similar Weber numbers when the injection temperature was increased. Figure 26 shows three of the distribution curves for water injected at Weber numbers between 12,4 and 15,2 at temperatures such that the bubble-growth-rate 1 constants were 5~0, 13.6, and 17o9 ft,/hr2o The best correlation that could be made for the drop-sizes of the sprays from the flashing water jets took the form 1840 - 5,18 T (CF) I o 90 -^ N (microns! (3) we This correlation is made from the jets from the type A and B nozzles, The standard deviation is 6,1 percent, The correlation is shown graphically in Figure 27 which is a plot of (D-0o)(Nwe) versus Co This can also be plotted against the injection temperature as the bubble-growtb rate is essential.ly directly proportional to the temperature for water, The correlation shows the fact that the orifice may be sharp-edged or have a rough surface has no

-630 cd 0 3:cj le) OD (D 4-) z~~~~~~~~U ~ 0 -P~~~~~~~~~~~~~~~~~~~~~ 0 rri I I I I I ~n: u~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. 0 o C0 0 0 t~~~~" 0 - kj +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -' C) z -- / 0 ~~~~~~~~~~~~~~~~~~ O~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I"-. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~U)0 o cl) P?I -.0 O z -o~ O== 3Z-S II Nn bl3d rN308) No0 Cflf I 0 OJ Q OQ) N 0 0~ K) N N - 0o 3ZIS J.lNn ~1d 1N3OD3d (G)&. ~~~~~~~~~~~~~-C — O w~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i —

-640 I- IC)IOI I0 U E.~~~~~~~~~~~~~~~~~~~~~H o0 ~0' U. 4I- NNNO 0 GD ON o=) 0 V: ~~~~~~~~~~~~~~~~~~~~0 U) 0 0 _ 0 I! 0 oULO t- 0 / -p tC O 0-O ( I' O t O Z..Il'd.3ld),I U) 0: - 2 4 N ~ a DC 3ZIS JINn i3d 1N3083d (0) I

-65WATER JETS 900 COR RELATIoN SHARP-EDGE ORIFICE TYPE A N~~ \to~ ||OROUGH SURFACE ORIFICE TYPE B 800 So A SAND ON ORIFICE TYPE C N`\ I I FREON JETS X TYPE A 700 700 E~Nv, I TYPE C 600 5000 o 400 300 200 100 2 4 6 8 10 12 14 16 18 20 22 GROWTH RATE CONSTANT (FT/HR 1/2) I I I I I I I I I l 220 230 240 250 260 270 280 290 300 INJECTION TEMPERATURE ~F (WATER POINTS ONLY) Figure 27. Effect of Bubble-Growth Rate and Weber Number on Drop-Sizes.

-66effect on the drop-sizeo The drop-sizes are affected by very rough surfaces (E 0ol)9 This is because the pieces of sand are large enough to tear ligaments off the jets and decrease the mean drop-sizeo It was pointed out before that only a small range of mean drop-sizes was recorded for the study of the flashing water jets, but if the very rough orifices are not included, the average drop-size range is further reduced, the linear mean varying only from 29~6 microns to 43~0 microns. The drop-sizes for the Freon-ll sprays are smaller than for the water sprays as one can see by the points in Figure 27~ These smaller dropsizes for Freon-l are probably a result of the lower surface tension0 A lower surface tension allows for the transient existence of smaller liquid ligaments and thinner liquid films during the jet shattering process, which disintegrate to smaller drops. The surface tension also affects the size of the larger drops because a large —-drop is more readily shattered if it has a low surface tensiono The drop-sizes for the sprays from the cold water jets were considerably higher than those from the flashing "etso The linear mean diameters of the two cold jet sprays were 82 microns and 142 microns, compared to the 24-43 microns lnle.r mean diameters for the flashing sprays. An attempt was rmade to fit the drop-size distributions to an empirical distribution function so that the uniformity of the various sprays could be directly compared0 The empirical distribution chosen (20) for this was the logarithmic-normal-probability distribution function 0

-67This form appeared to be suitable because the distribution curves plotted versus the logarithm of drop diameter in Figures 24, 25, and 26 looked symmetrical. TIis distribution function is given by f(D) _ - L n( ) + 2 jD (4) were 6 - cAaracterizing parameter which is measure of the size uniformity, and D v the volume median diameter. vmd An experimental distribution which follows this empirical function should yield a straight line when the cumulative number distribution, D f(D) =Jo f(D)dZD Z N (5) is plotted on the probability scale versus the logarithm of drop diameter. An example of such a plot is given in Figure 28 for the distribution for run No, 9o This gives a very good straight line except at the highest drop percentages. This is not too serious as the highest percentages are those where one would expect the least accuracy. Plots for most of the analyses also produced straight lines, with occasional discrepancies at cumulative percentages above 98~ Values of the uniformity parameter,,3 are readily obtained from the log-probability plots by the slope of the lines. 6 = 0.394 / log1O(Dgo/D50) (6) where Dg90 D50 = are the diameters for the cumulative percentages of 90 and 50, respectively.

-6899.99 99.9 99.5 99 98 95 cD a. o 90 a: 0 Lw 80 (D z 70 w 60 w 0.J w 40 30_ -J M 30 RUN NO. 9 D 20 WATER AT 287~F AND 90PSIG THROUGH 0.04-IN. DIAMETER TYPE B NOZZLE 10 5 2 0.5 10 20 30 40 50 60 80 100 200 DROP DIAMETER,MICRONS Figure 28. Typical Cumulative Distribution Function (Log-Probability Scales).

The magnitude of this parameter is a measure of the uniformity of the distribution, the higher values signifying the more uniform distributions. The values of 8 are given in Table IVo Attempts to correlate the uniformity parameter with the operating variables were not too successful. This is not too suprising) as the range of 8 is small, Lo21 < 8 < 1 95. The average value of 8 for the 14 analyses of the sprays from flashing water jets was 1l55o This may be compared to the average value for the sprays from the cold-water jets which was 0~80~ The uniformity parameters for the sprays from the water jets are plotted in Figure 29 versus the bubble-growth-rate constant. Although it is not conclusive, the uniformity appears to increase with bubblegrowth rate. The major difference is the difference in 8 between the sprays from the flashing jets and the cold jets (C=0)o The values of 8 for the spray from the flashing Freon-ll jet formed by the nozzle of type A lies within the range for the flashing water sprayso It is not valid to compare 8 for the Freon-11 spray from the nozzle of type C, because although the jet is superheated., it would not have shattered if a very rough surface had not been employed. Ranz(25) has given typicalvalues of 5 for sprays from various types of atomizers. TABLE V. TYPICAL UNIFORMITY PARAMETERS FOR ATOMIZERS Atomizer. Gas Atomizer........................ 0o93 Spill-Controlled Swirl Nozzle........ 1o 29 Vaned-Disk Sprayer................ o 54

-701.9 1.8 0 1.7 0 1.6 1.5 cc 0' 1.4 4 0 I. 0.8 * SHARP-EDGED ORIFICES TYPE A O ROUGH-ORIFICES TYPE B o I A VERY ROUGH-SAND TYPE C 0.6 2 4 6 8 10 12 14 16 18 20 BUBBLE-GROWTH-RATE CONSTANT, C(FT/HR;2) Figure 29. Uniformity of Sprays from Water Jets.

-71The size uniformity for the sprays from the flashing jets compares quite favorably with the uniformity of the sprays from these other atomizers. It is impossible to quote typical mean drop-sizes for various methods of spray formation as this parameter is very dependent on the. injection conditions. One can qualitatively say, however, that the mean drop-sizes for sprays from flashing jets are somewhat larger than drop-sizes from gas atoumizers, but somewhat smaller than drop-sizes from disk sprayerso The mean drop-sizes for the sprays from flashing jets are similar to those often observed in sprays from swirl nozzles. The mean drop-sizes correlated here are the linear mean diameters, which are simply the arithmetic averages of the drop diameters in one location or in a whole spray~ The choice of this particular mean to correlate the data is somewhat arbritrary, as any one of the various means might have been employed. The choice of a particular mean depends upon the application of the spray. For example, if the process being considered is controlled by the magnitude of the surface area. the surface-mean diameter would be the most desirable to correlate. The various mean diameters reported in Table IV are sufficient to cover the means required for the analysis of most processes where sprays are employed.

