ILASS-Americas 29th Annual Conference on Liquid Atomization and Spray Systems, Atlanta, GA, May 2017

X-ray Fluorescence Measurements of Hydraulic Flip in a Beryllium Nozzle

D. J. Duke∗

Energy Systems Division, Argonne National Laboratory,Lemont IL 60439 USA

Laboratory for Turbulence Research in Aerospace & CombustionDepartment of Mechanical & Aerospace EngineeringMonash University, Clayton VIC 3800 Australia

K. E. Matusik, N. SovisEnergy Systems Division, Argonne National Laboratory,

Lemont IL 60439 USA

A. L. KastengrenX-ray Science Division, Argonne National Laboratory,

Lemont IL 60439 USA

C. F. PowellEnergy Systems Division, Argonne National Laboratory,

Lemont IL 60439 USA

AbstractSpray nozzles with constant or diverging diameters are known to be subject to the phenomenon of hydraulicflip, where the fluid detaches from the nozzle wall prior to exiting the nozzle. This can have a significantimpact on atomization; it is well established that hydraulic flip can substantially increase the breakuplength of a jet. Geometric cavitation inside the nozzle often occurs under similar conditions to those thatproduce a flipped jet. The interactions between these phenomena are not fully understood. Hydraulic flipis challenging to study, particularly in round nozzles. Changes in refractive index between the nozzle wallmaterial, ambient gas, and liquid make it very difficult to obtain good optical access at the nozzle exit plane.Strong geometric dependence and hysteresis in onset conditions makes it difficult to extend observations inrectangular nozzles to the axisymmetric case. It is also difficult to measure the difference between a voidgenerated by cavitation inside the nozzle, and displacement of the liquid due to encroachment of the ambientgas. In this paper, we demonstrate a novel X-ray fluorescence experiment to study hydraulic flip in an X-raytransparent beryllium nozzle with diameter 330 μm and length 2 mm. The ambient gas was doped with 3%krypton and time-averaged measurements of krypton fluorescence allowed the volume fraction of ambientgas to be quantitatively measured both inside and outside the nozzle. A polycapillary X-ray optic was usedto allow the detector to observe only a small portion of the focused 15 keV X-ray beam where it intersectedthe nozzle. We found that for a fluid with a vapor pressure much lower than the back pressure, the ambientgas can travel as far upstream as the nozzle inlet lip due to stabilized flow separation and displacement ofcavitation voids.

∗Corresponding Author: daniel.duke@monash.edu

1 Introduction

Hydraulic flip occurs when a liquid inside anozzle issuing into a gaseous environment separatesfrom the nozzle wall upstream of the exit plane [1,2].When conditions become favorable for flow separa-tion, ambient gas can travel back upstream alongthe nozzle wall, causing the jet to contract. The jetbecomes surrounded by a sheath of low-velocity gas,which stabilizes it and delays the onset of atomiza-tion [3].

The abrupt change in jet breakup length anddischarge coefficient caused by the onset of hydraulicflip is particularly problematic for spray nozzles inrocket engines [4] and industrial manufacturing ap-plications [5]. It is also of particular concern in highpressure direct fuel injection systems for gasolineand diesel engines. There is a significant body ofwork studying hydraulic flip in diesel injectors [6].Using shadowgraphy and Mie scattering, Soteriouet al. [7] showed that there are strong interactionsbetween upstream cavitation near the nozzle inlet,changes in jet morphology due to supercavitation(cavitation extending beyond the nozzle exit), back-filling of air into the nozzle, and eventual hydraulicflip of the exiting jet. Direct rate-of-momentumexperiments in diesel injectors [8] have shown thatthe transition to hydraulic flip substantially changesthe discharge coefficient, and phase Doppler (PDPA)measurements also show changes associated with theincrease in breakup length [9]. Ultimately, this im-pacts combustion and emissions [10]. In diesel in-jectors, the hole is often tapered which prevents hy-draulic flip. However, in gasoline direct injectors(GDIs) which have much smaller length to diameterratios, hydraulic flip is difficult to avoid [11,12].

Hydraulic flip has traditionally been studied inscaled-up, optically transparent nozzles at relativelymodest pressures using shadowgraphy [3,13]. Trans-parent models are also used to perform laser diag-nostics such as Mie scattering [7], laser Doppler ve-locimetry [4, 14], and PDPA [9]. Recent develop-ments in small, real-size optical nozzles allow theseflows to be studied at pressures much closer to di-rect fuel injection conditions [11]. Numerical simu-lations are also used to provide insight into the flowphysics [12].

