study of a high-velocity liquid jet stressed by an...

PHYSICS OF FLUIDS VOLUME 10, NUMBER 11 NOVEMBER 1998

Study of a high-velocity liquid jet stressed by an electric fieldG. ArtanaCONICET–Departamento de Ingenierıá Mecanica, Facultad de Ingenierıá, Universidad de Buenos Aires,Paseo Coloń 850, (1063) Buenos Aires, Argentina

H. Romat and G. TouchardLaboratoire d’Etudes Ae´rodynamiques, U.R.A. C.N.R.S. 191, Universite´ de Poitiers,40 Av. du Recteur Pineau, (86022) Poitiers, France

~Received 26 November 1997; accepted 23 July 1998!

In this work we report an experimental study dealing with the modifications of the breakupphenomena of a high-velocity jet when stressed by an electric field. We considered an arrangementconsisting of a cylindrical electrode coaxial with the jet imposing an electric field at the jet exit.With this arrangement we analyzed the behavior of the electrified and nonelectrified jet. We testeda water liquid jet and measured the droplet size and velocity ratio of the droplets of the spray atdifferent positions by means of a Phase Doppler Particle Analyzer. Our results indicate that theelectric field increases monotonically the ratio of the components of the velocity in the radial andaxial direction and promotes an earlier detachment of droplets from the jet. No significant changein droplet size could be detected. With the aid of a previously reported linear stability analysis wehave analyzed the experimental data. This theory reveals itself as a good first approach to comparesome aspects of the breakup phenomena of electrified and nonelectrified jets of conducting liquidsflowing at high velocities. ©1998 American Institute of Physics.@S1070-6631~98!01511-6#

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I. INTRODUCTION

It is well known that electric forces acting on a liquid jmay change drastically the flow characteristics. Perhapsof the first works reported dealing with the coupling ofelectric field and fluid motion dates from 1600.1 Neverthe-less, this old subject is still ‘‘alive’’ and has recently received special interest, as active fluid mechanics has beca priority subject in the scientific policies of different coutries. Previous research has demonstrated that by meanselectric field we can change the stability of the flow,2–8 ex-cite the jet at a given frequency,9–14 and produce electricallycharged droplets.15 These droplets have special charactetics ~mutual repulsion, easy deflection, subdivision atRayleigh limit16,17!, and it is not surprising that many deveopments based on these principles have appeared~ink jetprinting, electrostatic painting, electrostatic pesticide spring, etc.!.

In this work we have mainly concentrated our effortsgaining some insight into the effects of an electric fieldthe instabilities that promote the breakup of the jet in drolets.

Usually the most important electric forces actingelectrified jets are Coulombian forces, and different arranments can be used to obtain an excess of free charge injet.18 The arrangement we consider here is the inductcharging system, in which an electrode is at a few kV andnozzle is grounded. This produces an electrified jet wcharges on the jet surface opposite in sign to the ones preat the electrode. With this device the high voltage sousustains a very low current~,0.1 mA! associated only to theelectrical leakage through the electrode insulators.

Though electrified jets have been widely studied, m

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of the previous research has been concerned with thevelocity jets corresponding to the Rayleigh regime. Soresearchers have studied electrified jets of dielectric liquflowing at relatively moderate jet velocities, usually incorprating charge to the liquid with an ion injection system.survey of this research work can be found in recepublications.19–20

In this article we consider high-velocity circular jets ofconducting liquid. The breakup process of jets flowing in thregime without any significant free electric charge~nonelec-trified jet! have the following characteristics: the mean drolet diameter is less than the diameter of the nozzle orifice;droplets have a velocity of ejection from the jet with a radcomponent that leads to the dispersion of the liquid inconical spray; and the intact length of the jet is quite smcompared with the breakup length.

Following the classification criteria given by Reitz anBracco,21 we analyze the effect of an electric field in thsecond wind regime and in the first stages of the atomizaregime.

These high-velocity jets find applications in industriprocesses or machines, which require us to disperse liqudroplet form with a high surface/volume ratio in a short tim~e.g., liquid combustion, chemical reactors, diesel engin!.In these regimes the electrification of the jet is of specinterest as~i! the electric field may be used as an external ‘‘exciter’’modify the characteristics of the jet breakup, giving a mesure of control of this phenomenon;~ii ! an additional valida-tion of the different and controversial models of the breakphenomena may be obtained by suitably adding to themeffects of the ‘‘perturbing’’ electrical forces.

2 © 1998 American Institute of Physics

license or copyright; see http://pof.aip.org/pof/copyright.jsp

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2923Phys. Fluids, Vol. 10, No. 11, November 1998 Artana, Romat, and Touchard

Our objective in this article is to present an experimenstudy that shows the changes that appear in the dropletduction phenomena of a high-velocity circular jet when itstressed by an electric field. The results are analyzed withaid of a previously reported stability analysis that includthe electrical forces.22–25

The article is organized as follows: first, in point II, wdescribe the experimental device used in our experimethen, in point III, we show the experimental results we haobtained; point IV is a discussion of these results, andpoint V we draw some conclusions of this work.

II. EXPERIMENTAL APPARATUS

In this paragraph we describe the experimental devwe have built to study high-velocity liquid jets submittedan external electric field. This device is composed of fosystems: injection system, electrification system, aerosoception system, and diameter and velocity measurementtem.