-72Characteristics of the Sprays It was pointed out earlier that the drop-size is not necessarily the most important spray characteristic for a particular application. This section will present some of the other characteristics of the sprays from the flashing jets. One characteristic that is available from these analyses is the variation in drop-size across a plane perpendicular to the spray axis. This particular characteristic is mainly of interest in the manner in which it relates to the break-up mechanism. Figure 30 shows the variation in drop-diameter across the sprays from the flashing water jets for the three types of nozzles. In most cases, the largest drops are the furthest away from the spray axes. The drop-size decreases approaching the axis. and then usually increases again at the spray axis~ This can be explained by the manner in which vapor bubbles disintegrate the jeto Consider a portion of a flashing jet in which one or more bubbles have expanded and shattered the jet. The drops from the shattered jet have two components of velocity. one parallel to the spray axis given by the original momentum of the jet, and one perpendicular to the spray axis and away from it caused by the rapid expansion of vapor bubbles inside the jet~ At a given distance from the orifice, the larger drops will have moved the furthest away from the spray axis because the drag has a greater effect on the smaller drops and reduces the distance they travel from the axis before coming to their terminal velocities (29)

-7360 50 40 (a) 30 NOZZLE TYPE A-236~F Nwe =15.2 -0- Nwe = 22.7 50 / (b) 40 // (b) NOZZLE TYPE A 287~F ~3 ~~~0 Nwe = 9.6 J3Oi -— 0 —- Nwe = 11.5 U, z o 50 40 2 (c) NOZZLE TYPE B 254~F 30 Nwe = 18.4 (d) 40 NOZZLTOZZLE TYPE B 270 ~F 40 3 0 - Nwe = 8.2 -— O- Nwe = 9.3 -— X —- N we = 18.4 (e) 4NOZZLE TE TYPEB 2870F 40'" - Nwe = 12.4 $0 -— 0 — Nwe = 13.3 -— X —- Nwe = 18.5 I 1 (f) NOZZLE TYPE C 30 T~F Nwe -- 278 7.0 -— 0 —- 270 7.6 0 ~~0.4 0.8 1.2 1.6 DISTANCE FROM SPRAY AXIS (INCHES) Figure 50. Variation in Drop-Diameters across Sprays from Flashing Water Jets.

The reason that the drop-size does increase at the spray axis is that portions of the jet are not exploded by the vapor evolution; and only have an initial velocity component in the direction of the spray axis. This tendency for large drops to exist at the spray axis should decrease as the intensity of the break-up is greater, for fewer portions of the jet could escape the expansion effect of the growing vapor bubbles. For example, in Figure 30c, 30d, and 30e, the tendency for the existence of larger drops at the axis almost disappears when the temperature is up to 287~Fo Weber number also affects this as can. be seen by comparing Figure 30b and 30eo Although both are at the same temperature, the drop-sizes increase at the axis in Figure 30b5 where the Weber numbers are lower. The sprays from the nozzles with sand on the surfaces have smaller drop-sizes because the sand particles tear ligaments off the outside of the jeto This is demonstrated in Figure 30f by the fact that the tendency for larger drops to be farther from the spray axis is less than with the other nozzles. The smaller drops are formed from the liquid ligaments which are torn off at the outside surface of the jet, and so downstream of the orifice, tend to be further from the axis. This is the same reason that the variation in dropsize across the sprays is very different when sprays are made merely by pressure injecti,on of cold liqui.d. The liquid jets are disintegrated by the action of stresses at the jet surface. This break-up action at 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 away from the spray axis, and the largest in the centero The velocities of the drops in a spray are also available from a spray analysis. The velocity of the drops in a plane perpendicular to the spray axis vary with the position with respect to the spray axis and with the size of the drops. Figure 31 shows the velocities for a spray from one of the flashing Jets. The velocities given are averages for the velocities found in a given location and lying within a given size range. The plot shows that the drops have the highest velocities at the spray axis and decrease with distance from the axis. The drop-size has a strong effect, the larger ones going the fastest. The smaller drops for each location appear to approach a constant velocity. This same general pattern of velocities was observed in all thespray analyses from the flashing jets. The fact that the larger drops are traveling the fastest is to be expected, because it takes longer for them to decelerate to a terminal velocity and their velocities during the deceleration and at the terminal, values are higher. This situation is considerably more complicated than a single drop in a large expanse of vapor, however, as in this case, the vapor starts to move. There is a net transfer of momentum from the drops to the vapor in the spray zone. The vapor will obtain more momentum at the morse dense parts of the spray, accounting for the higher velocities at the spray axis. The fact that the smaller drops approach

-76RUN NO. 9 120.04-IN.TYPE B NOZZLE 120 WATER AT 287 OF AND 90 PSIG Q. Uw I00 0 z 4 W N C'80 IO w 70 cr_ 0 IL n60 5 0 1 0I 0 W r_ 40! CD 40! I Lr) w 30 > LOCATIONS WITH RESPECT TO SPRAY AXIS AT AXI S 20 - - 0.4-IN. AWAY -K- -- 0.8-IN. AWAY 0 -,1.2-IN. AWAY I0 2,31 L4 I L5 I 1 171 I 1 18 10 20 30 40 50 60 70 80 90 100 110 AVERAGE DROP DIAMETER IN EACH SIZE RANGE-MICRONS Figure 31. Velocity of Drops in a Spray from Flashing Water Jet 6 Inches from the Orifice.

-77a constant; value at any lodation is probably because they are the only ones that have decelerated to their terminal velocities at that location. Their terminal velocities are so small relative to the vapor velocity, that they appear to be traveling at the same velocity of the vapor. The primary value of the velocity data in this study is to obtain temporal drop-size distributions. The velocity data are available as a by-product of the analyses if one would like to make a study of the velocity distributions in a spray zone. From the fact that it was only necessary to take spray samples at locations that extended to radii of 1.8 ino for the sprays from the largest diameter jets, we can see that the spray zones are fairly small. The greatest diameter of the spray zones six inches from the orifice was about four inches. The spray zones did not continue to expand at distances greater than six inches from the orifice. This may or may not be desirable depending on a particular application. The spray zones are much smaller than the zones of sprays from swirl nozzles, air atomizers, or disc atomizers at a given flow rate. For example, York (32) had to take samples of an air atomizer spray at radii up to nine inches to obtain an analysis when 50 lb./hro of water were injected. Samples at radii up to 1.4 inches would suffice for a spray from a flashing jet at this flow rate. The orifices were usually positioned about four feet above the ground in the spray analyses. The sprays appeared to have been almost completely vaporized by the time they reached the floor except

-78in the cases of the sprays from the largest diameter orifices. These high vaporization rates result from the spray being at the liquid saturation temperature when it is formed. We can see how the conditions affect the vaporization rate. The mass transfer rate for vaporization from a spherical drop is given by dm = k (Yi - Y) D' (7) dt where dm = instantaneous molar rate of vaporization of the liquid, dt D = the diameter of the drop, Yi, y = the mole fraction of the vaporizing liquid in the gas at the interface and at great distance, respectively, and kg = the mass transfer coefficient. The mass transfer coefficient for the vaporization of a liquid on a spherical surface into a moving vapor is given by Frossling8 by a correlation that has been confirmed by several investigators DgP= 2 1 + 0.276 (i g D1/2 1/3 ] where R = the gas constant, T = the absolute temperature of the gas, Dm = molecular diffusivity of the vaporized liquid through the surrounding gas, P = the absolute pressure, V = relative velocity between the drop and gas, 4 = viscosity of the gas, and pg = density of the gas. Substituting Frossling's relation into the mass transfer rate expression,

-79the vaporization rate is given by am 2irDm pvD 7p 07 1/2_ 1/37 (9) dt RT 1+ 0.276 Pg1 where Pv - the vapor pressure of the vaporizing liquid at the drop surface temperature. Equation (9) is written assuming the drop is a pure liquid and the mole fraction of the vaporizing liquid at great distances from the drop is negligible compared to the value at the interface. From Equation (9) it can be seen that the vaporization rate is proportional to the vapor pressure of the liquid which is an increasing function of the drop temperature. The molecular diffusivity of the vaporizing liquid in the gas also increases with temperature. The vaporization rate increases with drop velocity. The high vaporization rates for the sprays from the flashing jets are a distinct advantage in many applications. This is obvious for those applications where the purpose of spraying is to increase the liquid surface and therefore promote rapid vaporization.

CHAPTER VI CONCLUSIONS The Break-Up The break-up of a cylindrical superheated liquid jet is similar to that of a cold liquid jet up to a certain critical temperature range having a magnitude of about 5~F. Below this temperature range, the only difference between the break-up of a superheated jet and a cold jet is that there may be light spray around the jet. This spray is caused by the growth and bursting of bubbles on the surface of the jet. The spray is only evident for jets formed from rough-surface orifices, where the microroughnesses provide turbulent eddies to initiate the nuclei for the formation of surface bubbles. The diameters of these bubbles grow in direct proportion to time, and their presence has a negligible effect on jet break-up. Above the critical temperature range, the superheated liquid jet is completely shattered into a fine spray. The shattering of the jet is mainly a result of the growth of vapor bubbles inside the body of the Jet. If the jet is formed by an orifice with a rough surface, these bubbles are nucleated on the surface of the orifice and their subsequent growth inside the Jet a short distance from the orifice shatters the Jet. If the Jet is formed by a sharp-edged orifice, the bubbles which shatter the Jet are not necessarily nucleated at the orifice, but often slightly downstream of the orifice by a random disturbance. -80

The mean temperature of the critical temperature range at which a jet of a given low viscosity liquid shatters is a function of the Weber number of the jet. The shattering temperature decreases with increasing Weber number. There appears to be a discontinuity in the shattering temperature-Weber number relation at a Weber number of 12.5, the shattering temperatures above this Weber number being much lower than those below i.t. This break in the shattering temperatureWeber number curve corresponds approximately to the critical Weber number for the change in the mechanism of cold liquid jet break-up from that caused by sinuous deformation to that referred to as atomization The shattering temperatures for water and Freon-ll jets indicate that a general function relating the shattering temperatures of jets of all low-viscosity liquids to their Weber numbers may be found by plotting the bubble-growth-rate constant at the shattering temperature versus the Weber number. This relation, found from the data of water and Freon-ll jets, is C = 19.7 - 0.581 Nwe for Nwe < 12.5 C - 115 - 0.491 Nwe for Nwe > 12.5 (1) where C is given in ft./hrol/2 This equation is limited to temperatures above the saturation temperature of the liquid at the receiving pressure, as below this temperature, there would obviously be no vapor evolution from flashing. The bubble-growth-rate constant employed in this correlation