Despite these recent advances, there remain twosignificant challenges associated with studying hy-draulic flip in round nozzles. The first is an issue ofoptical access. Due to the curved nozzle wall and therefractive effects of the chaotic gas-liquid interfacesinside, it is difficult to quantify the volume of gas inthe nozzle. For this purpose, two-dimensional rect-angular nozzles are often used [14,15]. These nozzles

have different pressure recovery and flow behaviorcompared to an axisymmetric nozzle. The secondchallenge with hydraulic flip is the inability to dis-criminate cavitation vapor from ambient gas [16].One of the open questions associated with the on-set of hydraulic flip is what happens when the flowtransitions from supercavitation to a true hydraulicflip. In the first case, the gas inside the nozzle nearthe exit is cavitation vapor, and in the second it ispredominantly ambient gas [17]. Understanding thetransition from one to the other is particularly im-portant for atomizer design, since cavitation tends toenhance atomization and hydraulic flip suppressesit [18, 19]. Since the two gaseous phases are diffi-cult to identify experimentally, the degree to whichthe ambient gas travels upstream is not fully under-stood.

X-ray diagnostics provide a useful tool to inves-tigate these problems. X-rays have high penetrat-ing power and refract very weakly from gas-liquidinterfaces, and can be used to probe complex anddense multiphase flows [20–22]. X-ray radiographytechniques developed to measure the density distri-bution of external fuel sprays [23] have also beenextended to measuring cavitation vapor distributioninside plastic nozzles at low pressures [24]. Recently,measurements have been demonstrated using noz-zles manufactured from beryllium alloy [25]. It canwithstand much higher pressures than plastic noz-zles, can be more precisely machined, and it is aweak absorber of X-rays.

While X-ray radiography provides a quantita-tive measurement of fluid density, it cannot eas-ily discriminate between cavitation vapor and am-bient gas. X-ray fluorescence spectroscopy (XFS) isideally suited to this problem. An incident X-raybeam ionizes an atom by creating a core shell hole,and when the hole is filled, a characteristic fluores-cence X-ray photon is emitted. By measuring thefluorescence line for a particular element using anenergy-resolving detector, its mass concentration inthe path of the X-ray beam can be quantified. Sincemost fluid flows in question consist of low-atomicnumber elements such as hydrogen, oxgen and car-bon, whose X-ray fluorescence energies are too lowto escape the sample environment, the flow is typi-cally doped with a tracer element of higher atomicnumber. For example, XRF has been used to studygas jets using argon as a tracer [26], to study liquidsprays using bromine [27], and to measure dissolvedgas concentration inside a plastic nozzle using kryp-ton [28].

In this study, we present a proof of concept ex-periment in which we induce the flow in an axisym-

2

metric beryllium nozzle of 0.33 mm diameter and 2mm length to undergo hydraulic flip. The ambientnitrogen environment was doped with 3% krypton,allowing X-ray fluorescence measurements of the am-bient gas concentration to be performed inside thenozzle. Contraction of the liquid phase was quan-tified both internally and externally. In order toimprove signal to noise ratio, a polycapillary X-rayoptic was used to allow the fluorescence detector toobserve only a small section of the focused X-raybeam, where it intersected the nozzle hole cross-section. Time-averaged raster-scan measurementsare presented for a range of injection pressures upto 30 bar at 1 bar abs. ambient pressure. We showthat when the nozzle is hydraulically flipped, theambient gas encroaches as far upstream as the inletof the nozzle hole, displacing the attached cavitationbubble due to the difference in pressure.

2 Methodology

The experiments were performed at the 7-BMbeamline of the Advanced Photon Source at Ar-gonne National Laboratory [29]. A gas-driven pistonaccumulator was used to provide a constant pres-sure fluid flow to the spray nozzle, as shown in theschematic diagram in Figure 1. The nozzle had a di-ameter of D=0.33 mm and a length L=2 mm. Theworking fluid was a commercial gasoline surrogate(Viscor 16BR, Rock Valley Oil & Chemical Com-pany) doped with a cerium X-ray contrast agent(Rhodia DPX9) at approximately 8:1 volume ra-tio, giving a concentration of 4% cerium by mass.The working fluid had a density of ρl = 817 kg/m3

and a viscosity of 1.23 cSt at 25◦C. All the exper-iments were conducted at this temperature. Thevapor pressure of the fluid was 3.5 kPa.

In order to reduce the effect of dissolved gaseson the flow [30] the fluid was de-gassed by stor-ing it under a partial vacuum in a sealed fuel tankfor several hours prior to commencing the experi-ments. A dome-loaded regulator was used to pro-vide a continuous inlet pressure Pin to the nozzle,and a mini-turbine flowmeter was used to measurethe volume flow rate of the fluid. In combinationwith a static pressure tap upstream of the nozzle in-let, the nozzle’s discharge coefficient was measuredindependently. The cavitation number K, Reynoldsnumber and discharge coefficient are defined respec-tively as

pistonaccumulator

compressed gas supply

10µm filter

dome load regulator

regulated gas

magnetic turbine flow

meter

spray chamber

berylliumnozzle

3-waysolenoid

valve

evacuatedstorage

tank

refill pump

P ,Tin in

P a

vacuum

regulated N2

flow meter

liquidtrap

ambient gas in

ambientpurge

gas + liquid

Figure 1: Schematic diagram of hydraulic system.