A. Injection system

The main elements of this system are shown schemcally in Fig. 1. An adjustable pump~1! supplied water (r'1800V m, sampled at the nozzle exit! through the injec-tion system. The maximum flow rate was 21.1 cm3/s, at pres-sures between 0 and 13.8 Mpa. The flow rate couldchanged either by increasing the stroke of the piston orangular velocity of the pump~0–1500 rpm!. A hydropneu-matic accumulator with a nitrile membrane~3! was used todampen pressure fluctuations in the circuit. The liquid ising from the nozzle orifice~6! formed the jet. The nozzlethat were used are shown in Figs. 2~a! and 2~b!, and aresimilar to those used in other studies.26–29 They were madein stainless steel and the orifices~type 1: 220mm, type 2:295 mm! shaped by electroerosion. The ratio L/D was 4all nozzles@Fig. 2~c!#. Figure 3 shows the orifice of nozzltype 2 at the exit plane.

FIG. 1. Injection system: 1—adjustable pump; 2—liquid vessel; 3hydropneumatic accumulator; 4—manometer; 5—reception cylinder;nozzle; 7—valve; 8—receiver tank.


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B. Electrification system

In Fig. 4 we show the electrification system. The nozis earthed and a high-voltage source~0–3 kV, 100 mA! canbe connected by switch I2 to the electrode that electrifiesjet. This position of the switch corresponds to the caseelectrified jet, and the other position grounds the electroand corresponds to the case of the nonelectrified jet.

Switch I1 introduces in the circuit an ammeter thatnormal operation should read a very low leakage curr~,0.1 mA!. An important current reveals an insulation faure, such as a water bridge existing between the electrand the injector, situation to be avoided in the normal funtioning of the system. Measurements are taken only if this a negligible current in this branch, and when this is vefied I1 is switched to the other position.

Figure 5 is a detail of the electrode arrangement at

FIG. 2. ~a! Injector type 2. Jet velocity 60 m/s. Nonelectrified jet.~b! Injec-tor type 2. Jet velocity 60 m/s. Electrified jet (V52000 V). ~c! Scheme ofthe nozzle. Size in nm.L/D54.


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2924 Phys. Fluids, Vol. 10, No. 11, November 1998 Artana, Romat, and Touchard

nozzle. The electroded is a 3 mmthick annulus made ostainless steel. It is fixed in a Teflon bodyb, which electri-cally insulates it from the injector. Six orificesc with adiameter of 5 mm have been perforated in the Teflon bcommunicating the inner cylinder of this body with the eterior. A nylon screw fixes the electrode–Teflon systemthe nozzle; adjusting this screw at different positions wechange the distance from the tip of the nozzle to the etrode.

C. Aerosol reception system

This system is composed of a tank and a stainless scylinder that allows measurement of the current convecby the aerosol.

The Plexiglas tank~10 mm thick!, with dimensions 500350031000 mm, houses the current measurement systemlateral circular hole of 250 mm of diameter communicathe interior of this tank to the room.

The current measurement system is composed of anternal stainless steel cylinder~diameter: 250 mm, height: 40mm! located by means of six nylon screws coaxial withouter stainless steel cylinder. The inner cylinder is therefelectrically insulated from the external one, which acts aFaraday cage. A wire mesh~mesh opening 100mm! is fixedto the top and the bottom of the inner cylinder. The uppmesh has an orifice of 75 mm through which the spray enthe cylinder. The electrically charged droplets, when containg the wall or the meshes, discharge through a Keith610C electrometer to earth. The value of this current issame as that flowing in the conductor that grounds the intor, but of opposite sign. The constancy of this current durone test shows no electric insulation fault of the electrod

D. Diameter and velocity measurement system

These measurements were done using a Phase DoParticle Analyzer customized by Aerometrics, Inc. The stem used allows measurement of particles in the range0.5m–10 000mm, and velocities from 0 to 100 m/s.

The laser beam was emitted by an argon–ion sourceW. The Aerometrics Fiber Drive model FBD 1240 peformed frequency shifting, beamsplitting, and color sepation. The transmitter lens system produced two blue la

FIG. 3. Enlarged view of the orifice of the nozzle.


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beams~wavelength54883 Å! in the horizontal plane and twogreen ones~wavelength55145 Å! in the vertical plane. Thesystem also included a Bragg Cell to prevent ambiguitiesthe determination of the sense of the velocity vector.

The formation of the probe volume for particle size avelocity measurements was achieved by the probe h~Aerometrics Fiber Optic Transmitter, model XMT 120transmitter lens focal length 500 mm!. The light scattered bythe particles was collected by the Aerometrics Fiber OpReceiver, Model RCV 2204~receiver lens focal length 500mm!. The Phase Doppler light signal was converted intoelectronic signal with the Aerometrics Receiver Module. Tfrequency and phase of the laser Doppler bursts were demined with the signal processor DSA 3000 series DoppThe control of this signal processor, the data acquisitanalysis, and the presentation of results were performedthe DSA software installed in a PC. An oscilloscope enabthe monitoring of the signal quality.

As only the droplets traversing the probe volume aanalyzed, it was necessary to have a device to moveprobe volume; to this end a displacement system was cstructed@~Fig. 6!# which enabled the movement of the opticA balanced structure in aluminium supported the optics ait was mounted in the center of a horizontal plate, whicould move in three dimensions by means of micromescrews. The optics also could have vertical and rotatiomovement in this structure. The axis of the transmitter leand the reception lens were aligned to form an angle ofmeasured in a horizontal plane. The displacement sys

FIG. 4. Electrification system.

