ILASS Americas 19th Annual Conference on Liquid Atomization and Spray Systems, Toronto, Canada, May 2006

Internal Flows in Fluidic Spray Control

Kuo-Tung TsengSteven H. Collicott!

School of Aeronautics and AstronauticsPurdue University, West Lafayette, IN 47907

AbstractFluidic control of the cavitation in an axisymmetric orifice for the purpose of a!ecting droplet sizes in aspray is investigated using both experiments and computational modeling. Cavitation images, droplet sizemeasurements, discharge coe"cients, unsteadiness measurements, and computation flow-field results arecombined to study the mechanisms that result in the production of small droplets. The physical processesconnecting unsteady inlet cavitation to the creation of small droplets remain obscure because cavitation isa!ected by absolute size. Also, there is no e!ective method to measure the pressure field, velocity field, voidfraction field, etc., inside a small orifice. Recent work at Purdue demonstrated that a small step placed at thestrategic location is capable of both creating small droplets and increasing the pressure at which hydraulicflip occurs. The successful step inspired the fluidic spray control method described here that allows for theshuto! of the step e!ect. A secondary flow is fed into the orifice through an annular slot in the orificewall to control the cavitation, and thus the spray, at pressures up to 650kPa. Two di!erent orifice designsare explored. The cavitation and spray are photographed with a high resolution CCD digital camera anddroplet measurements were made using a laser di!raction particle-sizer. Computational Fluid Dynamicscodes developed at Purdue are used to model the flow as an axisymmetric, unsteady, non-equilibrium, two-phase flow. In general, a high pressure region upstream of the secondary flow injection slot, rapid wallpressure fluctuations, longer cavitation length, and thicker cavitation appear to influence the chain of eventsleading to production of smaller droplets.

!Corresponding Author

IntroductionAs early as 1959, Bergwerk[1] endeavored to

visualize the flow inside orifices and study the ef-fects the flow pattern has on the appearance of thespray and the e!ect of cavitation number, Reynoldsnumber, edge sharpness, and length-to-diameter,L/D, by measuring discharge coe"cient. He con-cluded that discharge coe"cient, Cd, is a functionof Reynolds number only before cavitation begins.Once cavitation occurs, Cd is a function of cavita-tion number, K1, defined as the ratio of driving pres-sure di!erence to absolute downstream pressure. Itis important to note that he also concluded that cav-itation is a!ected by absolute size.

In 1975, Furness and Hutton[2] used cinematog-raphy to observe the cavitation and summarized thatthe cavitation occurs periodically. The growth-and-collapse cycle results from the interaction between are-entrant flow from downstream and the free sur-face upstream. One year later, Nurick[3] developeda 2-D code, accurately predicting the discharge co-e"cient, Cd, for unflipped flow. He found that Cd

is proportional to square root of cavitation numberfor cavitating flow regime. In his paper, cavitationnumber, K2, is defined as the ratio of driving pres-sure di!erence to the di!erence between the absoluteupstream and vapor pressure.

Nearly one decade later, in 1985, Kato[4] re-ported results on cavitation growth. He summa-rized that low pressure, nuclei, and su"cient timeare the necessary factors for cavitation inception. Iflow pressure is not maintained, the nuclei will col-lapse. Hiroyasu, et al.[5] investigated the e!ect oforifice cavitation on spray properties in 1991. Theymeasured spray angle and the break-up length, anddiscovered if cavitation results in supercavitation,the spray angle is increased and break-up length isreduced. These suggest cavitation a!ects the sprayin several ways. In other words, cavitation can en-hance the atomization if properly controlled.

In 1995, Chaves[6] presented comprehensive re-search on diesel fuel injector. Conclusions werereached — cavitation can be triggered by minute dis-turbances at the orifice inlet. At low driving pressuredi!erence, (P1!P2), the cavitation is minor and ter-minates within the orifice. With increasing pressure,the cavitation may extend to the exit, also called su-percavitation. Aside from supercavitation, there isa layer of liquid between the wall and the cavitationto prevent the external pressure, P2, from penetrat-ing into the cavities. At supercavitating state, evena small increase in pressure, P1, may cause exteriorpressure penetration into cavities. Ultimately theflow becomes hydraulic-flipped. In the same year,

He and Ruiz[7] reported experiments on turbulencelevels generated by cavitation. The holes utilized inthe experiments are much larger than diesel injectororifices. They a"rmed that turbulence was createdby impingement of the free surface onto the orificewall.