-82is that which relates the proportionality of the difference in bubble radius and initial bubble radius to the square root of time for a vapor bubble growing in a superheated or supersaturated liquid. This constant provides a measure of comparison of the growth rates of vapor bubbles in various superheated and supersaturated systems. It is a function of the superheat or degree of supersaturation and the liquid physical properties. It may be calculated from ( LTCc )(P2) ( )(Dth)/ (2) for superheated systems, and from c ( - PCf) ( Dm) 1/2 1 cf (3) for supersaturated systems. The values of the calculated bubble-growth-rate constants for supersaturated systems indicate that the bubble-growth rates are so low, that flashing will have no effect on the jet break-up at low injection pressures (below 300 psig). This fact has been confirmed experimentally for carbon dioxide dissolved in water. The shattering temperatures for low viscosity jets have been found to be independent of the viscosity or the Reynold's number. This may not necessarily be the case for high viscosity jets. The information from these experiments is applicable to the break-up of superheated Jets all pure liquids injected into atmospheric pressure. This is true because the viscosities of all pure

-83liquids at their saturation temperature at one atmosphere are low and lie in a small range. The Sprays The mean drop-sizes of the sprays from flashing water jets that have been shattered by vapor evolution can be given by the relation Do0 1840 - 5.18 T (~F) (microns) (4) Nwe This equation is correlated from the drop-size data for jets injected at temperatures between 236~F and 287~F and Weber numbers ranging from 9~3 to 22.7. The equation correlating the drop-sizes for both the water and Freon-ll sprays can be given by = (246 - 830 C) (a)031 (Nwe) (5) when the interfacial tension is given in dynes/cm. and the bubblegrowth-rate constant at the injection temperature is given in 1 ft./hr.2-. Since Equation (5) is based upon only one point for Freon-ll and assumes only surface tension affects the drop-size at a given Weber number and bubble-growth rate, it should be considered as an extrapolation of the Freon-ll data point rather than as a true correlation. The range of the linear mean drop-sizes for the sprays from the flashing jets in these experiments was small, between 24 and 43 microns. This indicates that more intense conditions than those required to shatter the liquid jet do not have a great effect on the

drop-sizeo These drop-sizes may be compared to the drop-size of a spray from a cold water jet injected with a Weber number of 14o9 whose linear mean was 142 microns, There is no difference in the drop-sizes of the sprays from the sharp-edged and rough-surface nozzles, but the drop-size from the nozzle with sand on the surface is smaller This is because the sand particles tear liquid ligaments off the surface of the jets. Flashing is definitely a means by which fine sprays may be obtained from the break-up of cylindrical liquid jets at low Weber numbers and the corresponding low injection pressures. The drop-size: distributions can be correlated to the logarithmic-normal-probability distribution function The uniformity parameters for the distributions do not correlate well with any of the experimental parameters. The average value of the uniformity parameter, 5, for the sprays from the shattered water jets from the sharp-edged and rough-surface orifices is 1.55 ~ 0.12. This indicates that the uniformity of the drops from the flashing jets is as good or better than typical sprays from cold liquid jets, gas atomizers, swirl nozzles, or vaned-disc atomizers. In a plane perpendicular to the axis of the sprays. from the flashing Jets, the mean drop-size is usually the highest for the drops the farthest from the spray axis. The drop-size decreases approaching the axis, and often increases again slightly at the axis. This pattern is caused by the manner in which the

expanding bubbles inside the jet explode the jet and push the largest drops the furthest away from the axis. The larger drops in the center of the spray result from portions of the jet that are not exploded by the expanding bubbles. The velocities of the drops are the highest at the spray axis, and decrease with distance from the axis. At any location with respect to the axis, the larger drops have the highest velocity. The drops in any location smaller than about 20 microns appear to approach a constant celocityo The sprays are contained in relatively small zones, the greatest diameter in this study being six-inches. The vaporization rates of the sprays are high because the liquid drops are formed at their saturation temperatures.

CHAPTER VII RECOMMENDATIONS High Viscosity The results of this study are applicable to low viscosity liquids. This includes all superheated jets of pure liquids injected into a region of atmospheric pressure, as the viscosities of most pure liquids at their saturation temperatures at one atmosphere are low, usually below 0~5 cpo This does not include, however, mixtures such as high concentration sucrose solutions and wide-boiling-range hydrocarbon mixtureso The minimum temperature for the shattering of a high viscosity jet would probably be higher than for jets of low viscosity, because the investigations of Rayleigh (26) Weber(30) and Hinze(l1) have indicated the jet stability is increased with high viscosities. Hinze(ll) found that thecritical Weber number for the transition of the region of break-up of a cold liquid jet from sinuous break-up to atomization was increased with liquid viscosity. Since there appears to be a "critical" Weber number for the shattering temperature -- Weber number relation for a flashing jet, it seems reasonable that this critical Weber number would also be affected by liquid viscosity. The effect of high visocisty on the bubble-growth rate in a superheated liquid is unknown, as the assumptions included in the theoretical treatment of the problem included one of the inviscid liquid. The solution of the bubblegrowth-rate problem is also for pure liquids, not liquid mixtures or solution. -86

-87The break-up of flashing high-viscosity jets is mainly of interest as applied to spray drying, where viscous mixtures or sludges are generally injected. The small spray zones and high vaporization rates of the sprays from flashing jets are particularly attractive as regards this application. An experimental study of the break-up of high-viscosity flashing jets is therefore recommended. The approach may have to be entirely empirical as a result of the complicating effects of high viscosity on the bubble-growth-rate relation and the jet stabilityo Orifice Design Vapor evolution inside the orifice throats was avoided in this study because of its deleterious effect on the flow-metering. The reduction in flow rate is not too serious if its magnitude can be predicted accurately and reproducibly from theoretical or experimental studies. Vapor evolution inside of a small long orifice may be employed to advantage as a fine spray may be attained at a low superheat in this manner. Extreme care would probably have to be employed in design of the nozzles so that the bubble nucleation would occur at the same point in the orifice throat and cause mixing of the evolved vapor and liquid inside the orifi.ce. For example, a sharp obstruction at the upstream end of the orifice might promote continuous bubble nucleation at that point.

-88A long orifice nozzle made of a transparent material could be employed to make a photographic study of the growth of vapor bubbles in the superheated liquids. This would provide experimental evidence for the theoretically predicted hypothesis that the bubblegrowth rate is independent of turbulence for the degrees of turbulence in this study.

APPENDICES A. SUPPLEMENTARY EXPERIMENTAL DETAILS B. SUMMARY OF DATA AND CALCULATED VALUES Co SAMPLE CALCULATIONS D. LITERATURE CITATIONS -89

APPENDIX A. SUPPLEMENTARY EXPERIMENTAL DETAILS 1. Determination of the maximum orifice length. When injecting a flashing jet, vapor evolution can occur inside the orifice throat if the orifice is long enough. If this takes place, the evolved vapor and liquid mix inside the orifice throat and the specific volume of the mixture is considerably greater than that of the pure liquid phase. This can reduce the volumetric flow rate through the orifice at a given pressure to well below that when vapor is evolved outside of the orifice. Therefore, all of the noz:zles employed in this study had to be tested to insure that vapor evolution did not occur inside the orifices throughout the range of experimental conditions. One way in which the location of vapor evolution, inside or outside the orifice, can be determined is by visual observation. Liquid is injected at a constant pressure and the temperature increased. When the jet is shattered, a short section of the Jet is observed near the orifice exit if vapor evolution occurs outside the orifice. If vapor evolution has been initiated inside the orifice, no jet is visible and a mixture of liquid and vapor issues from the orifice. However, complete mixing of the liquid and vapor inside the orifice does not always occur when vapor is evolved inside the orifice. Occasionally, roughness conditions will be such that the phases separate inside the orifice. In these cases, a short section of jet may be visible although vapor has been evolved inside the orifice. Therefore, a more reliable method of checking the nozzles had to be employed. -90

_91There should be no decrease in volumetric flow rate at a given injection pressure as injection temperature is raised if vapor evolution occurs exclusively outside the orifice. The flow rates were measured for all the experimental nozzles at 80 psig and 120 psig at temperatures varying from about 1000F to about 3000F. The temperature of the liquid that is passing through the flowmeter is constant throughout a run, the temperature adjustments of the liquid taking place downstream of this location. The flowmeter therefore measures flow at constant density, or mass flow rates. The flow meter readings therefore were reduced somewhat as temperature was raised because the liquid density through the orifice was reduced and thus the mass flow rate. The readings could easily be corrected for volumetric flow rate by multiplying them by the ratio of the liquid density through the orifice at the highest flowmeter reading to the liquid density at the injection temperature. The volumetric flow rates for all the experimental nozzles employed here remained constant at both injection pressures and throughout the temperature ranges. A reductionin volumetric flow rate was experienced in several nozzles that had L/D ratios of four to six. 2. Calibration of Pressure Gauge, Thermocouple, Flowmeter, and Time-Delay Unit. The pressure gauge was calibrated with an Amthor dead weight gauge tester. The indicator on the pressure gauge could be adjusted so that all the pressure readings, from 10 psig to 140 psig, agreed with the weights on the gauge tester to within 0o. lb. Flow conditions during operation of the apparatus were