FIG. 5. Details of the electrode arrangement at the nozzle~dimensions inmm!: a Stainless steel body nozzle,b Teflon electrode holder,c pass-through holes,d electrode,e connector.


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also enabled to align vertically the nozzle by intersectinnonelectrified jet flowing in the Rayleigh regime with a lasbeam at different heights.

III. EXPERIMENTAL STUDY

A. Experimental procedure

Previous research work in electrified jets18,30 shows thatat different flow rates different phenomena may be observAt low or moderate jet velocities a multibranch kink instbility has been reported where the jet adopts an arboresform with lateral ejection of droplets. When operating osystem at the low flow rates corresponding to those ofRayleigh regime, we could observe this multibranch instaity with the electrified jet. However, this instability disappeared with increasing flow rates, and this could occurflow rates still corresponding to the Rayleigh regime or atfirst stages of the first wind regime. At these flow rateslateral ejection of droplets was observed either in the elecfied and nonelectrified conditions. As an example, for injtors with an orifice of 220mm, and imposing to the electroda potential of 2 kV, we observed the multibranch instabilwith flow rates below approximately 0.21 cm3/s, and the in-stability disappeared for higher flow rates. As the flow rawas increased the second wind regime appeared and drowere ejected with a lateral velocity in the both nonelectrifiand electrified jet cases. Our experiments have been untaken with jets flowing in this regime and in the first stagof the atomization regime that appears at larger flow rate

As stated in Clopeau’s work,30 multibranch kink insta-bility corresponds to large volume flow rates when compawith other instabilities like type A~very heavily charged jet!or like type B~lateral kink instability!. When a comparison ismade with the second wind regime, multibranch instabilitcorrespond to very low flow rates. The jet velocities thathave considered in our work are more than ten times higthan those where we have observed the multibranch instity, and the liquid flow rates are about 100 times larger.

As the kink instabilities correspond to a very high liqusurface charge to volume ratio, the limit of the multibraninstability depends on the electrification system consideFor dielectric liquids and using an injection system that iproves the electrification of the jet, the multibranch kink i

FIG. 6. Optics and displacement system.


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stability could be observed at larger jet velocities,20 but stillthese velocities remain quite far from those of our intere

We started our experiments by operating the pumpobtain the desired flow rate and waiting for its stabilizatioBy means of the displacement system, the probe volumeplaced at the measurement location. With the electrgrounded we obtained the data corresponding to the nonetrified case, the data acquisition finishing when 1000 busignals of the scattered light were accepted as good sigby the PDPA system; this was achieved in 15–30 s. Thenapplied different voltages to the electrodes and obtainedresults corresponding to the different electrified cases.probe volume was then displaced to a new measuremensition.

At a given flow rate, the parameters set for the drejection criteria of the PDPA software were maintainedall measurements on a given horizontal plane. Howevthese parameters were changed when necessary to acbetter signal quality between different horizontal planes.very large radial distances some droplets may be attractethe electrode, and to avoid a double counting we disregardroplets having a vertical component of velocity with aupward direction.

After all the test points at a given flow rate were otained, we sampled water from the nozzle exit to verify ththe electric conductivity remained within bounds~6150V m!.

B. Experimental considerations

The goal of our study is to analyze the changes in drlet production when we stress the jet with an electric fieTo achieve this goal we should measure the size and veloof the droplets immediately after ejection from the jet. Hoever, because of the high density of the spray, the PDcannot distinguish individual burst signals when measurquite close to the jet axis; hence, measurements mustaken at a distance where this phenomenon is not so imtant. As a result, the droplets have a certain flight time befwe can measure their characteristics, and in their trajectorthe test point some phenomena modify the ‘‘real’’ diameand the ‘‘real’’ velocity of ejection of the droplet.

Regarding droplet size, we can mention the phenomof evaporation, coalescence, and droplet breakup after etion. The first phenomenon is more important for the smadroplets, coalescence is important for very dense sprays,droplet breakup for high-velocity droplets. Considering tdifferent research analyzing these phenomena,31–39 the mea-sured droplet size distribution will be closer to the ejectidroplet distribution for low Weber numbers. The Webnumber We is a ratio between inertial forces and surftension forces, being proportional to the square of thevelocity U0 , to the liquid densityr1 , and to the jet radiusa,and inversely proportional to the surface tensiong,

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As for droplet velocities, the forces that are of intere


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are viscous forces and Coulombian forces. The gravitatiofield has no significant effect given our liquid jet velocitie~.60 m/s!.

In a quiescent fluid viscous forces depend on differparameters~droplet diameter, velocity, viscosity, etc.!,18,31

but we can expect that they do not modify the ratio betweradial and vertical components of the droplet velocity, sinthese forces act in the direction of the velocity vector. Tratio of velocity components is of great importance as it cbe associated to the spray cone angle produced by droejection. For these reasons it is easier and preferable to sthe influence of the electric field on this ratio than on tindividual velocity components.