Since 1996, a series of numerical computationswere undertaken. In 1996, Chen and Heister[8] de-veloped a numerical method for predicting 2-D cav-itating flow. This model treats the flow as unsteady,viscous, two-phase flow. To account for the densityin cavitation region, they introduced a constitutivepseudo-density relationship. In this relationship, thepseudo-density values always vary between that ofliquid and vapor. In constituting the pseudo-densityequation, the hydrodynamic non-equilibrium e!ectswere also taken into account. The Navier-Stokesequations were then solved together with continuityequation and pseudo-density equation. Experimen-tal data from Henry[9] were used to justify the CFDresults. Subsequently, in 1998, Bunnell[10] extendedthe code to three dimensional flow. Years later, in2001, Xu and Heister[11] used a ! ! " model to ac-count for e!ects of turbulent boundary layer[12].

Since 1998, Li and Collicott[13, 14] used vari-ous orifices, including straight channel ones and theothers angled at 14 degrees with respect to surfacenormal to investigate the cavitating flow. The latterones are intended to simulate the actual geometry ofdiesel engine injectors. In straight hole cases, theymentioned that cavitation thickens, and the sprayangle increases with the increase of driving pressure.Considering the tilted holes, the cavitation firstlyexists along the obtuse angle side. Through the in-crease of pressure, the cavitation thickens, and movedownstream if the cavitating flow is further pressur-ized. In their experiments, UCF-1 calibrating fluid isused as working liquid to simulate the diesel fuel, andthe pressure was as high as 200MPa. To highlightthe cavitation e!ects, Li[15] compared the experi-mental flow rate with computational result. Withe!ective flow area reduced, of course the experimen-tal result is lower.

In the same year, Ruiz and He[16, 17] appliedLDV to measure velocities in a super-scale orifice,and discovered that the flow with cavitation is dis-tinct from the case without cavitation. The presenceof cavitation at the orifice exit leads to a jump in theturbulence level through the orifice. They assertedthat cavitation is a greater influence on the turbu-lence than Reynolds number. Their data show thatturbulence persists to the exit plane, where it canaid in droplet formation.

In 1999, Sanchez[18] delved into the nature of

unsteadiness of cavitating flow in a 2-D slot byrecording numerous cavitation lengths and imagingcavitated regions at di!erent pressures. The statis-tics reveals that the extent of cavitation increases asthe driving pressure is increased. Usually the growthof cavitation length is limited until noticeably a largequantity of bubbles occupies the region. Moreover,the fluctuation magnitude increases with pressure.The statistics also confirms that the fluctuation ofthe cavitation length is asymmetric, agreeing withwhat predicted by Bunnell[10]. Generally the dis-tributions slant to the shorter lengths. Later in thesame year, Chandra and Collicott[19] made e!ortsto gain more insight into the unsteady cavitatingflow in 2-D slot by measuring the frequencies of cav-itating flow, and successfully detected two strongestsignals corresponding to two distinct frequencies ina power spectrum. The higher frequency, corre-sponding to locally periodic bubble-formations andbreak-ups, is accompanied by smaller-magnitudepower spectral density, while the lower frequency,with larger-magnitude power spectral density, corre-sponds to the growth and collapse cycle of the cav-itation region. The aforementioned frequency andmagnitude are also compared at varying longitudi-nal locations for the same conditions. In general, thetwo noticeable peak frequencies are of the same val-ues in spite of di!erent magnitude. The strongestsignals taking place the most downstream indicatemost intensively periodic cycles. Later, Chandra[20]further confirmed that the characteristic frequencyincreases with larger driving pressure.

In 2000, Gopalan and Katz[21] confirmed thatthe collapse of vapor cavities in the closure regionleads to vorticity production and contributes to theincrease of turbulence levels. In their paper, they af-firmed that a small change in cavity size is capableof resulting in a substantial change in the turbu-lence level and the turbulent kinetic energy. Theirmeasurements show that turbulence produced in theorifice can propagate to the exit plane.