K =Pin − PvPin − Pa

, (1)

ReD =4m

πDρlνl, (2)

CD =4m

πD2√

2ρl (Pin − Pa), (3)

where Pa is the ambient pressure, m is the mass flowrate through the nozzle, Pv and νl are the test fluid’svapor pressure and kinematic viscosity.

The nozzle was mounted on a rotating clamp ina pressurized spray chamber with kapton film win-dows which allowed the X-ray beam to pass throughwhile maintaining either a partial vacuum or ele-vated ambient pressure inside the chamber. A cross-section of the nozzle geometry and the spray cham-ber mounting geometry are shown in Figure 2. Thespray from the nozzle impacted on a series of meshscreens far downstream of the X-ray windows, toreduce splashback. The krypton-doped ambient gaswas continuously purged through the chamber at ap-proximately 10 L/min to clear stray droplets. Thegas-liquid mixture drained from the bottom of thechamber. The liquid flowed back to the evacuateddrain vessel through a throttling valve and the purgegas was exhausted through a coalescing filter.

The experiment was set up as per the plan viewshown in Figure 3. A monochromatic X-ray beam

3

614

46

30

ø2.5

D=0.330

static pressuretap (Pin)

convergingsection (5º)

upper wall ofspray chamber

x-ray window

spray jet

L=2.00

inflow

mounting clamp

rotating thimble

beryllium nozzle

straight section

Figure 2: Cross-section of the beryllium nozzle andclamping assembly from the viewpoint of the incom-ing X-ray beam, showing the upper flow passage ge-ometry. Dimensions are in millimeters.

with a mean energy of 15 keV (1.0% full width at halfmaximum bandpass) was focused to a 5 × 6 μm spotusing a pair of Rh-coated Kirkpatrick-Baez focus-ing mirrors. The incoming beam intensity (I0) wasmonitored with a diamond transmission photodiode,to correct for any fluctuations in the incident beamflux. The beam then passed through the kapton win-dows of the spray chamber, and through the beryl-lium nozzle. Approximately 2/3 of the beam wasabsorbed by the ambient gas, kapton windows andberyllium nozzle. The transmitted beam was col-lected by a 200 μm thick PIN diode, which was usedto record the total transmission of X-rays. As perFigure 3, fluorescence X-rays were collected by anenergy-resolving silicon drift diode through a thirdkapton window placed at right angles to the incidentX-ray beam.

The chamber gas was a mixture of 97% N2 and3% Kr (v/v) at 1 bar and 25◦C. The incident X-raybeam excited K-edge fluorescence from the krypton,which resulted in the emission of 12.6 keV Kα X-raysat a yield of 63% [31, 32]. The emission of Kr fluo-rescence occurs isotropically along the entire path ofthe X-ray beam where it intersects the ambient gas.Since there is a large path length of gas either side ofthe nozzle hole, this creates a high background sig-nal level which can make it difficult to detect small

changes in the fluorescence inside the nozzle hole asthe liquid is displaced by ambient gas. The changein the total path length of Kr in the X-ray beamis less than 1% when the nozzle is completely filledwith liquid as compared to being filled with gas. Fur-thermore, elastic and Compton scattering add to thebackground level and reduce the detector’s effectivecollection efficiency for the Kr Kα photons.

To overcome the problem of measuring a smallsignal against a large background, we used a poly-capillary X-ray optic with a fixed 100 mm workingdistance, placed between the detector and the kap-ton window. The polycapillary acts to slightly focusand collimate the X-rays (the effect is exaggeratedin Fig. 3 for illustrative purposes). This has thepractical effect of allowing the detector to view asmall region of the X-ray beam and increase the ef-fective solid angle of detection within this region,while reducing the sensitivity of the detector to X-rays emitted from outside this region. The end resultis an effective probe volume of approximately 5 × 6× 300 μm (x, y, z) where the X-ray beam intersectswith the nozzle hole. The nozzle and spray cham-ber are translated vertically and horizontally whilethe X-ray beam and the detectors remain fixed, al-lowing the system to probe different locations in araster scan pattern while the position along the zaxis (incident beam direction) remains fixed.

A sample raw spectrum from the detector isshown in Fig. 4. Here, the nozzle hole is completelyfilled with ambient gas. The Fe and Ni lines arecaused by fluorescence excited by scattered X-rayswhich hit the stainless steel support that holds thenozzle in place. The benefit of using the polycapil-lary optic is seen in the relative height of the Kr Kα

peak (the energy that is useful for the measurement)as compared to the elastic and Compton scatteringpeaks at higher energy.