In this analysis it should be highlighted that the electforces acting on the droplet trajectory may modify this ratIn our system electric forces are caused by mutual repulor electrode attraction. Mutual repulsion will be of interesthighly charged and extremely dense sprays,40 and should benegligible in our tests. As for the electrode attraction forwe can disregard its influence in our experiments considethe following: the change in momentumDmn due to theelectric forcesFel acting during the intervalDt,

Dmn5FelDt,

shows that droplets of a typical diameter~'20 mm! chargedat one-tenth of the droplet Rayleigh limit18 ~a charge 10 000times larger than that corresponding to the measured mspecific charge of approximately 0.05 C/m3! and subjected toa uniform electric field of 0.1 MV/m are accelerated inDt51 ms to about 1.5 m/s. At small distances from the injecand the axis of the jet, flight time is small and droplet vlocities are very large, thus only slight changes should ocin the droplet trajectory or in velocity ratios and we cneglect the effect of electric forces. At larger distances~say,20 mm from the jet axis! the droplets have lower velocitieand the flight time may be large. At these distances the efof the electric forces and others like viscous drag forces mbe important and the experimental results should be analycarefully.

As a conclusion to these considerations, for the measment of droplet size and velocity ratio, it is advisableconsider not too high Weber numbers, and to measureclose as possible to the jet axis and the nozzle exit.

It should be remarked that when we use a PDPA syswe obtain a temporal distribution of diameter and velocitythe droplets passing through the volume probe. If the sprahomogeneous in space this measurement gives all the inmation required. However, in general, sprays are not hogeneous, and the changes caused by an electric field odroplet production phenomena will only be fully describedwe consider a stationary state and different test pointsspace. Then, after a suitable processing of data we can oa ‘‘global’’ information instead of the ‘‘local’’ one.

Taking this into account, we have done our tests at thdifferent level horizontal planes~z513.5, 23.5, and 33.5mm! at radial distances from 1.4 to 11.5 mm, and withvelocities in the range of 60–80 m/s.

We should also mention that in our case the PDPA msurements need no correction due to the Kerr effect. Foll


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ing Zahn’s work,41 the change of the refraction indexDr andthe change of phaseDa due to the electric field is

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Considering an electric fieldE of 106 V/m, a wavelength ofthe laser oflL55000 Å, a Kerr constant for water38 B53.49310214 m/V, and an optical length 1 of 1024 m, thisphenomena has only a small influence (Da'231025), andso results issued from the electrified case and nonelectrcase can be directly compared.

C. Droplet size measurements

We present in this paragraph the droplet size data wthe following considerations: with the PDPA we obtained tdifferent ‘‘local’’ histograms at each test pointj representingthe number of dropletsDni , j corresponding to a size intervaDf i ; after that we normalized our data with the time takby the measurement (tm, j ) and the cross section of the probvolume Sp ~for all testsSp50.114 mm2!. As a result, weobtained a flux density histogram,

Dni , j5Dni , j

tm, jSp, ~1!

which represents the number of droplets of theDf i dropletsize interval passing through the probe volume located atposition j in the unit of time and area. For differentj posi-tions in the same horizontal plane a continuous function rresenting the droplet fluxni , j can be obtained by interpolation in space of these points.

Figures 7~a! and 7~b! show a typical result ofni , j as afunction of the radial position for the nonelectrified case aan electrified case at 2000 V. In these figures we show resfor different droplet size intervals (Df i55 mm), identifiedby the mean value of the intervalf i .

The radial distribution ofni , j can be modified with anelectric field. The electric field promotes the opening of tangle of the spray as we find more droplets at larger radistances. This can be easily visualized in the experimentthe scattering of the laser beam by the droplets. Whenelectric field is applied, an increase of the length of the sment where the scattering occurs can be clearly obserindicating a larger area occupied by the spray@see Figs.2~a!–2~b!#.

The integral of the functionni , j , in the region of thehorizontal planeSm where we have undertaken the measuments gives the number of droplets of the intervalDf i pass-ing throughSm ,

Ni5ESm

ni , jdS. ~2!

These values, when represented as a function ofdroplet size interval, enable us to construct the ‘‘globahistogram of one plane. Obviously these histograms exclthe region quite close to the axis because of the difficultiemake measurements there.


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Figure 8 shows a typical example of the influence ofelectric field on the global histograms. From this figurecan see that, for each size interval, the electric field increathe number of droplets passing throughSm in the unit oftime. These and similar results, when plotted inprobability-logarithmic scale, show an alignment of the dthat indicates that the different distributions can be expresby a lognormal function.

Table I shows, for one injector and different electrovoltages, the geometric mean diameter and geometric detion, at different jet velocities and horizontal levels; similresults were obtained for the other types of injectors.observe that slight changes in the mean geometric diam

FIG. 7. ~a! Radial distribution of droplets fluxni , j for different dropletintervals ~interval size 5mm!. The label indicates the mean values of tintervals in mm. Injector type 2. HereU0573 m/s (Pi56.7 Mpa); z533.5 mm;V50 V. ~b! Radial distribution of droplets fluxni , j for differentdroplet intervals~interval size 5mm!. The label indicates the mean valuesthe intervals inmm. Injector type 2. HereU0573 m/s (Pi56.7 MPa); z533.5 mm;V52000 V.

FIG. 8. Global histogram of droplet diameters for different electrode vages. Injector type 1. HereU0580 m/s (Pi56.5 Mpa); z533.5 mm.


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are detected at the different horizontal planes as a resuthe application of an electric field, and, in general, in tlower planes the mean geometric diameter increases. Nonificant change is observed on the geometric deviation.

Considering the values ofDni , j we can obtain the vol-ume flux density as

D v j5(i

pDni , j f i3

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with f i the mean value of the droplet size in the intervDf i . Again, by interpolation in space we may obtain a cotinuous functionv. A typical result ofv as a function of theradial distance is shown in Fig. 9. We can see from tfigure that the electric field changes the radial distributionthe volume flow rate: a larger volume of liquid in droplform passes through regions at a larger distance from theaxis.