From 1998 to 2001, Tamaki et al.[22, 23]and Hiroyasu[24] demonstrated that a strong dis-turbance arising from cavitation in the nozzle isthe main cause responsible for water-jet breakup.Furthermore, Hiroyasu[24] studied spray formationmechanisms intensively. He proved that cavitationhas a great influence on atomization because the cav-itation causes the flow to be turbulent, and resultsin surface disturbances. In Rayleigh’s theory, thecause of disintegration of a jet is the surface insta-bility. Thus a surface disturbance, when interactingwith the surrounding air, can enhance atomization.To understand the e!ect that the orifice geometry

has on jet atomization, he installed a wire mesh overthe inlet of the orifice, and a gap at the middle ofthe orifice hole. In his paper, he mentioned thatthe installed wire mesh can transform the jet fromnon-cavitating hydraulic-flipped flow into cavitatingflow. He also pointed out that the spray angle islarge, and the liquid jet is atomized rapidly for arelatively large gap contrasted to the orifice length.To the contrary, the spray angle becomes small, andthe liquid jets do not atomize as much.

In 2001 Y. Laoonual[25] observed the spray us-ing plain, counterbore, rounded inlets, and beveledinlets of di!erent angles. The results suggest thatsome counterbore nozzle, allowing presence of su-percavitation throughout the whole injection time,is appropriate for maintaining good atomization.The largest spray angle caused by supercavitation isclearly demonstrated. Observation of the flow alsoimplies that beveled nozzles having a bevel angle of60 degrees or less are shown to be able to greatlyincrease the pressure for hydraulic flip. This e!ectis an analogy to that of a small step placed at thestrategic location. Nozzles with larger bevel angleshave similar flow pattern to plain orifices. Moreover,examinations of the e!ect of orifice length led to con-clusions that a longer orifice requires higher pressurefor cavitation to occur.

In 2001, L.C. Ganippa et al.[26] investigated thestructure and evolution of cavitation in a transpar-ent scaled-up diesel nozzle with a orifice inclined atdi!erent degrees to the axis of the injector. Theyconcluded that non-symmetric atomization arisesfrom non-symmetric cavitation distributions, thatis, the side with higher degree of atomization hasthicker cavitation on the same side upstream.

GoalThe present research e!ort grows from the work

of Ong et al.[27] in 2003, in which they sought to con-trol a spray (i.e., to create di!erent sized droplets)by placing a small step at a strategic position in aplain orifice. The position is chosen on the groundsthat a partially cavitated flow re-attaches to the ori-fice wall at this location at some driving pressure.With the step in place, high pressure is formed inthe vicinity of the small step, prohibiting cavitationfrom extending downstream, that is, the extent ofcavitation is limited. The placement of the step notonly increases the pressure for hydraulic flip, butalso induces noticeably small droplets downstream.The work of Ong shows that small changes in holegeometry can create substantial changes in a spray.An ability to turn the control authority on and o!,and perhaps, to modulate the control is sought in

Figure 1. Comparisons of small step and secondary flow.

the present research.Knowledge of how the orifice geometry a!ects

the cavitation distribution is crucial to enable bettercontrol of sprays. Unfortunately, little of the internalflow details are explored because of the tiny orifice.Though recent e!orts focused on placing a small stepat a strategic location (Fig.1) proved successful inchanging the downstream droplet size distributions,the causes and fluid mechanisms inducing creationof small droplets remain obscure. Moreover, the stepe!ect is unable to be turned o!. The lack of abilityto shut o! the small step e!ects inspired us to devisethe secondary flow orifice.

To connect the flow structure to how smalldroplets are created, we resort to numerical means.With this access to internal flow physics we cancorrelate how the changes in the internal flow withdroplet sizes.