-92such that a constant pressure only to the nearest 1 psig could be maintained. The accuracy of the pressure gauge was therefore entirely satisfactory for these experiments. The iron-constantan thermocouple was calibrated in a mineral oil bath by a -5~ -2500C mercury thermometer. The calibration is shown in Figure 32. The potentiometer circuit was a Leeds & Northrup # 72010 with an externally connected standard cell #PL-127-130000. The accuracy of the calibration is such that temperature readings may be made to the nearest 0.5~F. The thermocouple wire was attached to the outside of the pipe just upstream of the place the nozzles were connected. The pipe and wire were heavily insulated. There was a thermowell just upstream of the flexible tubing that led to the pipe to which the nozzles were connected. There was a reduction in temperature between the thermowell and the thermocouple location. At a given: flow rate, however, this temperature reduction should be constant at any given injection temperature. This provided a means to check how accurately the thermocouple measurement of the pipe temperature corresponded to the actual liquid temperature in the pipe. The thermocouple was attached to the pipe and insulated, and then the thermowell and thermocouple readings were recorded through a range of temperature when water was injected through a given nozzle at constant pressure. The thermocouple wire was removed, and then attached to the pipe again with heavier insulation than the first time. The thermowell and thermocouple readings were taken again with the same nozzle and injection pressure. The

-930 CK) cm, to 0 0 too r~r O CI O0 0 U.LL o O 0 k N cr jw h 0 I — CIo ODW 0 LO N 04 0 0 S.L1OAIIIW I eNIaVH3t 9313WVOI1N310d

readings maintained the same correspondence as in the preceding trial. It was concluded from this that the insulation was sufficient so that there was negligible temperature reduction between the liquid and outside of the pipe. The water in the storage tank was saturated with steam at 120 psig during the flowmeter calibration and all flow rate measure — ments, the injection temperature and pressure adjustments taking place downstrean of the storage tank and flowmetero This provided that the water passing through the flowmeter was always at the same temperature and pressure. The liquid injected through a nozzle was collected in a graduate cylinder for 30 to 60 seconds while the injection pressure remained constant. The volume and temperature of the collected liquid was recorded and the volume corrected to 80~Fo The calibration curve is presented in Figure 33a The time-delay unit was designed so that when one of the photolights was triggered, an impulse would be sent to the other photolight after a definite time-delay that could be set from about 10 to 25 microseconds. The actual time-delay could not be measured electronically so the unit had to be calibrated photographically. This can be done by taking double-flash photographs of an object moving at a known velocity and measuring the distance between the exposures of the object on the photograph. The calibration was made by taking double-flash silhouette photographs of a moving band saw blade. The blade velocity was determined by measuring the

-95w I.ScI2 2 t0 r ao 3:1. 0 H 10 O' _j~~~~~~~~~~~Q U) ~~~~~~04-' 0 0 0) ~LL. 0 Id~~~~I Ur w ~0~ In co 0 0~~~ U) -i OD~~~~Nb FLL. 0~~~~~~~~~~~~~0 0 -i 0 I- o In U a 0 9NIUV) 313 39fl 0~ o 0 0 0 ~1' ~ 0 oD SD CY' N 0 OD D N*j.....*j 9NIOVgt:l 3"IVOS 3al'tlr

rotational frequency of the driving wheel with a Strobotac, whi.ch is a variable frequency flash unit. After the band saw blade was run for about five minutes, the driving wheel motion could be l!stopped" by the flashes from the Strobotac and the rotational frequency recorded. Several photographs were taken of the saw blade at a few delay unit settings. The distance between the two exposures of a saw tooth was found from the photographs. It was easy to distinguish a saw tooth in each exposure as each one had a unique profile from chips and dirt particles. The time:ielay from seven photographs at the setting for the spray analyses i.n these experiments was 22.4 ~ 0.4 microseconds, 3. Control of the Exposure. It has been pointed out that the aperture opening on the camera lens must, remain constant for all, spray analyses to maintain. a constant depth of field. The light intensity must therefore be controlled by filters in fronrt of the photolights. The optical density of a photograph from a certain type of film and developed by a standard technique will be a function of the light intensity and the exposure time. The optical density is a measure of the degree by which the exposed negative can transmit light~ Hanson(lO) has photographed circular ink spots on a miscroscope slide with Kodak Contrast Process Ortho film and under various exposure conditions to obtain negatives over a range of optical density. The actual sizes of the spots were measured with a microscope and compared to the size of the drops on the negatives. Hanson found that

-97T the size of a 16.5 micron spot on a negative was within ten percent of its true size if the optical density of the negative could be maintained between 1.6 and 2~0. The accuracy improves as the drop size increases, the measured size being within five percent of the true size for a 3708 micron spot, The exposure conditions for these experiments are controlled to maintain the optical density within the aformentioned limitso The effect of the filters on the light intensity was determined by taking several photographs with 1 to 7 C0002-inch thick Mylar film filters in front of the photolight when the aperture setting was f-3o5, all. the way open. The optical densities of the negatives were measured with a Kodak Color Densitometer Model No., 1 The effect of the filters on the optical density is shown in Figure 34. Note that the density is not always constant for a given number of filters because the light intensity from the photolight can vary from flash to flash. The density of the negatives were essentially independent of the location on the negativeo If a photograph is taken with no filters, an approximately four inch diameter region of the 4 x 5 negative is exposed, leaving unexposed cornerso In addition to the filters, the lights were enclosed in 3/8 inch thick plexiglass cases9 which apparently were sufficient to diffuse the light beam so that the whole field of the lens was exposed to the same degree. During a spray analysis, a dense spray can reduce the light intensity considerably. A photo floodlight was therefore directed to the lens through a plexiglass sheet and six filters and

-983.0 2. 8 1 GE PHOTO FLASH WITH CONTRAST PROCESS ORTHO FILM 2.6 f -3.5 Co I I I I I FILTERS ARE L 2.4 0.002- IN. MYLAR FILM I2.0 1.8 i.6 I 2 3 4 5 6 7 8 NO. OF FILTERS Figure 34~ Effect of Filters on Optical Density.

-99the light intensity at the lens measured with a Weston Master II universal exposure meter model 735 No. 6583722. For any location in a spray formed under certain conditions, the photo floodlight could be directed at the lens through the spray. The number of filters to be employed during the analysis could then be determined by the number required to obtain the same exposure meter reading as with the plexiglass and six filters with no spray. Employing this technique, it was fairly easy to maintain the optical density of the negatives within 1.6 and 2.0. In the early phases of the study, photographs of the sprays were often underexposed and showed no drops although the lighting conditions seemed to be all right. It was found that this was caused by cor4densation of vapor on the lenso A shutter was placed over the lens and opened just before taking each photograph. The camera had to be backed away and the lens wiped dry before taking the next photograph as the lens became fogged before the shutter could be closed again. This was a serious problem when photographing the high-flow-rate sprays because if the picture was not taken immediately after the shutter was opened, the lens would fog. The shutter was employed in all the analyses, although it made the analyses more tedious. It is recommended that a mechanical shutter that could be triggered with the photolights be employed to provide a more convenient solution to this problem. 4. Developing Technique. The optical density of the negatives can vary considerably with variations in the developing technique. A standard procedure which

-100was carefully adhered to for the developing of all spray photographs was therefore employed. The developing tanks were immersed in a bath of running water at 68~F. The films were developed in Kodak D-ll developer for five minutes, with agitation the full first minute, and intermittently every minute thereafter. The films were then rinsed, and fixed in Kodak acid fixer for ten minutes with agitation every minute. The films were taken from the fixer, rinsed in water for 30 seconds with agitation, and then immersed in Hypo clearing agent for two minutes. The films were then washed in water from five to ten minutes and dried. A Wratten Series two red safelight filter was employed for lighting during the developing process. 5e Minimum Drop Sample. Each photograph at a spray location has a certain number of drops within the limits of focus that are classified into size ranges to obtain the experimental distributiono The more drops in a sample, the closer will the measured size distribution approach the actual size distribution for that location in the spray. The accuracy of the sample distribution is not only dependent on the number of drops, however, but also on whether the distribution remains constant at that location, as the spray may pulse and fluctuate. The number of photographs at a given sample location must therefore satisfy two conditions: (1) provide the minimum number of drops for an accurate distribution, and (2) provide the average spray condition at that location.