The integral of the functionv in Smgives the total liquidflow rate passing through the measurement zone in the fof droplets,

- FIG. 9. Radial distribution of liquid volume flux. Injector type 2. HereU0

573 m/s (Pi56.7 MPa);z533.5 mm.

TABLE I. Global geometric mean diameterfg , global geometric deviationsg , volume flowrate in droplet formV passing through the measuremezone, for different jet velocitiesU0 , horizontal planesz from the jet exit andelectrode voltageV. Injector type 2.

U0 ~m/s! z ~mm! V ~Volt! fg ~mm! sg ~mm!V

~10-9 m3/s!

60 13.5 0 10.78 1.42 3760 13.5 2000 10.21 1.38 4660 23.5 0 10.90 1.37 7860 23.5 2000 10.72 1.36 8360 33.5 0 11.58 1.40 14460 33.5 2000 12.00 1.38 16866 13.5 0 10.63 1.47 6766 13.5 2000 10.52 1.49 7766 23.5 0 11.36 1.49 28266 23.5 2000 11.98 1.46 62266 33.5 0 14.06 1.52 137366 33.5 2000 14.11 1.47 175473 13.5 0 18.30 1.44 47073 13.5 2000 20.34 1.42 83673 23.5 0 18.28 1.51 182873 23.5 2000 20.36 1.49 271673 33.5 0 19.37 1.57 355673 33.5 2000 20.61 1.50 3779


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The last column of Table I shows the liquid volume florate in droplet form at different experimental conditions. Wobserve that in the experiments at the same jet velocityU0

and in the same horizontal plane, the electric field increathe liquid volume flow rateV passing through the measurment zone.

D. Velocity ratio measurements

These measurements were done by the PDPA simuneously with the droplet size measurement. Figures 10~a!–10~b! show a typical result of velocity ratio distributions atgiven position for the electrified and nonelectrified case.we can see from these figures, the velocity ratio distributiare in fairly good agreement with a Gaussian distribution~adotted line in the figures!. So we can summarize our dausing the mean value and the standard deviation and ecompare the electrified and nonelectrified cases.

When representing the correlation of the ratio of veloties and droplet diameter of the nonelectrified and ofelectrified cases~not shown in this paper!, we observe that inboth cases the dispersion from the mean value of the Gaian distribution is more important for the smaller droplewhile being quite symmetric around the mean value fordroplet sizes.

In both electrified and nonelectrified cases there exissmall number of droplets having a negative velocity ratWe think that drag forces or droplet breakup after the ejtion possibly explain this.

Our experiments indicate that the velocity ratio is nconstant with radial distance. Figure 11 shows the radialtribution of the mean value at different electric field intenties. This figure shows that the velocity ratio for the elecfied and nonelectrified cases show a similar dependenceradial distance, and that the changes in the velocity ratiomonotonic with the electric field at all distances, even whquite close to the jet axis.

Column 4 of Table II summarizes for different jet velocities and types of injectors the relative variation of tmean value of the velocity ratio for the electrified and noelectrified cases~associated with a subindex 0! that we haveobserved in our experiments~subindex exp!,

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The results shown have been obtained at 1.5 mm frthe jet axis and at a horizontal plane at 33.5 mm from theexit; similar results were obtained at different horizontal leels. From this table we observe that for different velocitand injectors the velocity ratio is increased by the elecfield, this effect being more important at larger electric fieand, for a given injector, at lower jet velocities.


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IV. ANALYSIS OF RESULTS

As a synthesis of our experimental results we canthat the effects of the electric field on the spray are thelowing: A slight increase of the droplet geometric meanameter at the lower horizontal planes; an increase ofmean velocity ratio of the droplets at all test points; the

FIG. 10. ~a! Histogram of Vr /Vv. Injector type 2. HereU0573 m/s(Pi56.7 Mpa). Herez533.5 mm;V50 V. Radial distance51.80 mm. ~b!Histogram ofVr /Vv. Injector type 2. HereU0573 m/s (Pi56.7 Mpa); z533.5 mm;V52000 V. Radial distance51.80 mm.


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gion traversed by the droplets is larger; and the dropletsvolume flux increase in the measurement zone.

We will analyze these results by means of a previoureported linear stability analysis,22–25 which examined thestability of a liquid jet flowing in a gaseous atmosphereside a coaxial cylindrical electrode at constant potential. Teffects of gravity, magnetic fields, viscosity, and mass trafer at the interface were neglected. The liquid jet andgaseous atmosphere were considered isothermal and inpressible and their electrical properties were those ofOhmic conductor with uniform conductivity and a dielectrconstant. The electric charge on the jet was at the jet surand no free charge source in the bulk of the liquid or ofgas phase existed. Accepting these hypotheses, a dispeequationD(v,n,k)50 was obtained, which establishes trelationship of complex frequenciesv, wave numbersk andthe mode numbern. The parameters of the problem thenter in the dispersion equation are the density ratior d

5r2 /r1 , the Euler numberEu5g/r1U02a51/We, and the

electrical Euler number Eue5e0En2/r1U0

2. Hereg is the sur-face tension,a is the jet radius,r1 andr2 are the jet and gasdensities,e0 is the vacuum dielectric constant, andEn is thenormal electric field in the nonperturbed situation. For o

FIG. 11. Radial distribution of the mean values ofVr /Vv at different elec-trode voltages. Injector type 1. HereU0580 m/s;z533.5 mm.