In order to perform this measurement, a highflux synchrotron source is required, as the X-ray fluxrecieved by the detector is orders of magnitude lessthan the incident flux. Approximately 1/3 of theincident beam is absorbed by the windows, ambientgas and nozzle walls before the beam arrives at thetest section. With the orifice completely filled withgas, only 0.3% of the incident flux is absorbed by Kr.The total emission from the Kr inside the nozzle istherefore only 0.2% of the incident flux. Of this, thedetector captures a small fraction of the solid angle.Within the solid angle of collection, approximately85% of the emission is absorbed by the nozzle wall,ambient gas, and kapton window before reaching thedetector. With an incident beam flux of 1011 pho-tons/s, the signal at the detector is on the order of

4

z

y

x

X-ray focusing mirrors

Incoming x-ray beam(monochromatic)

Incomingbeam intensity

monitorfluorescence

spray chamber

x-ray windows

PIN Diode

Polycapillaryoptic

Silcon drift diode

beryllium nozzle

DIAGRAM NOT TO SCALE

mounting clamp

θ

Figure 3: Plan view of experiment setup (not to scale). The incident X-ray beam is shown in red, and theemitted fluorescence in blue.

Figure 4: Sample energy spectrum recorded by the fluorescence detector. The krypton Kα peak is integratedto measure the quantity of ambient gas inside the nozzle.

5

Figure 5: Calibration curve for the krypton fluorescence signal, measured by filling the nozzle hole with aknown density of ambient gas at 3% Kr, 97% N2.

104 photons/s. This limits the measurement to be-ing time-averaged, as a sampling time on the orderof 1 second is required at each position.

The underlying theory for the fluorescence mea-surement is described in detail in previous publica-tions [28]. Here, a brief overview is given. The in-tensity of fluorescence X-rays dIf emitted along asegment of the incident beam (dz) is described by

dIf = ωI0µgρgdz, (4)

where ω is the fluorescence yield [33], I0 is the in-cident flux, µg is the X-ray attenuation coefficientof the ambient gas, and ρg is its density. For thepurposes of this study, we wish to know the integralof the intensity

∫dIf along a segment of the beam

in the focus of the polycapillary optic, and from thiswe can determine the projected density of the gasphase in this region, defined as

Mg =

∫ρgdz (mass/area). (5)

If the density of the ambient gas is fixed, the quan-tity of gas in the path of the beam can also be ex-pressed as a path length, which is easier to interpret:

lg =Mg

ρg. (6)

In order to convert the measured level of X-rayfluorescence from the Kr Kα values at the detector(which are in arbitrary counts) to an absolute pro-jected mass, several corrections are required. Knowncorrections for incident flux and the nonlinear re-sponse of the detector with count rate [34] were ap-plied based on the measured values. Corrections for

solid angle and the concentration, absorption coeffi-cient & yield of the fluorescing species in the ambientgas were fixed properties of the experimental setupand were corrected using a lumped calibration con-stant. The nozzle hole was filled with gas, and thenozzle was traversed through the beam. The abso-lute path length of gas in the X-ray beam was deter-mined by radiography measurements of the nozzlehole geometry. The intensity of transmitted X-raysat the PIN diode were converted to a path lengthequivalent to eqn. 6 using the Lambert-Beer law;

lg,cal =−1

ρgµgln

(IPIN

I0

). (7)

The result of the calibration (with a least squaresregression fit) is shown in Fig. 5.

Once the fluorescence measurement is cali-brated, a final correction must be made to accountfor variable signal trapping; the absorption of flu-orescence photons by the liquid inside the nozzle.While the signal loss due to the nozzle wall geom-etry and ambient gas are corrected for in the cal-ibration, the signal trapping in the liquid must becorrected post-hoc as it depends on the position ofthe X-ray beam and the measured path length offluid between the beam and the detector. The sig-nal trapping correction was made by scanning thenozzle transversely through the beam at each ax-ial position and measuring both the Kr fluorescencesignal from the gas, and the path length of liquidin the beam using X-ray radiography. At each axialmeasurement position, an Abel inversion was usedto estimate the cross-sectional density distributionof the liquid and gas from the calibrated projection

6

data. The transmission (τ) of fluorescence emissionfrom the gas at each point in the measurement planeprojected in the direction of the detector (y′ axis)was made using the Lambert-Beer law, with the ab-sorption coefficient calculated at the lower energy ofthe fluorescence photons (µfluor);

τfluor(x, y, z) = exp

−∑j=l,g

µfluor,j

∫ ymax

y′=y

ρjdy′

,

(8)In the above equation, j is a summation over theliquid and gas phases. The higher density of theKr gas also has a measurable signal trapping effectwhich is accounted for, although secondary emissionfrom this reabsorption is below the noise floor of themeasurement and is disregarded. From an estimateof the two-dimensional signal trapping and distribu-tion of the fluorescing species, a weighted reabsorp-tion correction for the projection data is calculated,giving an estimate of the net signal trapping for agiven line of sight projection;