-10 - The drops from photograph Noo 131, taken of Location 2 in Run Noo 59, were counted 50 at a time and the cumulative distribution obtained after counting each successvie group of 50 drops. The cumulative distribution curves for the samples are given in Figure 35. The curves for 50 and 150 drops are omitted to eliminate confusion between the curves. Note that the curve for 100 drops is much lower than the curve for 300 drops for the small drops and much higher for the large drops. The curves for 200 and 250 drops, however, lie fairly close to the curve for 300 drops on either side. This shows that as the sample includes between 200 and 300 drops, the distribution curve is approaching a constant function. About 85 percent of the samples from each location for each run contained over 200 drops, and often considerably more, sometimes up to 1000. In those cases where less than 200 drops were counted, the drop density in that location was small enough so that the drops did not contribute greatly to the anlaysis for the entire sprayo In the preliminary tests for the minimum sample, two photographs of the same sample location of a spray injected under given conditions gave almost the same distribution if there were at least about 200 drops on a photograph. For example, the cumulative distributions for two photographs at location 2 of Run No. 5 are shown in Figure 36. The curves are fairly close. Two photographs of each sample were therefore taken in all analyses. In view of the difficulty in taking the photographs of the flashing jets resulting from the lens fogging problem, it was desirable to keep the number of photographs down to a minimum, The distributions obtained from

-102CO) cO 0) (/ 0 000 0 im ~~N 0 0r 0I 0 0000 * N~~z 0 1K 00z.~~~ I C.-' 0 ~~~~'-z,[ 7o o g -S o ~ 0 oO Q i ~~~~~~~~~~~~~~~~~~~~~~~0 4:2 ~,~- 0 (U RI 0000~~~ 0 0 0 0 0 0 0 0 0 0 0 0m)~~ 0 i ( c0 InO N -- (a).- 39VIN3::3d 3AI.LV"Inwno

-1030 0~~~~~~~~~~~~~0 C*.i~~~~~~~~~~~~~~~~dI) -o H N ~ ~ ~ c 0 zz "'z~~~~od Z oo0 0 0 z 00 c~ 0 mo x x~~~ as - oi CL ed 4o 0 z Z o0 HE-o 00 k 0N o~ W0 m U ) -IC) Q.'%b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~H 0 0 0 0 ~ ~~~~~~~~~~~~~ 0 O Q m.r I (a) i 9VIN3H3d 3Iiv-in wn N C o 0 ~ () I~1N3' 3 (0 0 0 0 U)Z N -~~~~~~~~~~~(G)4 3V.LN3~i3d AI.LVfl~Ifo

10o4TABLE VI. DETERMINATION OF MINIMUM SAMPIE (t-rconditions off-iRun NO. 5 -,- Location 2 ) A. Drops counted 50 at a time - photo No. 131. No. of No. of Drops and Cumuiat'ive Percentage in Each Size Range Drops Counted 1 2 3 4 6 7 8 - 9 50 No. 1 7 23 12 5 1 1 k 2.0 16.0 6200 86.0 96.0 98.00 980o 100o0 100 No. 2 11 46 27 10 3 1 % 2.0 13.0 59.0 86.0 96.0 99.0 99.0 100.0 150 No. 7 21 60 38 17 4 2 1 % 4.7 18.7 58.7 83.9 95.3 98,0 99.3 100,0 200 No. 12 26 75 49 26 6 4 2 6.0 19.0 56.5 81.o 94,o 97.0 99.0 100o0 250 No. 12 35 95 59 30 8 5 5 1 4.8 18.8 56.8 80.4 92.4 95.6 97.6 99.6 100.0 300 No. 15 42 117 71 34 9 6 5 1 5.0 19.0 58.0 81.7 93.0 96.0 98.0 99.7 100.0 B. Comparison of Photo No, 130 and 131 No. of No. of Drops and Cumulative Percentage in Each Size Range Drops Counted 1 2 3 4 5 6 7 8 9 #130 No. 14 38 123 72 25 6 5 2 1 286 % 4.89 18.17 61.18 86.35 95o10 97.20 98.95 99.65 100 #131 No. 17 46 128 77 37 10 6 6 1 328 % 5.18 19.20 58.22 81z.70 92098 96.03 97.86 99.69 100

two photographs are usually accurate because of the large number of drops per photograph for these relatively dense sprays. 60 Flow Rate Check There are two major sources of error in the photographic analysis of sprays, One is in the determination of which drops should be accepted as part of the photographic sample~ Although standard drops are referred to in order to define the limit of focus, the decision as to whether to accept or rej.ect many drops is often arbitrary. Another source of error is in the velocity measurements~ The velocities are measured assuming that all drops remain in. the plane of the sample locations that is parallel to and intersects the spray axiso In reality, many drops cross this plane, In a double-flash photograph of the sprays, most of the drops are traveling in the same direction, but there are often. se'veral that seem to be going in other directionso Only drops that are going i.n the same direction as the majority are sa1mpled in these analyses for the velocity measurements. Employing this techniques, the drops in a giAren size range for a certain sample location did not di.ffer in velocityv by more than 25 percent. The aiverage veloc ities in each size range at each location were plotted versus the average drop diameter5 and the velocities for the calculations obtained for the best curves through. these points One way in which the overall accuracy of the spray analyses may be measured is by comparing the computed flow rate of the spray from the drop-s ize analyses and their velocities9 and the flow rate of the injected liquid jeto This computed flow rate from the analyses

-1o6CMI~, " H-r Je.u// _,:., LL 6 5 0~~~~~~~~~ (3 (r)3~~~~/ IIt 10: / dL i 1 2 $ 4 5 6 7' 8 9 I0 II 12 FLOW RATE COMPUTED FROM PHOTOGRAPHS FT3/HR Figure 37. Comparison of Spray Flow Rates and Injection Flow Rates. N 8o o / ~~~~~~ LL62 / 9 1 1 w~~~FO 0AECMUE RMPHTGAH T3H I-ur /7 oprsno pa lwRae n neto lwRts

is dependent on both the accuracy of the depth of focus and the accuracy of the velocity measurementso The standard drops that were chosen for these analyses were Oo91 mm from the point of focus so that the depth of focus was 182 mm, The sample volume is known from this figure and the total nlmber of drops passing a 00o inch thick plane perpendicular to the spray axis can then be computed by multiplying the number of drops in each size range for each location by the ratio of the volume of the annulus of which the sample is a portion to the volume of the sample. The flow rate of the spray is then determined by computing the volume of the drops in each size range in each annulus and multiplying by their velocities. These computed spray flow rates are compared to the flow rates calculated from the jet diameters and the jet velocities in Figure 37 for the sprays from the water jets. The computed values from the sprays are within 45 percent on the low side and 36 percent on the high side of the values computed from the jet diameter and velocity. The standard deviation is 27 percent. The flow rates computed from the sprays are usually lowo This is to be expected from the rapid vaporization rate of the spray and the fact that drops less then five microns are not resolved on the photographs~ 7o The Time-Delay Unit. A circuit diagram of the time-delay unit is shown in Figure 38~

-108oa I B o O. 0 ~ ) g Ir;z 0.<\t t W l_ I ~o" i, d~ 14 W it 0 __]"O I- ~O _~( 111 1~~~~ N _ i~~~~~~~~~~~~~l 0~~~~~~~~~~~ 0~ ~ ~ x o O 3 n o o 00A 0 6 0 -3 4D F\3~~~~~, - — alr Lj OD icj In~~~~~~~~~~~~~~~~~~ "d r~ o ~i ~i:[~~~~~~~~~~~~~~~~~~~~~~I',E >~~~~~ O O~~~~~~~~Y Z Z o~ (O~~

APPENDIX B.o SUIMMARY OF DATA AND CALCULATED VALUES LIST OF TABLES Page AI. Break-Up Temperatures for Water and Freon-ll....... 110 AII Bubbles on Surface of a 0.031 Inch Diameter, 268~F Water Jet Injected at 120 psig.................... 111 AIII. Run No. 1....................................... 112 AIV. Run No, 2............................. o..... 113 AV. Run No. 3o,................................ 113 AVIX. Run No. 7,... 4.. 0 0 O O o o e @ *e ~ 114 AVII. Run No. 5......,.............................. 11 AV.IIo Run Noo 63....................................... 11 115 AVIX. Run No................................... 115 AX. Run No. 8 1..................................... 116 AXIo Run No. 9..Q........................................ 116 AXIIo Run Noo 10.......................................... 117 AXIII. Run No. 11...............o......................... 1-17 AXIV. Run No. 12...............e... e........ e.............. 118 AXVIX. Run No. 13 7................o.....,,............, 1208 AXVII. Run No. 15.......................................... 119 AXVIIIo Run No- 16.......................................... 120 AXVIX Run Noo 1......................................... 120 AXX. Run No. 18......................................... 121 -g10

APPENDIX B. SUMMARY OF DATA AND CALCULATED VALUES The original data are in two data books under the author's name and dated December 29, 1958 and February 17, 1960. These data books, and the photographs are located in the Multi-Phase Fluids Laboratory in the Fluids Building at the North Campus of the University of Michigan, Ann Arbor, Michigan. 1. Break-Up Data. TABLE AI. BREAK-UP TEMPERATURES FOR WATER AND FREON-11 Run Nozzle Injection set Shattering 7 No. Type Pressure Diameter Temperature Re Nwe (ft./hri2) (psig) (inches) (OF) Water 1B A 120 0.025 282 125,000 8.81 16.3 2B A 131 0.025 280 131,000 9.60 15.9 3B A 100 0.032 272 143;000 9 34 14.0 4B A 120 0.032 268 152 000 11.20 13.1 5B A 130 0.032 266 157, 000 12.12 12. 6 6B A 80 o0o66 237 220,000 15.16 5n8 7B A 120 o0o66 215 239,000 22.53 0.7 8B B* 120 0.031 273 150,000 10o83 14.3 9B B 93 0.031 272 132,000 8042 14.0 10B B 134 0.031 270 157,000 12.12 13o6 11B B 84 0.035 268 139 000 8.56 13o1 12B B 128 0.035 237 148,000 12. 87 5.8 13B B 60 0.053 270 170,000 9.24 13.6 14B B 80 0.053 258 197.9000 12.28 10.8 15B B 96 0.053 235 192,000 14.60 5.4 16B B 120 0.053 223 200,000 18.15 2.5 Freon-ll 17B A 94 0.025 152 86,600 18.10 5.0 18B A 95 0.032 118 99,200 23.60 2.8 * With Sharp Downstream Edge