TABLE II. Experimental and theoretical values@formula ~9!# of the relativevariation of the spray angleV obtained when electrifying the jet. Results fodifferent nozzle diametersf inj at different electrode voltagesV, and jetvelocitiesU0 , horizontal planesz from the jet exit at 33.5 mm, and radiadistance 1.5 mm.

f inj. ~mm! U0 ~m/s! Volts100S D tanV

tanV0Dexp.

100S D tanV

tanV0Dth.

220 80 1000 12.1 1.8220 80 1500 19.7 4.7220 80 2000 27.2 8.1220 80 2500 66.7 12.4295 60 2000 152.3 9.2295 66 2000 99.5 7.6295 73 2000 22.2 6.2


nd

y

-e

s-em-n

ceeion

r

different experimental conditions, these nondimensionumbers are listed in Table III.

As a summary of the results obtained from the dispsion equation when performing a temporal analysis22–24 wecan say that for high-velocity jets an electric field acting onjet with its surface at constant electrical potential destabilithe jet. It increases the growth rate of the perturbation aincreases the wave number corresponding to the maximgrowth rate of the perturbation.

This analysis corresponds with the so-called theoryaerodynamic interaction28 supplemented here with the effeof electric forces. In nonelectrified jets flowing in the secowind regime, this theory is accepted as a very good tooexplain the jet breakup phenomena.28 In the atomization re-gime, the application of this theory is somewhcontroversial,42 several authors have pointed out that diffeent phenomena were not taken into account~liketurbulence,43 cavitation inside the nozzle,44,45velocity profilerelaxation on emergence from the nozzle,46 liquid supplypressure oscillation47!, and others suggested that a spattheory was more appropriate to describe the evolution ofperturbation.48,49 As we see, the atomization regime may ivolve very complex phenomena; however, the tempotheory has revealed itself to be a useful tool to obtain a fiapproach to the breakup process in many cases,29–50,51so wewill use it to analyze the changes that appear when we etrify a high-velocity jet.

Some researchers,50,51 considering that the jet is excitewith a white noise, have proposed that the droplet meanameter of the sprayf is of the order of magnitude of themost unstable wavelength and that can be obtained from

f'Almx52pA

Kmx, ~6!

whereKmx is the wave number of the more unstable pertbation andA an experimental constant. They also propothat the spray angle or the velocity ratio can be obtainfrom

tan V'Bvmx

KmxU05BHmx , ~7!

where vmx is the growth rate corresponding to the mounstable perturbation,U0 the jet velocity, andB an experi-mental constant.

TABLE III. Typical nondimensional numbers for the different experimenr d : density ratio; We: Weber Number, Eue: electric Euler number.

Jetvelocity~m/s!

Electrodepotential~Volts!

Nozzlediameter

~mm! r d We Eue* 106

60 2000 295 0.0012 7355 29.366 2000 295 0.0012 8899 24.273 2000 295 0.0012 10 886 19.880 2000 220 0.0012 9751 36.7


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re

; w

tiene

vt

othntouaol.n

reheeb

apel

ur-ro-ms

um-etnogueby

ta-dear inandeltivede-

earludethe

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etsea-nts

nceles-riesthedi-

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rtseldgndns.

er-theti-.d

th


We will assume that these formulas are still valid felectrified jets and we will also assumeA andB independentof the electric field. We then find the following relativvariations:

Df

f0U

th

5lmx2lmx0

lmx0

5Kmx0

2Kmx

Kmx

, ~8!

D tan~V!

tan~V0!U

th

5Hmx2Hmx0

Hmx0

, ~9!

with the subindex 0 indicating the nonelectrified case asubindex th indicating results obtained from the dispersequation.

Table IV shows the experimental results and the theoical ones@obtained with formula~8!# for droplet diameter. Adisagreement between theory and experiment is evidentthink that a possible explanation of this is that formula~8!only considers that droplets are generated from instabiliwith wavelengths corresponding to the most unstable oHowever, as pointed out by Levich,50 a spectrum of differentinstabilities develops in the flow, with some instabilities haing an important increase of their amplitude quite closethe nozzle, and others attaining a large amplitude mdownstream. As a result of the change of the stability ofjet with the electric field, the growth rate of the differeunstable waves is higher and these last instabilities shdevelop closer to the nozzle exit. So, the theoretical compson of the electrified and nonelectrified cases cannot be ddirectly with formula~8! and requires a more refined mode

Columns 4 and 5 of Table II show the experimental atheoretical results@obtained with formula~9!# concerning thevelocity ratio. Again, the experimental results do not agquantitatively with the theoretical results; however, ttrends obtained through the stability analysis seem corrConsequently, though more experimental efforts shouldundertaken at different situations~i.e., different chamberpressures! this theory enables us to understand in a firstproach the changes to the spray angle produced by thetric field application.

TABLE IV. Experimental and theoretical values@formula ~8!# of the rela-tive variation of the mean droplet diameter obtained when electrifyingjet. Results for different nozzle diametersf inj. at different electrode voltagesV, and jet velocitiesU0 . The horizontal plane from the jet exit atz533.5 mm.

f inj. ~mm! U0 ~m/s! V ~Volts!100S Dfg

fgD

exp.

100S Df1

f10D

th.