1 ExperimentThe flow rig for this experiment delivers pressur-

ized water flow to a spray orifice. It consists of anair compressor, a reservoir, optically accessible ori-fices (Fig.2). Devices, including a Xenon flash lamp,a digital CCD, camera lens, a pressure transducer,an in-line flow rate meter and a Sympatec laser dif-fraction particle-sizer, are used to image cavitationand to measure pressure, flow rate and droplet size.The air compressor supplies air up to 150 psi to thereservoir. The water in the reservoir is split into themain and secondary flow that are controlled by thecorresponding valves, and are then delivered to the

test section. The flow rate of the secondary flow ismeasured by an in-line flow meter and the total flowrate measurement is made by collection of the ef-flux. A Druck pressure transducer, sampled at 300Hz and accurate to 0.03% is connected to the volumejust upstream of the orifice to measure the plenumpressure. The output voltage for the transducer isbetween 1 and 5 Volts, corresponding to 0 and 150psi, respectively, and increases linearly with increas-ing pressure. The cavitation, recorded on a 1024 by1024 square-pixel CCD, and transferred to a PC, isilluminated from behind with a Xenon flash lampflashing at 15 Hz.

1.1 Injection OrificeThe fluidic control orifice is formed by two

pieces: the main housing and the inner plug (Fig-ures 3, 4, and 5). Both are machined from trans-parent acrylic to be optically accessible. Althoughacrylic has this advantage, it is not sturdy enough towithstand high stress. Multiple disassembly and as-sembly cylces appear to distort or damage the acrylicorifices.

Two orifices are reported on here. Orifice 1 hasLs = 0.81mm with # = 22.5!, and orifice 2 hasLs = 0.41mm with # = 75! (Fig.6). Orifice 1 isbased on the successful steps which were guesses atwhat would work well, whereas the latter one is de-termined from CFD results. The detailed dimen-sions are listed in Table 1.

The slot length, h (Fig.6), is observed to be crit-ical to determining hydraulic flip pressure. Origi-

Table 1. Principle dimensions for orifices

Orifice D h Ls L #Orifice 1 0.81mm 0.08mm 0.81mm 5.08mm 22.5!Orifice 2 0.81mm 0.08mm 0.41mm 5.08mm 75!

Figure 2. Schematic of the flow rig.

nally, the slot length was 0.25mm. But this slotacted like a step for no secondary flow and no hy-draulic flip is seen even at 700kPa driving pressure.This phenomenon conforms to Hiroyasu’s thesis[24].The slot e!ect was not controllable until the slotlength, h, was shortened to 0.08mm. Actually theideal slot length appears to depend on both the ori-fice length and diameter. For the orifices utilizedhere, 0.08mm slot length permits the spray controlto be turned o!.

1.2 Particle-sizerThe spray measurements are made with a Sym-

patec Helos laser di!ractionparticle-sizer. The lightsource of the particle-sizer is a Helium-Neon-laserwith 632.8 nm wavelength. The graphical presenta-tions include a volume cumulative distribution curveas well as volume density distributions defined asthe ratio of a class, that is, the mass fraction for aparticle size interval, to its class width, as a percent-age. Both are relative quantities. Since the spray ishighly unsteady in nature, adequate sampling time isrequired to obtain consistent results. In this exper-iment, the measuring time is 10 seconds. The char-

acteristic frequency for 550kPa and 350 kPa drivingpressure di!erence is higher than or equal to 6537Hzand 5173Hz, respectively, at least more than 50000cycles or 20000 samples are included in the dropletsize distributions.

1.3 CCD CameraThe flow is a two-phase flow once cavitation oc-

curs. While light passes through these regions, it isscattered by the liquid-bubble interface because ofthe di!erent refractive indices of vapor and liquid.Light refracted outside of the imaging lens apertureis unable to reach the CCD detector. Therefore, theappearance of cavitation is always indicated by adark region in the images. This technique di!erenti-ates two-phase from single-phase flow. Nevertheless,it is unable to distinguish vapor from air, that is, adark region also emerges for hydraulic flip as a resultof light-scattering by liquid-air interface. Hydraulic-flipped flow is not of interest for spray productionand is generally not studied here.

The cavitation images are recorded with a back-lit imaging. A Xenon arc lamp with 2 µs duration,activated by a function generator, is utilized as thelight source to backlight the test section. The lightradiated from the lamp, focused by an aspheric lensand di!used by a ground glass, finally gets to theorifice. A Nikon lens is used on the other side toimage the orifice onto the Redlake 1024 by 1024square-pixel 8-bit grayscale CCD camera equippedwith built-in electronic shutter. Exposure time forthe shutter can be as short as 127µs, enabling usto capture fast-moving cavitation or droplets. Thehigh resolution CCD camera is capable of captur-ing 30 images per second. Imaging is triggered byoperating the XCAP software developed by RedlakeMASD, INC.. In this experiment, the depth of fieldis 0.9 cm or 11 orifice diameters; the depth of focusis 1.1 cm and the di!raction limit is 11.1µm in theobject plane. The F# and focal length of the lensare set to 4 and 7 cm, respectively. The layout forimaging the spray structure is the same as that forcavitating flow. Without the distortion of the cir-cular orifice, the spray images are better than thecavitation images.