..I-11 2. Bubble Size Data. TABLE AIIo BUBBLES ON SURFACE OF 0.031 INCH DIAMETERO 268~F WATER JET INJECTED AT 120 PSIG Photograph Bubble Distance from Time Predicted Growth for Number Diameter* Orifice* (4 sec.) Submerged Bubble, (Inches) (Inches) 2Ct2 (Inches) 27 0.020 0.280 168 0o066 64 0.022 0.235 141 0o 060 64 0.018 0.200 120 0.055 64 0.017 0.175 105 0.052 64 0.010 0.140 84 0o046 97 0.023 0.345 207 0.073 97 0.027 0.377 226 0.076 93 0.029 0.394 236 0.078 93 0.031 0.425 255 0oo081 99 0.019 0.183 110 0.053 99 0.021 0.239 143 o061 100 0.018 0.173 104 0.052 101 0.015 0.145 87 0.047 101 0.o019 0.162 97 0.050 103 0.017 0.155 93 0.049 104 0.028 0.363 218 0.075 107 0o014 0.136 82 0.046 107 0.018 0.214 128 0.057 * These are the measured values on the photographs divided by 10, representing the actual values.

3. Drop-Size Data The number of drops and their average velocities are given for the drops found to lie in each size range at each sample location. The sample locations referred to are shown in Figure 4~ The size ranges referred to are given in the following table~ Size Range No. Size Range (Microns) 1 0- 1.0 2 10 - 14ol 3 14.1 - 20 4 20 - 28~2 5 28~2 - 40 6 40 - 56.4 7 56.4 - 80 8 80 - 113 9 113 - 16o 10 16o - 226 11 226 - 320 12 320 - 453 13 453 - 640 TABLE AI o RUN NO. 1. 0.040 INCH DIAMETER TYPE A ORIFICE WATER JET AT 287~F AND 120 PSIG Loca- Pho- Total Number of Drops in Each Size Range tion tos Drops 1 2 3 4 5 6 7 8 9 10 1 2 593 14 67 145 130 107 61 41 18 9 1 2 2 596 6 36 124 136 154 84 35 18 2 1 3 2 406 5 25 56 116 129 60 15 4 2 351 3 6 25 56 95 101 54 10 1 Average Velocities in Each Size Range (fps) 1 2 66 85 97 104 121 129 2 2 60 61 63 89 89 108 115 3 2 47 51 65 76 4 1 17 16 24 31 48 77

- 13TABLE A!V, RUN' NO. 2. 00031 INCH DIAMETER TYPE B ORIFICE WITH SHARP DOWNSTREAM EDGE WATER JET AT 287~F ATND 1,20 PSIG Loca- Photos Total Number of Drops in Each Size Range tion Drops 1 2 3 4 5 6 7 8 9 10_ 1 2 634 7 h.2 11 165 164 109 32 2 1 1 2 2 397 8 28 61. 112 109 73 6 3 2 128 3 14 44 65 66 25 1 4 2 93 5 26 38 24 Average Velociti.es in, Each Size Range (fps) 1 1 36 40 42 46 74 2 1 35 37 43 49 3 1 30 30 32 34 36 62 74 4 1 14 15 24 23 27 52 53 TABLE AVT RUN NO. 3. o0o80 INCH DIAMETER TYPE A ORIFICE WATER JET AT 2040F AND 80 PSIG Loca- Photos Total Number of..:rops i.n Each Size Range tion Drops 1 2 3 4 6 7 8 9 1.0 11 12 13 1 4 192 1 3 1.4 23 36 26 31 15 14 15 12 2 2 4 109 1 4 7 13 20 16 17 1.1 8 4 6 2 Average Velocities in Each. Size Range (fps) 1 2 34 61. 68 85 86 88 99 2 2 a 33 34 50 82 95

-114TABLE A VI RUN NO. 4. 0.080-INCH DIAMETER TYPE A ORIFICE WATER JET AT 236~F AND 80 PSIG Loca- Pho- Total Number of Drops in Each Size Range tion tos Drops 1 2 3 4 5 6 7 8 9 10 11 12 1 4 648 21 93 183 145 88 53 28 17 10 7 2 1 2 2 685 1 45 145 228 181 6o 18 4 1 2 3 2 539 5 31 96 118 136 115 26 8 2 2 4 2 384 7 30 43 8o 154 51 17 2 5 2 212 1 14 26 27 60 62 18 4 average velocities in each size range (fps) 1 1 42 44 52 62 68 74 126 127 2 1 34 35 38 45 6o 80 92 3 1 32 35 37 40 48 78 95 103 4 1 21 22 24 40 62 85 5 1 10 17 20 32 61 TABLE A VII RUN NO. 5. 0.080-INCH DIAMETER TYPE A ORIFICE WATER JET AT 236~F AND 120 PSIG Loca- Pho- Total Number of Drops in Each Size Range tion tos Drops 1 2 3 4 5 6 7 8 9 10 1 2 373 11 74 137 68 42 20 8 10 2 1 2 2 614 31 84 251 149 62 16 11 8 2 3 2 596 11 35 116 201 168 51 9 5 4 2 366 6 29 72 66 81 68 31 13 5 2 273 8 23 43 54 81 61 3 average velocities in each size range (fps) 1 1 50 54 61 69 80 95 110 135 2 1 41 46 48 50 72 90 3 1 35 42 44 52 60 92 4 1 20 22 24 25 40 62 90 93 5 1 10 14 25 37 68 72

-115TABLE A VIII RUN NO. 6. 0.050-INCH DIAMETER TYPE A ORIFICE WATER JET AT 287~F AND 130 PSIG Loca- Pho- Total Number of Drops in Each Size Range tion tos Drops 1 2 5 4 5 6 7 8 9 10 11 12 1 4 386 5 16 64 81 86 54 34 17 15 11 4 1 2 4 748 12 82 187 205 207 49 5 1 3 4 501 6 20 94 119 135 108 18 1 4 average velocities in each size range (fps) 1 2 75 95 105 155 1422 1 11 16 28 51 5 2 4 5 8 10 21 TABLE A IX RUN NO, 7. 0.051-INCH DIAMETER TYPE B ORIFICE WATER JET AT 287~F AND 90 PSIG Loca- Pho- Total Number of Drops in Each Size Range tion tos Drops 1 2 5 4 5 6 7 8 9 10 1 2 469 6 60 132 142 86 32 6 3 2 2 2 178 9 36 55 53 16 3 4 1 1 3 2 209 1 1 54 53 76 41 2 1 4 2 54 1 1 14 17 1 average velocities in each size range (fps) 1 1 56 54 65 73 82 125 2 1 35 37 43 56 63 72 81 113 3 1 11 10 10 21 57 61 4 1 6 12 16

- 116TABLE AX RUN NO. 8. 0o 040-IIN. DIAMETER TYPE B ORIFICE WATER JET AT 270~F AND 130 psig Loca- Photos Total Number of Drops in Each Size Range tion Drops 1 2 3 4 5 6 7 8 9 10 11 1 2 294 2 9 56 84 -- 28 16 1.0 2 1 1 2 2 610 6 56 142 181 174 43 6 1 1 3 2 760 1 20 128 223 260 110 16 2 4 2 198 4 25 51 81 33 3 1 Average Velocities in Each Size Range (fps) 1 1 50 52 60 67 76 100 1_40 2 1 28 30 39 42 52 80 94 3 1 30 33 34 48 61 90 4 1 16 17 24 28 38 TABLE AXI RUN N0o 9. 0o040-IN, DIAMETER TYPE B ORIFICE WATER JET AT 287~F AND 90 psig Loca- Photos Total Number of Drops in Each Size Range tion Drops 1.2 3 4 5 6 7 8 9 1 2 657 8 72 223 221 123 4 3 2 1 2 2 583 9 54 167 203 131. 17 1 1 3 2 395 1 7 51. 73 156 90 14 3 4 2 337 2 26 53 115 1.04 34 3 Average Velocities in Each Size Range (fps) 1 1 50 54 71 81 91 120 134 2.1 38 44 50 63 77 98 3 1 22 24 34 51 60 4 1 12 12 27 36 41 48