τfluor(x, y) ≈∫τfluor(x, y, z) · ρg(x, y, z)dz∫

ρg(x, y, z)dz. (9)

Dividing the calibrated measurement (Fig. 5) withthe signal trapping transmission (Eq. 9) gives thefinal calibrated measurement of the path length ofambient gas inside the nozzle. The largest signaltrapping corrections for these experiments were ap-proximately 5%, when the nozzle was filled with liq-uid. The average signal trapping correction was ap-proximately 3%. The assumption of axisymmetryin the signal trapping correction introduces a smallerror into the correction. Since the correction isonly several percent of the final measurement, theincrease in error due to this assumption is withinthe uncertainty level of the measurement. The as-sumption of axisymmetry in the signal trapping doesnot require that the final data be axisymmetric.

Propagation of uncertainty through the calibra-tion and corrections has been described in detail inprior work [28]. The two main contributors to mea-surement uncertainty are photon shot noise and cal-ibration uncertainty. The signal trapping correctionalso amplifies the uncertainty. For this experiment,the integration time and photon count rates wererelatively high, and the primary contributor to un-certainty was due to calibration (Fig. 5). The esti-mated uncertainty in the path length of gas (lg) wasapproximately 5%, or ±15 μm.

3 Results and Discussion

In the experiments, the ambient pressure wasmaintained at 1.05 bar abs. and the injection pres-

sure was increased from 1.50 bar up to 23.10 barabs. Measurements were made transversely acrossthe nozzle at 32 positions, and repeated over 20 ax-ial positions both inside and downstream of the noz-zle. Ten injection pressures were tested, and eachmeasurement condition was repeated twice.

The results for four of the injection pressure datasets are shown in Figure 6. The magnitude of the Krpath length (equation 6) is given in units of nozzlediameters on the vertical axes. The horizontal axisis the transverse position, with the nozzle center-line at y/D = 0. The reference condition to whichthe measurements are compared is with the nozzlecompletely filled with liquid, and the outlet regioncompletely filled with gas. The solid lines in Figure 6are measurements made inside the nozzle (x/L < 1)and the dashed lines are measurements made down-stream of the nozzle (x/L > 1). The axial posi-tion is also indicated by the color bar. The ellipticalshape of the profiles in Fig. 6a shows that at verylow injection pressure, the nozzle is almost uniformlyfilled with liquid (solid lines) and the exiting jet isrelatively axisymmetric with a vena contracta of ap-proximately 10% (dashed lines). The width of theexit jet is approximately the nozzle diameter (indi-cated by the black vertical lines). The small, positiveKr signal inside the nozzle in Fig. 6a is caused bybackground fluorescence from the gas surroundingthe nozzle, and Kr which has become dissolved inthe fluid due to the recirculation of the liquid in thehydraulic system.

As the injection pressure increases (Figs. 6b,6c) we see the exiting jet contract slightly due toincreased velocity, but the measurement inside thenozzle does not change substantially. In Fig. 6c, thecavitation number of the nozzle is K ≈ 1.56, justbelow the critical K value. We expect the nozzleto be cavitating at this condition. High-speed poly-chromatic phase-contrast imaging of the nozzle un-der these conditions has confirmed that cavitation ispresent under these conditions, before any hydraulicflip occurs. When the injection pressure is increasedslightly to 3 bar (Fig. 6d) we see an abrupt increasein Kr concentration inside the nozzle, indicating thata hydraulic flip has occurred. Here, K ≈ 1.49, so thenozzle discharge coefficient due to cavitation effectsalone should change by less than 3%. However, werecord an abrupt decrease in flow rate; the dischargecoefficient drops abruptly from approximately 0.75to 0.65. This corresponds to similar measurementsof the effect of hydraulic flip on discharge coefficientmade by others [35]. As injection pressure continuesto increase (Figs. 6e, 6f) the profiles remain similar,and the exit jet profile continues to contract.

7

(a) Pin = 1.50 bar abs, Pa = 1.05 bar abs. (b) Pin = 2.50 bar abs, Pa = 1.05 bar abs.

(c) Pin = 2.75 bar abs, Pa = 1.05 bar abs. (d) Pin = 3.00 bar abs, Pa = 1.05 bar abs.

(e) Pin = 10.00 bar abs, Pa = 1.05 bar abs. (f) Pin = 23.10 bar abs, Pa = 1.05 bar abs.

Figure 6: Transverse plots of magnitude of net change in Kr path length at varying axial positions (x axis,indicated by color). Results are shown with increasing injection pressures, both (a) without and (b-d) withhydraulic flip. The solid lines indicate measurements made inside the nozzle, and the dashed lines indicatemeasurements made downstream outside the nozzle.