220 80 1000 1.3 20,64220 80 1500 4.2 21,89220 80 2000 2.1 23,11220 80 2500 7.9 24,30220 80 3000 5.2 26,59295 60 2000 3.6 23,28295 66 2000 0.4 22,72295 73 2000 6.4 22,23


dn

t-

e

ss.

-oree

ldri-ne

d

e

ct.e

-ec-

An increase in the growth rate of the nonstable pertbations due to the application of an electric field should pmote the earlier detachment of droplets of the jet. This seeto agree with the results concerning the increase in the nber of droplets and liquid volume flux density in droplform at a given level caused by the electric field. Thoughexact theoretical estimation is proposed here, we may arthat at least qualitatively we can explain these resultsusing the linear analysis.

As a result of the comparison of the temporal linear sbility analysis with the experimental results we can concluthat a rough estimation of the changes expected to appethe breakup process of a high-velocity jet stressed withelectric field can be obtained; however, a more refined moof the breakup phenomena is needed to obtain a quantitaagreement. Given that in the Rayleigh regimes a betterscription of the breakup of the jet is obtained when nonlinphenomena are considered, it appears advisable to incthe nonlinear aspects of the phenomena in future work inanalysis of high-velocity jets.

V. CONCLUSIONS

In this work we report the changes produced by an eltric field acting on a high velocity jet of water. By meanssome spray parameters we try to analyze the effect ofelectric field on the phenomena of jet breakup.

The determination of the characteristics of the droplimmediately after ejection is not possible because of msurement system limitations. We have done our experimein the regions where it was possible to do so, and heexperimental results are affected by evaporation, coacence, droplet breakup, and forces acting on the trajectoof the droplets. We tried to reduce these effects by takingmeasurements within experimental conditions that shouldminish their influence.

With these limitations, when the electric field was aplied an increase in the spray angle and of droplets andume flux density was observed in the outer regions. Slichanges in the geometric mean diameter of droplet sizetributions have also been measured.

The results were analyzed using a linear stability anasis combined with some simple formulas for the jet breakThis analysis gives the right trends for the droplet breakphenomena but fails in the prediction of droplet sizes.

Though more refined models and experimental effoare needed, this work makes evident that the electric fidestabilizes the flow of a high-velocity jet of a conductinliquid, modifies the droplet production phenomena, acould be used as a control parameter in some applicatio

ACKNOWLEDGMENTS

In this article we report experiments that were undtaken at the Laboratoire d’Etudes Aerodynamiques ofUniversity of Poitiers. We would like to express our gratude to the technicians of this laboratory: M. A. Vigner, MS. Macia, M. R. Messy, and M. C. Reffin, who kindly helpeus in our research.

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1W. Gilbert, De Magnete (1600), translated by P. Mottelay~Dover, NewYork, 1958!.

2F. Rayleigh, ‘‘On the instabilities of jets,’’ Proc. London Math. Soc.10, 4~1879!. @See also,Scientific Papers~Cambridge University Press, Cambridge, 1899!, Vol. I, pp. 361–371.

3A. Basset, ‘‘Waves and jets in a viscous liquid,’’ Am. J. Math.16, 93~1894!.

4J. Schneider, N. Lindblad, C. Hendricks, and J. Crowley, ‘‘Stability ofelectrified liquid jet,’’ J. Appl. Phys.38, 2599~1967!.

5G. I. Taylor, ‘‘Electrically driven jets,’’ Proc. R. Soc. London, Ser. A313,453 ~1969!.

6A. Huebner and H. Chu, ‘‘Instability and breakup of charged liquid jetsJ. Fluid Mech.49, 361 ~1971!.

7D. Saville, ‘‘Electrohydrodynamic stability: Fluid cylinders in longitudinaelectric fields,’’ Phys. Fluids13, 2987~1970!.

8A. Mestel, ‘‘Electrohydrodynamic stability of a slightly viscous jet,’’ JFluid Mech.274, 93 ~1994!.

9J. Melcher,Field Coupled Surface Waves~MIT Press, Cambridge, 1963!,pp. 123–139.

10J. Crowley, ‘‘Growth and excitation of electrohydrodynamic surfawaves,’’ Phys. Fluids8, 1668~1965!.

11J. Crowley, ‘‘Ink jet electrohydrodynamic excitor,’’ U.S. patent 4 220 951980.

12J. Crowley, ‘‘Electrohydrodynamic droplet generators,’’ J. Electrost.14,121 ~1983!.

13A. Spohn and P. Atten, ‘‘EHD multi-electrode simulation of a conducticapillary jet,’’ IEEE IAS Annual Meeting, 1993, p. 1960.

14B. Barbet, P. Atten, and A. Soucemarianadin, ‘‘Two mode EHD stimution of a conducting liquid,’’ J. Electrost.40&41, 39 ~1997!.

15A. Bailey, ‘‘The theory and practice of electrostatic spraying,’’ Atomiztion Spray Technol.2, 95 ~1986!.

16Lord Rayleigh, ‘‘On the equilibrium of liquid conducting masses chargwith electricity,’’ Philos. Mag.5, 184 ~1882!.

17Lord Rayleigh, ‘‘Mathematical theory of vibrations of drops,’’ inTheTheory of Sound~Macmillian and Co., London, 1926!.

18A. Bailey, Electrostatic Spraying of Liquids~Wiley, New York, 1988!.19J. Miller, O. Biblarz, A. Zajdman, W. Manning, and J. Mavroudis, ‘‘Ele

trostatic spray modification in gas turbine combustion,’’ J. Propul. Po3 ~2!, 187 ~1987!.