-117TABLE AXIL RUTN NO. 10o 0o 040o- INo DIAMETER TYPE B ORIFICE WATER JET AT 287~F AND 130 psig Loca- Photos Total Number of Drops in Each Size Range tion Drops 1 2 3 4 5 6 7 8 9 1 2 9 56 118 121 76 24 3 3 2 2 1095 29 117 331 316 243 51 8 3 2 611 4 48 123 1,58 169 99 9 2 4 2 271 3 11 40 57 100 47 11. 2 Average Velocities in Each Size Range (fps) 1 1 34 35 46 52 73 104 97 2 1 21 22 27 32 34 3 1 20 20 26 33 35 42 4 1 14 17 27 29 28 TABLE AXIII RUN NOo 1.1 0o0o6o0IN. DIAMETER TYPE B ORIFICE WATER JET AT 254~F AND 120 psig Loca- Photos Total N1umber of Drops in Each Size Range tion Drops 1 2 3 4 5 6 7 8 9 10 1 ~ 2 378 ~- 30 111i 108 87 25 9 4 2 1 2 2 680 14 77 213 178 123 52 17 5 1 3 2 831 24 105 259 192 159 66 17 7 1 1 4 2 658 5 33 112 153 204 112 28 7 3 5 2 199 5 22 26 42 66 29 8 1 Average Velocities in Each Size Range (fps) 1 1 I 42 43 64 83 98 134 138 145 2 1 38 39 57 72 87 118 135 145 3 1 18 18 20 24 38 46 83 4 1 17 19 23 28 44 62 5 1 13 13 17 20 29 50

TABLE AXIV RUN NO. 12. 0.060-IN. DIAMETER TYPE B ORIFICE WATER JET AT 270~F AND 80 psig Loca- Photo Total Number of Drops in Each Size Range tion Drops 1 2 3 4 5 6 7 8 9 10 1 2 139 3 29 47 33 15 8 3 1 2 2 362 21 111 107 77 27 12 3 2 2 3 2 736 1 30 155 233 249 54 9 2 3 4 2 686 2 34 137 200 223 70 18 2 5 2 497 8 65 152 180 78 12 2 Average Velocities in Each Size Range (fps) 1 1 35 35 54 68 107 114 2 1 30 32 44 54 100 106 115 3 1 20 18 24 31 48 62 4 1 13 14 19 24 35 5 1 9 9 11 20 26 30 TABLE AXV RUN NO. 13. 0.060-IN. DIAMETER TYPE B ORIFICE WATER JET AT 270~F AND 120 psig Loca- Photos Total Number of Drops in Each Size Range tion Drops 1 2 3 4 5 6 7 8 9 1 2 229 6 48 64 79 21 6 4 1 2 2 1264 54 170 442 371 195 27 4 1 3 2 686 7 64 164 199 152 77 19 4 4 2 681 7 51 145 183 192 87 13 3 5 2 166 3 18 29 30 61 21 4 Average Velocities in Each Size Range (fps) 1 1 42 43 64 83 98 134 138 145 2 1 38 39 57 72 87 118 135 145 3 1 18 18 20 24 38 46 83 4 1 17 19 23 28 44 62 5 1 13 13 17 20 29 50

TABLE AXVI RUN NO. 14. 0.020-IN. DIAMETER TYPE C ORIFICE WATER JET AT 80~F AND 94 psig Loca- Photos Total Number of Drops in Each Size Range tion Drops 1 2 3 4 5 6 7 8 9 10 11 12 13 1 4 253 12 24 40 33 32 35 14 22 20 13 8 2 4 351 5 33 78 116 50 30 21 10 6 1 1 Average Velocities in Each Size Range (fps) 1 3 54 54 53 72 80 88 104 115 114 115 2 1 21 20 22 58 65 90 99 TABLE AXVII RUN NO. 15. 0.020-IN. DIAMETER TYPE C ORIFICE WATER JET AT 270~F AND 130 psig Loca- Photos Total Number of Drops in Each Size Range tion Drops 1 2 3 4 5 6 7 8 9 10 1 2 584 14 32 130 183 155 47 11 6 4 2 2 2 949 26 98 272 289 227 35 2 3 2 746 12 49 170 287 210 16 2 4 2 403 17 64 152 116 51 3 Average Velocities in Each Size Range (fps) 1 1 48 57 76 94 115 140 145 2 1 30 32 42 47 48 58 78 3 1 12 13 16 20 29 30 4 1 6 6 8 10 14

-1,20TABLE AXVIII RTUN NO. 16. 0o020-INT', DIAMETER TYPE C' ORIFICE WATER JET AT 278~F and 120 psig Loca- Photos Total, Number of Drops in Each. Size Range tion Drops 1 2 3 4 5 6 7 9 1'2 949 23 87 301,'326 i8L 21 5 2 2 2 810 43 117 289 1.93 135 28 5 3 2 508 37 101 187 91 65 23 4 4 2 404 2 34 98 109 1,1.7 40 4 Average Velocities in Each Size Range (fps) 1 1 44 44 59 72 92 98 130 2 1 28 31 50 59 79 88 3 1 1.8 20 24 31 41. 50 4 1 8 8 12 20 26 TABLE AXVTIX RUN NO. 17. 0 0030-IN. DIAMETER TIRPE A ORIFICE FREOT1-11. JET AT 152'F AND 94 psig Loca- Photos -Total urnumber of Drops in Each Size Range tion Drops 1 2 3 4 5 6 7 8 1 4 840 3 30 166 289 238 72 32 10 2 4 165 1. 16 56 57 24 1.1. Average Vel.ocities in Each Size Range (fps) 1 2 30 30 32 40 52 71 92 2 2 2i 23 29 35 40

TABLE AXX RUN NO. 18. 0o020-IN. DIAMETER TYPE C ORIFICE FREON-11 JET AT 125~F AND 95 psig Loca- Photos Total Number of Drops in Each Size Range tion Drops 1 2 - 3 4 5 6 7 J 9 1q 11 - 1 3 1042 10 53 86 219 286 228 94 50 12 1 2 3 133 5 26 43 42 13 4 3 3 35 1 5 15 8 5 1 Average Velocities in Each Size Range (fps) 1 2 35 37 42 55 71 79 90 2 2 20 21 25 30 39 3 2 12 1.3 15 19 22

APPENDIX C SAMPLE CALCULATIONS.o 1. Calculation of Jet Velocity. v = (2ga0Pv2) (1) For Run No. 4B conversion factor = 32.2 ft./sec.2 injection pressure AP= 120 + 1 psig (x 144 in.2/ft.2) liquid specific volur.e v2 = 001715 ft 3/lbo at liquid temperature (21) (2680F.) V = (2 x 32.2 x 120 x 144 x 0.01715)2 V = 138.2 ft./sec. 20 Calculation of Weber number, pg V2d N = — (2) we 2gca For Run No. 4B surrounding gas density pg = 0o0591 lb/ft.5 at 212~F. (air)(12) jet velocity (Calc. 1) V = 138.2 ft./sec. jet diameter d = 0,032 ino (x 1/12 ft./in.) conversion factor gc = 32,2 ft./sec.2 interfacial tension a = 58.9 dyne/cm, (x 6.85 x 10-5 lb./ft. at 2120F.(21) dyne/cm. 0.0591 x (138,2)2 x 0.032 Nwe 12 x 2 x 32.2 x 58.9 x 6.85 x 10-5 Nwe = 11.2 we~~~~~~12

-1233. Calculation of Reynoldl's Number. R = Vd (3) v2pFor Run No. 4B jet velocity (calc. 1) V = 138.2 ft./sec. jet diameter d = 0.032 in. (x 1/12 ft./in.) liquid specific volume at V2 = 0.01715 ft.3/lb. liquid temperature (2680F.) liquid viscosity at liquid ~ = 0.21 cp. (x 0.000672 temperature (21) cp. R 1538.2 x 0.032 12 x 0.0175 x 0.21 x 0~000671 R = 152,000 4. Calculation of Bubble-Growth-Rate Constant. C C2 - (4) For Run No. 4B, or water at 2680F. under 1 atmosphere superheat T = 56~F. average liquid heat capacity (2120F.-268~F.) C2 = 1.014 b.t.u./lb.-OF. latent heat of vaporization at 2120F. L = 970.3 b.t.u./lb. note that: X TC2 h2i - h2f (5) L hlf- h2f

- 124liquid enthalpy at initial h2i = 236.80 b.to.u/lb. temperature (2680F,) liquid enthalpy at final h2f = 180.07 b.t.u./lb. temperature (2120F ) vapor enthalpy at final hlf = 1150.4 b.to.u/lb. temperature (2120F.) 236.80 - 180o07 X - = 0.0585 wt, fraction flashing 115o.40 - 180.07 liquid density at 2680~Fo P2 58.3 lb./ft.3 vapor density at 2120F. p1 = 0.0373 lb./ft,3 liquid conductivity(212-268~F) k = 0,394 bot,u,/hro-fto.-Fo 1 C = (O.o58)( 58~3 )(3.o14 x 0.394 )2 0.0373 58.3 x 1.014 C = 1352 fto/hr.2 Calculation of Bubble-Growth-Rate Constant for Dissolved Gas. C' Qi Cf\ (,TDm)2 (6) For hexane saturated with methane at 300 psig when pressure is reduced to 1 atmosphere at 860F. initial gas concentration Ci = 0.1076 mole fraction from bubble point = 0.224 wt, fraction calculation(l4) final gas concentration Cf = 0.0035 mole fraction from bubble point(14) = 0.0007 wt, fraction density of gas dissolved in p = 21o 33 lb/ft 3 liquid (calcul te from expansion dat a