Figure 3. Plane section view of main housing andinner plug.

Figure 4. Top view of the orifice

ResultsActually the droplet distributions are a!ected

by both primary atomization and secondary atom-ization. The degree of primary atomization is de-termined by the interaction of the jet with the sur-rounding air [28], which causes the jet to break-upinto droplets. Besides, cavitation also a!ects theprimary atomization because the existence of cavi-tation can elevate the turbulence level [21] and mod-ify velocity profiles at the orifice exit [29], and thus,enhance atomization [29].

The secondary atomization ensues shortly af-ter the completion of the primary atomization.Thereafter, the drop will deform into an ellipsoidalshape [30] before the onset of the secondary atom-ization. Secondary atomization is influenced by thedroplet sizes, droplet velocity and the properties ofthe system such as pressure, temperature, viscosityand surface tension [31]. The Weber numbers inthis experiments are " 100. Therefore, the dropletscan experience both shear [28, 32] and catastrophicbreakup [28], and these two mechanisms [33, 34] maytransform the large droplets into smaller droplets.

In other words, the droplet size distributionsshown in this thesis are the results of both pri-mary and secondary atomization. However, this re-search focuses on the study of internal flow struc-tures. Hence it is not justified to conclude that somespecific mechanism found in the orifice is mainly re-sponsible for the production of small droplets 35 cmdownstream. Instead, we could only state that someflow structure is favorable for atomizing the jet (pri-mary atomization), and this condition is advanta-geous to the creation of small droplets far down-stream. After all, the degree of secondary atomiza-tion also depends on the after-primary atomizationdroplet sizes [31], that is, the cavitation has an in-direct influence on the secondary atomization.

Orifice 1 ResultsThe flows with 0%, 1%, 2%, 3%, 4%, 15%, and

20% secondary flow at 350kPa and 550 kPa drivingpressure di!erence were photographed, with 0%, 4%,and 20% presented here (details are in [35]). Thecorresponding sprays 35 cm downstream of the exitwere also imaged and measured. Here percentageof the secondary flow is defined as the ratio of thesecondary mass flow rate to the total mass flow rate.Cavitation images are present in Figs. 7, 8, and 9.Droplet size data follow in Figs. 10, 11, and 12.

Figures 7(a) and (b) show the cavitation with nosecondary flow. Fig.7(a) corresponds to the 350kPadriving pressure di!erence, while Fig.7(b) is the pic-ture for 550 kPa driving pressure di!erence. At

350kPa driving pressure di!erence, the flow is cav-itating, whereas the flow appears hydraulic flippedwith some 3-D structure at 550 kPa driving pressuredi!erence.

The 4% secondary flow rate results in creationof droplet sizes in the 100µm diameter range, whichare absent in the zero secondary flow case (Fig. 11).This, incidentally, is nearly the same for the 3% case.At 350 kPa driving pressure di!erence, 4% secondaryflow creates a slightly smaller impact of cavitationthan the 3% case. The 550kPa case shows the great-est impact of cavitation for the cases examined. The350kPa droplet data are not presented in this paperas they are of lesser interest that the higher pres-sure data but are available in the upcoming thesisby Tseng[35].

The highest secondary flow rate, 20%, shown inFig. 12, appears to entirely confine the cavitationto the vicinity of the orifice inlet (Figs. 9). In spiteof the vanishing cavitation, the production of smalldroplets for the 550kPa case still exists, as Fig. 12shows. The 350 kPa case, however, behaves to thecontrary — there are almost no tiny droplets, thus,some mechanism arising from higher pressure ap-pears to be crucial to the creation of small droplets.The unproductive 20% case in Orifice 1 is shown forcontrast with Orifice 2.

Orifice 2 ResultsOrifice 2 results di!er from Orifice 1 results.