20W. Balachandran, D. Hu, A. Yule, J. Shrimpton, and A. Watkins, ‘charge injection nozzle for atomisation of fuel oils in combustion applitions,’’ IEEE IAS Annual Meeting, Denver, 1994, p. 1436.

21R. Reitz and F. Bracco, ‘‘Mechanisms of breakup of round liquid jetsEncyclopedia of Fluid Mechanics, edited by N. Cheremisinoff~Gulf Pub-lishing, Houston, 1986!.

22G. Artana, H. Romat, and G. Touchard, ‘‘Instability of high velocity ccular jets stressed by electric fields,’’ Institute of Physics Conferenceries, No. 143, 1995, p. 177.

23G. Artana, Ph.D. thesis, University of Poitiers, Poitiers, France, 199624G. Artana, H. Romat, and G. Touchard, ‘‘Theoretical analysis of lin

stability of electrified jets flowing at high velocity inside a coaxial eletrode,’’ J. Electrost.43, 83 ~1998!.

25G. Artana, H. Romat, and G. Touchard, ‘‘Absolute and convective inbilities in an electrified jet,’’ J. Electrost.40&41, 33 ~1997!.

26M. Arai, M. Tabata, H. Hiroyasu, and M. Shimizu, ‘‘Disintegrating process and spray characteristics of fuel jet injected by a diesel nozzle,’’ SPaper No. 840275, 1984.


-

r

-

e-

r

-

E

27R. Reitz and F. Bracco, ‘‘Ultra high speed filming of atomizing jetsPhys. Fluids22, 1054~1979!.

28R. Reitz and F. Bracco, ‘‘Mechanisms of atomization of a jet,’’ PhyFluids 25, 1730~1982!.

29K. Wu, R. Reitz, and F. Bracco, ‘‘Measurements of drop size at the spedge near the nozzle in atomizing liquid jets,’’ Phys. Fluids29, 941~1986!.

30M. Clopeau and B. Prunet-Foch, ‘‘Electrostatics spraying of liquidscone-jet mode,’’ J. Electrost.22, 135 ~1989!.

31W. Hinds,Aerosol Technology~Wiley, New York, 1982!.32C. Davies, ‘‘Evaporation of air borne droplets,’’ inFundamentals of Aero-

sol Science, edited by D. T. Shaw~Wiley, New York, 1978!.33N. A. Fuchs,Evaporation and Droplet Growth in Gaseous Media~Perga-

mon, Oxford, 1959!.34G. Faeth, ‘‘Mixing, transport and combustion in sprays,’’ Prog. Ener

Combust. Sci.9, 1 ~1983!.35P. O’Rourke and F. Bracco, ‘‘Modelling of drop interactions in thic

sprays and comparison with experiments,’’ Proc. Inst. Mech. Eng.194,101 ~1980!.

36G. I. Taylor, ‘‘Coalescence of closely spaced drops at different elecpotential,’’ in The Collected Works of G. I. Taylor, edited by G. K. Batch-elor ~Cambridge University Press, Cambridge, 1963!.

37G. I. Taylor, ‘‘The shape and acceleration of a drop in a high-speedstream,’’ in Ref. 36.

38W. Lane and H. Green, ‘‘The mechanics of drops and bubbles,’’ inSur-veys in Mechanics of G. I. Taylor, edited by K. Batchelor and C. Davie~Cambridge University Press, Cambridge, 1956!.

39J. Nicholls, ‘‘Stream and droplet breakup by shock waves,’’ NASA S194, edited by D. T. Harrje and F. Reardon~Nasa Lewis Research CenteWashington, D.C., 1972!.

40K. Haarstad and J. Bellan, ‘‘Electrostatic dispersion of drops in clusterCombust. Sci. Technol.63, 163 ~1989!.

41M. Zahn, ‘‘Space charge effects in dielectric liquids,’’ inThe Liquid Stateand its Electrical Properties, edited by E. Kunhardt, L. Chrsituophourouand H. Luessen~Plenum, New York, 1988!.

42N. Chigier, ‘‘The physics of atomisation,’’ ICLASS-91, GaithersburMD, 1991, pp. 1–15~1991!.

43P. Schweitzer, ‘‘Mechanism of disintegration of liquid jets,’’ J. AppPhys.8, 513 ~1937!.

44W. Bergwerk, ‘‘Flow pattern in diesel nozzle spray holes,’’ Proc. InMech. Eng.173, 655 ~1959!.

45R. Sadek, ‘‘Communication on flow pattern in nozzle spray holes adischarge coefficient of orifices,’’ Proc. Inst. Mech. Eng.173, 671~1959!.

46J. Rupe, Jet Propulsion Laboratory Report No. 32, 1962, p. 207.47E. Giffen and A. Muraszew,The Atomization of Liquid Fuels~Wiley, New

York, 1953!.48S. Lin and D. Kang, ‘‘Atomisation of a liquid jet,’’ Phys. Fluids30, 2000

~1987!.49S. Lin and Z. Lian, ‘‘Mechanisms of the breakup of liquid jets,’’ AIAA J

28, 120 ~1988!.50V. Levich, Physicochemical Hydrodinamics~Prentice–Hall, Englewood

Cliffs, NJ, 1962!, pp. 591–667.51W. Ranz, ‘‘Some experiments on orifice sprays,’’ Can. J. Chem. Eng.36,

175 ~1958!.


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