8

(a) Pin = 1.50 bar abs, Pa = 1.05 bar abs.

(b) Pin = 2.75 bar abs, Pa = 1.05 bar abs.

(c) Pin = 3.00 bar abs, Pa = 1.05 bar abs.

(d) Pin = 10.00 bar abs, Pa = 1.05 bar abs.

Figure 7: Contour plots of net change in Kr path length at four injection pressures, both (a,b) withouthydraulic flip and (c,d) with hydraulic flip. The region from 0 < X/L < 1 on the left is measured inside thenozzle, and the region of X/L > 1 on the right is the free jet.

9

(a) x/L = 0.05

(b) x/L = 0.90

(c) x/L = 1.04

Figure 8: Transverse plots of net change in Kr path length at varying inlet pressures (indicated by line color),at (a) the nozzle inlet, (b) just upstream of the nozzle outlet, and (c) just downstream of the nozzle outlet.

10

The shape of the Kr distribution in Figures 6d-6fis approximately axisymmetric and matches the pro-jection that one would expect if the liquid were sur-rounded by an annular sheath of gas. Interestingly,we see that elevated Kr levels are recorded not onlyat the nozzle exit plane (where we expect hydraulicflip to occur) but also as far upstream as the nozzleinlet plane. This can be visualized more clearly inFigure 7. Here, the measurements are shown as colorcontour plots with the axial position (normalized bydiameter) on the horizontal axis and the transverseposition (normalized by nozzle length) on the verti-cal axis. The liquid flow is left to right as indicatedby the arrows. The beryllium nozzle wall is shownby the hatched region, and the vertical dashed linesindicate the nozzle inlet and outlet planes. In Figure7, a two-tone color bar scale is used to show positiveand negative net change in Kr level relative to thereference condition where the nozzle is filled withliquid and the outlet is filled with gas. The red colorindicates additional Kr (displacement of liquid dueto the gas) and the blue color represents a deficit inKr (displacement of the gas by the liquid). Figures7a-7b show the results for cases without hydraulicflip. Figure 7b is a condition in which cavitationis expected, but no hydraulic flip. Figures 7c-7dshow the distribution of Kr for cases with hydraulicflip. We see that once the flow transitions, excessKr is measured along the nozzle walls all the wayfrom the inlet to the outlet. This ‘total’ hydraulicflip is a known feature of perfectly straight nozzles.However, these measurements quantitatively demon-strate that the cavitation voids are completely dis-placed by the ambient gas, even at the nozzle inlet.The path length of Kr for |Y/D| > 0.45 is sufficientlylarge with respect to the path length through the ge-ometry to indicate an annulus of 100% ambient gasby volume fully connecting the outlet plane to thenozzle inlet.

Further insight can be gained by visualizing theresults as a function of injection pressure for a fixedaxial position. Figure 8 shows the transverse mea-surement of Kr path length colored by the injectionpressure, with low pressures in dark colors and highpressures in light colors. Figure 8a shows the changein gas distribution 100 μm (0.3 diameters) down-stream of the nozzle inlet plane. Once the transitionto hydraulic flip occurs, the gas level along the nozzlewalls rises rapidly to nearly 100% of the path lengthfor |y/D| > 0.4. The total volume of gas increaseswith increasing injection pressure, and the profileflattens out as the pressure rises. Figure 8b showsthe gas distribution 200 μm upstream of the nozzleexit plane. Here, the onset of hydraulic flip causes a

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.6 0.65 0.7 0.75 0.8

Con

tract

ion

coef

ficie

nt

Discharge Coefficient (CD)

Internal contractionExternal contraction

Hydraulic fliptransition

Figure 9: Area contraction coefficients for the liquidphase due to displacement by the ambient gas, mea-sured both inside the nozzle and downstream of thenozzle, plotted against nozzle discharge coefficient.

much larger increases in gas path length, indicatinga greater contraction of the jet, and a sharper inter-face. Figure 8c shows the displacement of the gasby the exiting jet, 80 μm downstream of the nozzleexit plane. We see that the jet uniformly contractsand retains its elliptic profile as pressure continuesto increase.