Cavitation images are shown in Figs. 13, 14,and 15 with the respective droplet measurements inFigs. 16, 17, and 9.

Figures 13(a), (b), and (c) display the cavitationwith no secondary flow. At 350 kPa driving pressuredi!erence, cavitation is present in the regions up-stream of the slot. Apparently the presence of cavi-tation does not favor atomization, and therefore, fewtiny droplets exist (Fig. 16). Also, the alternation ofhydraulic flip and cavitating flow at 550kPa drivingpressure di!erence fails to bring on changes in atom-ization (Fig. 16). The occurrence of cavitating flowhere seems to exert a smaller influence than in ori-fice 1. Probably some other mechanism is importanthere.

With the secondary flow increased to 4%, theflow at 350kPa driving pressure di!erence behavessimilarly to the 3% secondary flow case, as Fig-ures 14(a), and 17 show. At 550kPa driving pressuredi!erence, the cavitation sometimes reaches the exitplane (Figures 14(b) and (c)). The longer extent ofcavitation appears to induce more turbulence, andboosts the impact of cavitation (Fig. 17(b)), thoughradical changes are not observed compared to the

3% case.At the highest secondary flow rates, 20%

(Fig. 18), the supercavitation-like 3-D flow occurs,as Fig. 15(a) and (b) show. The accompanying dark-est cavitation regions and noticeably small droplets(Fig. 18) indicates that some other conditions be-sides cavitation length and unsteadiness of cavitat-ing flow are also crucial for atomization.

Figure 19 contrasts the two orifices at the 20%secondary flow rate. Details for many other casesare in[35]. In this figure, note in the top and bottomleft plot that the streamwise extent of the cavitationin Orifice 1 is near zero for most times but that inOrifice 2 there is much greater streamwise extent ofcavitation. The current version of the code has asingle-phase exit boundary condition so LC/L = 1is not to be expected but further e!orts can improvethis boundary condition. Note then in the pseudo-density fields that again the cavitation in Orifice 1is of minimal extent. In Orifice 2 the cavitation ap-pears to begin at the secondary injection slot, in-dicating that the secondary flow is both preventingcavitation at the inlet and either cavitating itself orcausing cavitation in the primary flow that extendsto the exit plane. This di!ers from the 4% secondaryflow case that acts like the step orifice[35].

ConclusionsThe research sought to determine the internal

flow physics that result in the observed productionof small droplets. The two orifices that were studiedlead to the conclusion that there may be two dif-ferent mechanisms or two di!erent methods for onemechanism to produce small droplets.

Fluidic control is shown to be capable of thesame type of spray control as the step — it cancreate substantially small droplets and increase thepressure necessary to produce hydraulic flip. Usingof droplet measurements, flow visualization, and un-steady CFD we found the likely internal flow featuresresponsible for the production of small droplets. Un-derstanding how the secondary flow creates theseflow features is important to creating functional de-signs and to understanding or expanding the limitsof operation. Though the results available cannot af-ford us knowledge of how small droplets are a!ectedby secondary atomization, they are evidence of thelink between internal flow structures and dropletsizes, which may be an important basis for spraycontrol. After all, the primary atomization has agreat influence on the secondary atomization.

Two orifices were tested. Orifice 1 is found towork exactly like the step orifice at some secondaryflow rate. CFD and flow visualization show that the

secondary flow restricts cavitation to the regions up-stream of the slot. This creates shorter cavitationlengths that lead to higher-frequency fluctuations ofthe internal flow and then small droplets. CFD fur-ther helps to find out that the combined e!ects oflarge variations over time of high pressure regionsand long cavitation extent are likely causing the en-hanced creation of small droplets because collapse ofcavitation under the aforementioned combined ef-fects may result in more turbulence, thus favoringatomization.

Creation of small droplets is a maximum near4% secondary flow. For orifice 1, with high pressureregions upstream of the slot, cavitation interactswith the above regions more violently, and hencepromotes a greater impact of cavitation than for cav-itating flow in orifice 2. Moreover, even with thincavitation, a significant impact of cavitation is pos-sible. In other words, a low total flow rate is not aprerequisite to cause a great impact of cavitation.