-125density of gas coming out of p -0o0402 1bo/ft.3 solut;lion (12 molecular diffusivity of gas Dm 0o000395 fto2/hro in liquid(14) c (0o224 - ~0,000~7 )21,335 (3014 x oo000oo395)2 1 0000- OO 040 C = (0.0214) (531) (00353) 1 C' 0,398 fto/hro2 6. Calculation for One Location in S ray,* Run No, 11, 0060-ino diameter type B orifice water jet at 2540F, and 120 psig location No, 2.. 1 2 3 4 5 — 6:........8! 9 0O size size no, of drop drops x % in. cumu- % per geomo; av, range inter- drops velo- velocity each lative unit av.' diam val city (3x4) range I size diamo x (micron) RFt/sec) (%ofs (612) _(62) _ 6x9) 1 10 14 37 518 1,39 1.39 0o14 5 6:. 2 4,1 77 37 2849 7o,61 9,00o.i.86 11, 9 906go. 3 5o9 213 39 8,07 22,20 531,20 5376 16,81 37350 4 8.2 1.78 54 9612 25~69 56,89 3.13 23~7 608.9 5 11,8 123 72 8856 23o67 80o56 2o01 32o04 766,9 6 16.4 52 86 44,72 1195 92.51, 0o73 47o4 56604 7 23~6 17 117 1989 5032 97083 0~23 67~2 357~5 8 35 5 134l 670 1,79 99,62 005 95o1 1.70.2 g9 147 1 144 144 0o38 100 0o01 134 5009 totals 680 37417 LO0o00 total 2991.8 ____Dl 29o9 * Column 7 is experrimental cumulative dist.ribu.tionr, FD)) for tis l ocatiorn., Column 8 is experimen.tal. prolbatblity dist,ri:;,,ton f(D)9 for tfis location0

-1267. Calculation for the Whole Spray. RUN NO. 11. 0.060-INCH DIAMETER TYPE B ORIFICE WATER JET AT 254~F. AND 120 PSIG loca- sample no. drops x velocity x volume ration f r each size range tion annulus t volume 1 2 3 4 5 6 7 8 9 10 totals ratio 1 1 43 1290 4773 6912 7221 2675 1179 556 288 145 25082 2 8 4144 22792 664561 76896 70848 35776 15912 5360 1152 299336 3 16 6912 30240 745921 58368 61056 35904 14144 9296 1600 1760 293872 4 24 2040 13464 45696 66096 107712 77952 28224 10416 5040 1920 358560 5 32 2560 11264 13312 24192 52800 32480 13568 2240 152416 totals 13139 70346 2027811221584 271029 205107 91939 39169 8080 6065 1129266 1 percent 1.16 6.23 17.96. 19.62 24.00 18.16 8.14 3.47 0.72 o.54 100o.o00 2 cumulative percent, F(D) 1.16 7.39 25.355 44.97 8.97 87.13 95.27 98.74 99.46 100 3 size range (microns) 10 4.1 9 8.2 11.8 16.4 23. 33.0 47.0 66.0 4 percent per size range, f(D) 0.12 1,52 3.04 2.39 2.03 1.11 0.34 o.11 0.02 0.01 5 geom. av. diameter 5 11.9: 16.8 3 23.7 32.4 47.4 67.2 95.1 134 190 6 geom. av. diameter2 25 142 282 562 1050 2247 4516 9044 17956 36100 7 geom. av. diameter3 125 1690 4738 13319 34020 106508 50347536oo84 240610o6859000 8 percent x Dav 9| 6 74 302 465 778 861 547 330 96 103 3561 9 percent x D2v 29 885 5065 11026 252a0-4o8o6 760 31585 12928 19494 183576 10 percent x Dav 145 10528 85094 261319 816480 934185 2407286 987115q732393 5703860 14001408 NOTES: Row 2 is experimental cumulative distribution, F(D), for the whole spray. Row 4 is experimental probability distribution f(D), for the whole spray. The sum of row 8 is Dav AN. so that: D -= ( avoNu 10, N D1 3561 = 35.6 microns. 1 100 The sum of row 9 is Z D2 AN, so that: av - ='(,D oN) 1/2 20 ( 1/N 4 n _ q:83,576> 1/2 _= 42. microns. 720 io

-127The sum of row 10 is 7 D3 A N, so that: av 30.. ~aN J D = 014,008o408) /3 = 520O microns. 30 \ 100 Also,;D3- 2 D370 m 20 - D32 i' 8 = 76.3 microns. 11\1835-76

APPENDIX D LITERATURE CITATIONS 1. Bankoff, S. G. and Mikesell, R. D. Growth of Bubbles in a Liquid of Initially Nonuniform Temperature, Paper No. 58-A-1052 Annual Meeting ASME, New York, N.Y., Nov. 30-Dec. 5, 1958. 2. Baron, T. Atomization of Liquid Jets and Droplets, University of Illinois Technical Report No. 4, Feb. 15, 1949. 3. Carslaw, H. S. and Jaeger, J. Co Conduction of Heat in Solids, London, England: Oxford University Press, 1947, 219. 4. Castleman, R. A., Jr. The Mechanism of Atomization Accompanyin_ Solid Injection, NACA Report No. 440, 1932. 50 Castleman, R. A.o Jr. "The Mechanism of the Atomization of Liquids)" Buro Std. Jour. of Research, 6, No. 3, (1931), 369. 6. Deragabedian, P. Paper No. 53-SA-10, Heat Transfer and Fluid Mechanics Institute, Los Angeles, Calif., June, 1953. 7. Forster, Ho K. and Zuber, N. "The Growth of a Vapor Bubble in a Superheated Liquid," Journal of Applied Physics;, 25, No, 4, (1954) 474-478. 8. Frossling, N. "Uber die Verdunstung fallender Tropfen," Gerlands Beitre Geophys o 52, (1938), 170. 9. Hanlein, A. "Uber den Zerfall eines Flussigkeitsstrahles," ForschunE auf Gebeite des Ingenieurewesens, 2, No. 4, (1931), 139Q 10. Hanson, A. R. The Effect of Relative Velocity on the Yvaporation of i Liquid Fuel Spray, Ph. D. Thesis, University of Michigan, 1951. 11. Hinze, J. 0. AIChE Journal, 1, (1959)3 189. 12. Hodgman, C. D., Weast, R. C. and Wallace, C. W. (ed.). Handbook of Chemistry and Physics, 35th Edition, Cleveland, Ohi.o Chemical Rubber Publishing Company, 1953. 13. Holroyd, H. B. "On the Atomization of Liquid Jets," J. Franklin Inst., 215, (1933), 93. -128

-12914. Katz, D, L. et al, Handbook of Natural Gas Engineering, New York: McGraw-Hill Book Company, Inc,, (1959), Chapter 4, 15, Lamb, Go Hydrodynamics, New Yorko Dover Publications, 1945, p. 131L 16. Lane, W, Ro "Shatter of Drops in. Streams of Air," Ind. Eng, Chem.9 4L3 (1951), 1312o 170 Lee, D, W. and Spencer, R, C, Photomicrographic Studies of Fuel Sprays, NACA Report No. 454, 19330 18. Littaye, Go "Influence de la Vitesse de l'Air sur le Diametre des Petites Gouttes Obtenues par Atomisation," Comptes Rendus, 218, (1944), 4400 19. Miesse, Co C. "Correlation of Experimental Data on the Disintegration of Liquid Jets" Ind. Eng. Chem.,, 4_, (1955), 16900 20. Mugele, Ro A. and Evans, H. D. Ind. Eng. Chem., 43, (1951-), 1317o 21o Perry, J. H, (ed.), Chemical Engineer's Handbook, 3rd Edition, New York: McGraw-Hill Book Company, Inc., 1950. 22, Plesset, M. S. and Zwick, So A. "A Nonsteady Heat; Dif fusion Problem with Spherical Symmetry," J, Appl. Phys., 232 No, 1, (1954), 95-98. 235 Plesset, M. S. and Zw.ick, SO A. "The Growth of Vapor Bubbles in SuperHeated Liquids," J. ApPl. Phys., 25. No. 4: (1954)? 492-500, 24~ Putnam, A. A. et al. Injection and Combustion of Liauid Fuels, WADC Technical Report 56-344, March, 19570 25, Ranz, W, E. On. Sprays and Spraying, Dept. of Engineering Research Bu,l1etin No. 65, The Pennsylvania State Uni.versity, 1956. 26. Rayleigh, Lord. Proc. Lond. Math. Soc., 34. (1892), 153. 27. Rayleigh, Lord. "On the Instability of Jet," Proc. Lond. Math, Soc. 1-0 (1A878)9 4O 28, Tyler, E. "Instability of Liquid Jets," Phil. Mag. (London), 16, (1933)Y 501. 29. Walker, W. H., Lewis, W. K., McAdams, W. H. and Gilliland, E, R. Princi.ples of Chemical Elngineering,, 3rd Ed:ition., New York' McGrawHill Book Compan.y, Inc,, 19379 296-300.

- 13030. Weber, C. "Zum Zerfall eines Fluessigkeitsstrahles," Zeit. fur _ewandte Mathematic, 11, (1933.), 106o 31. York, J. L. Photographic Analysis of Sprays, Ph, D. Thesis, University of Michigan, 1949. 32. York, J. L. and Stubbs, H. E. "Photographic Analysis of Sprays," Trans. ASME, 74, (1952-), 1157. Illll llll I Slll HERSIjY OF MICHIlllGAN 3 9015 02526 1366