One of the distinct advantages of having quan-titative measurements of the gas distribution in thenozzle is that the area contraction of the liquid canbe measured by integrating the measurement of liq-uid path length across the nozzle plane and dividingby the nozzle area;

Ca(x) = 1− 4

πD2

∫lg(x, y)dy. (10)

Since the x-ray fluorescence measurements aremade both inside and outside the nozzle, a contrac-tion coefficient (Ca) can be calculated for both theinternal flow, i.e. the vena contracta caused by theinternal displacement of liquid due to the ingress ofgas, and the external flow, the area contraction ofthe exiting jet. We find that these contraction coef-ficients are strongly correlated with the nozzle dis-charge coefficient. The results are shown in Figure 9,where the error bars indicate the uncertainty due tothe propagation of experimental error through equa-tion 10. At low injection pressures, the discharge co-efficient is high, and as expected, the internal areacontraction is close to 1, since there is very littlegas inside the nozzle. The external area contrac-tion of the jet is low, as the jet velocity is very lowand the jet is being pulled downward under the in-fluence of gravity. As CD drops and pressure in-

11

creases, we find that the internal contraction coeffi-cient drops approximately linearly, and the externalcontraction increases approximately linearly. Thediscontinuity in contraction coefficient suggests thatthe back-filling of gas in the nozzle rapidly displacespre-existing cavitation voids rather than generatinga gradual displacement of the liquid as has been ob-served in rectangular nozzles and scaled-up flows.

4 Conclusions

In this paper we have presented a series of time-averaged, raster-scan x-ray fluorescence measure-ments of the quantitative distribution of ambientgas inside a beryllium nozzle. One novel advantageof this measurement is the ability to quantiaativelymeasure the distribution of ambient gas independentof any cavitation voids inside the liquid. Cavita-tion and ambient gas in the nozzle would otherwisebe indistinguishable using conventional optical tech-niques. Another advantage is the ability to makenearly simultaneous measurements both inside andoutside the nozzle without any change to the ex-perimental setup. This permitted correlations to bemade between the changes in internal and externalliquid and gas distribution.

The measurements clearly showed that the on-set of hydraulic flip caused gas to abruptly back-fill along the nozzle wall. An important observationwas that a significant quantity of ambient gas wasmeasured as far upstream as the nozzle inlet. Thestraight axisymmetric nozzle did not show any evi-dence of a stable partial hydraulic flip. The shapeof the transverse profiles suggests that the gas dis-tribution forms an annular ring around the liquid,similar to classical geometric cavitation.

As the injection pressure was increased, we ob-served a contraction of the liquid flow inside thenozzle, and an expansion of the jet outside the noz-zle. The change in contraction followed an approxi-mately linear trend with the nozzle discharge coeffi-cient, which was measured independently.

The correlation between the discharge coeffi-cient and area contraction coefficients both insideand outside the nozzle suggest that the discontinu-ity caused by the onset of hydraulic flip does notcause a significant deviation in the relationship be-tween contraction coefficient and discharge coeffi-cient. This suggests that the onset of hydraulic flipoccurs when ambient gas displaces previously exist-ing cavitation voids inside the nozzle. Since the am-bient pressure is much higher than the fluid’s vaporpressure, it makes sense that any continuous cavita-tion voids would be completely filled with ambientgas in a short time once the cavitation voids reached

the exit plane of the nozzle. However, this hypoth-esis will require further investigation, as the dataavailable in this preliminary study are limited. Fu-ture work could combine fluorescence and radiogra-phy measurements of the cavitation voids in orderto build a more complete picture of the exchangebetween cavitation and ambient gas ingress. Thisexchange occurs rapidly (in milliseconds) and theflow is unstable around the transition pressure. Thetransition is difficult to capture using time-averagedmeasurements such as those shown here. High-speedx-ray phase contrast imaging [36] and time-resolvedx-ray radiography techniques [37] could be used tobetter understand how ambient gas displaces pre-existing cavitation voids.

Acknowledgements

The x-ray experiments were performed at the7-BM beam line of the APS at Argonne NationalLaboratory. Use of the APS is supported by theU.S. Department of Energy (DOE) under ContractNo. DE-AC02-06CH11357. The authors gratefullyacknowledge the computing resources provided onthe Blues and Fusion high-performance computingclusters operated by the Laboratory Computing Re-source Center at Argonne National Laboratory. Fuelinjection research at Argonne is sponsored by theDOE Vehicle Technologies Program, under the di-rection of Gurpreet Singh and Leo Breton.

References

[1] J I Ito. Proc. 7th JANNAF Meeting, pp. 417–426, February 1971.

[2] C Dumouchel. Exp. Fluids, 45(3):371–422, June2008.

[3] W Bergwerk. Proc. Institution of MechanicalEngineers, 173:655–660, 1959.

[4] R Santoro. Combustion Enhancements in Ad-vanced Liquid Rocket Engines. Technical Re-port Air Force Office of Scientific ResearchGrant F49620-97-1-0224, Propulsion Engineer-ing Research Center, Pennysylvania State Uni-versity, 1999.

[5] H V Tafreshi and B Pourdeyhimi. Textile Re-search Journal, 74(4):359–364, April 2004.

[6] C Soteriou, R Andrews, and M Smith. SAETechnical Paper, 950080, January 1995.

[7] C Soteriou, R Andrews, and M Smith. SAETechnical Paper, pp. 1999–01–1486–20, May1999.

12

[8] L C Ganippa, S Andersson, and J Chomiak.SAE Technical Paper, pp. 2000–01–2788, Octo-ber 2000.