Orifice 2 appears to work di!erently. CFD andflow visualization show that cavitation in orifice 2is not confined to the regions upstream of the slot.Perhaps the slot is too far upstream to act like astep. Small droplets increase with secondary flowrate. 20% secondary flow has the most advanta-geous conditions for boosting up atomization: thehighest pressure upstream of the slot, the largesthigh pressure variations over time, and the longestcavitation length. Therefore, this case creates thegreatest impact of cavitation or the largest numberof small droplets. The mechanisms corresponding tothe conditions are the same as those of orifice 1. Atlow secondary flow rates, the increase of secondaryflow scarcely a!ects the flow behavior, despite theincreasing cavitation length. Cavitation length ap-pears not to be important for atomization for thesecases. At large secondary flow rate, the pressure ishigh throughout the upstream regions, causing thecavitation to vanish in this region.

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Figure 5. Picture of the main housing and the inner plug

Figure 6. Dimensions for the orifices

No flow (a)350 kPa (b)550 kPa

Figure 7. Cavitation images for Orifice 1 (Ls = 0.81mm and # = 22.5!), and 0% secondary flow at: (a)#P = 350kPa; cavitating flow (b) #P = 550kPa; hydraulic flip.

No flow (a)350 kPa (b)550 kPa

Figure 8. Cavitation images for Orifice 1 (Ls = 0.81mm and # = 22.5!), and 4% secondary flow at: (a)#P = 350kPa; possible cavitating flow (b) #P = 550kPa; cavitating flow.

No flow (a)350 kPa (b)550 kPa

Figure 9. Cavitation images for Orifice 1 (Ls = 0.81mm and # = 22.5!), and 20% secondary flow at: (a)#P = 350kPa; possible cavitating flow (b) #P = 550kPa; possible cavitating flow.

(b)550 kPa

Figure 10. Droplet size distributions for Orifice 1 (Ls = 0.81mm and # = 22.5!), and 0% secondary flowat #P = 550 kPa and 35 cm downstream.

(b)550 kPa

Figure 11. Droplet size distributions for Orifice 1 (Ls = 0.81mm and # = 22.5!), and 4% secondary flowat #P = 550 kPa and 35 cm downstream.

(b)550 kPa

Figure 12. Droplet size distributions for Orifice 1 (Ls = 0.81mm and # = 22.5!), and 20% secondary flowat #P = 550 kPa and 35 cm downstream.

No flow (a)350kPa (b)550 kPa (c)550kPatype(1) type(2)

Figure 13. Cavitation images for Orifice 2 (Ls = 0.41mm, # = 75!), and 0% secondary flow at: (a)#P = 350kPa; cavitating flow (b) #P = 550kPa; hydraulic flip (c) #P = 550kPa; cavitating flow.

No flow (a)350 kPa (b)550 kPa (c)550 kPatype(1) type(2)

Figure 14. Cavitation images for Orifice 2 (Ls = 0.41mm, # = 75!), and 4% secondary flow at: (a)#P = 350kPa; cavitating flow (b) #P = 550 kPa; supercavitation-like 3-D flow (c) #P = 550 kPa; cavitatingflow.

No flow (a)350 kPa (b)550 kPa

Figure 15. Cavitation images for Orifice 2 (Ls = 0.41mm, # = 75!), and 20% secondary flow at: (a)#P = 350kPa; supercavitation-like 3-D flow (b) #P = 550kPa; supercavitation-like 3-D flow.

(b)550 kPa

Figure 16. Droplet size distributions for Orifice 2 (Ls = 0.41mm, # = 75!), and 0% secondary flow at#P = 550kPa and 35 cm downstream.

(b)550 kPa

Figure 17. Droplet size distributions for Orifice 2 (Ls = 0.41mm, # = 75!), and 4% secondary flow at#P = 550kPa and 35 cm downstream.

(b)550 kPa

Figure 18. Droplet size distributions for Orifice 2 (Ls = 0.41mm, # = 75!), and 20% secondary flow at#P = 550kPa and 35 cm downstream.

Figure 19. Cavitation histories, pressure contours, streamlines and pseudo-density contours for Orifice 1(top) and Orifice 2 (bottom) at 20% secondary flow rate. The field quatity plots at at time t"=180. Theleft-hand border of each field plot is the orifice centerline. The computational domain extends above andbelow the small region of the orifice that is shown here (Z" = 6.25 is the exit plane).