[9] H K Suh and C S Lee. International J. Heatand Fluid Flow, 29(4):1001–1009, August 2008.

[10] F R Westlye, M Battistoni, S A Skeen, J Manin,L M Pickett, and A Ivarsson. SAE TechnicalPaper, volume 2016–01–0860–15, April 2016.

[11] J Serras-Pereira, Z van Romunde, P G Aleiferis,D Richardson, S Wallace, and R F Cracknell.Fuel, 89(9):2592–2607, September 2010.

[12] B Befrui, G Corbinelli, P Spiekermann,M Shost, and M-C Lai. SAE Int. J. Fuels Lubr.,5(2):620–636, April 2012.

[13] R H Pratama, A Sou, Y Wada, and H Yoko-hata. Valencia, Spain, September 2014.

[14] A Sou, A Tomiyama, S Hosokawa, S Nig-orikawa, and T Maeda. JSME InternationalJournal Series B, 49(4):1253–1259, 2006.

[15] A Sou, M I Maulana, K Isokazi, S Hosokawa,and A Tomiyama. J. Fluid Science and Tech-nology, 3(5):622–632, 2008.

[16] D P Schmidt, C J Rutland, M L Corradini,and P Roosen. SAE transactions, 1999-01-0518,1999.

[17] A Thompson and S D Heister. Atomization andSprays, 26:93–119, 2015.

[18] R H Pratama, A Sou, Y Wada, and H Yoko-hata. Proc. ICLASS-2015 International Con-ference on Liquid Atomization and Spray Sys-tems, Tainan, Taiwan, August 2015.

[19] R Prasetya, M Mashida, and A Sou. Proc.ICLASS-2015 International Conference on Liq-uid Atomization and Spray Systems, pp. 1–9,Tainan, Taiwan, November 2016.

[20] A Kastengren and C F Powell. Exp. Fluids,55(3):1686, February 2014.

[21] D J Duke, A B Swantek, A L Kastengren, andC F Powell. J. Physics: Conference Series,656:012110–5, December 2015.

[22] D J Duke, A Swantek, A Kastengren, K Fez-zaa, and C Powell. SAE Int. J. Fuels Lubr.,8(1):135–146, April 2015.

[23] A L Kastengren, F Tilocco, D J Duke, C Powell,X Zhang, and S Moon. Atomization and Sprays,24(3):251–272, May 2014.

[24] D J Duke, A L Kastengren, F Tilocco, A BSwantek, and C F Powell. Atomization andSprays, 23(9):841–860, October 2013.

[25] D J Duke, A B Swantek, K E Matusik, N Sovis,A L Kastengren, J P Viera, R Payri, and C FPowell. Int J. Engine Res., 18:39–50, February.

[26] A L Kastengren, C F Powell, E.M. Dufresne,and D A Walko. J. Synchrotron Rad., 18:811–815, July 2011.

[27] D J Duke, A L Kastengren, N Mason-Smith,Y Chen, P M Young, D Traini, D Lewis,D Edgington-Mitchell, and D Honnery. PharmRes, 33:816–825, November 2015.

[28] D J Duke, A L Kastengren, A B Swantek, K EMatusik, and C F Powell. Exp. Fluids, 57:1–14,September 2016.

[29] A Kastengren, C F Powell, D Arms, E MDufresne, H Gibson, and J Wang. J. Syn-chrotron Rad., 19(4):654–657, May 2012.

[30] M Battistoni, D J Duke, A B Swantek, F ZTilocco, C F Powell, and S Som. Atomizationand Sprays, 25(6):453–483, 2015.

[31] J A Bearden and A F Burr. Rev. Mod. Phys.,39, 1967.

[32] J A Bearden. Rev. Mod. Phys, 39, 1967.

[33] J H Hubbell, P N Trehan, Nirmal Singh,B Chand, D Mehta, M L Garg, R R Garg,Surinder Singh, and S Puri. J. Phys. Chem.Ref. data, 23(2):339–364, 1994.

[34] D A Walko, D A Arms, A Miceli, and A L Kas-tengren. Nuclear Inst. and Methods in PhysicsResearch, A, 649(1):81–83, September 2011.

[35] K Ahn, J Kim, and Y Yoon. Atomization andSprays, 16(1):15–34, 2006.

[36] D Duke, A Swantek, Z Tilocco, A Kastengren,K Fezzaa, K Neroorkar, M Moulai, C Pow-ell, and D Schmidt. SAE Int. J. Engines,7(2):1003–1016, July 2014.

[37] D J Duke, A L Kastengren, A B Swantek, K EMatusik, R Payri, J P Viera, and C F Pow-ell. Proc. ILASS-Europe, 27th European Con-ference on Liquid Atomization and Spray Sys-tems, Brighton, UK, September 2016.

13