ILASS-Americas 25th Annual Conference on Liquid Atomization and Spray Systems, Pittsburgh, PA, May 2013

Synchrotron X-Ray Measurements of Cavitation

D.J. Duke1∗, A.L. Kastengren2, F. Zak Tilocco1 and C.F. Powell11 Energy Systems Division, Argonne National Laboratory, Illinois, USA

2 X-ray Science Division, Advanced Photon Source, Argonne National Laboratory, Illinois, USA

AbstractCavitation plays an important role in the formation of sprays from small nozzles such as those found infuel injection systems. However, cavitation occurs over very short time and length scales, and is difficult tomeasure in-situ. Precise experimental measurements of cavitation vapor distributions in three-dimensionalnozzle geometries are valuable tools for the improvement and validation of numerical simulations. Theprimary quantity of interest is void fraction or local density, which is difficult to measure using visible lightdiagnostics. X-rays scatter very weakly and can be used to make precise measurements of the projectedmass distribution of a spray, and these same techniques can be extended to cavitating flows. In this paper,we present the preliminary results of an x-ray radiography experiment on a model nozzle of 500 micronsdiameter. The advantages of a focused x-ray raster scanning method over traditional flat-field x-ray imagingare demonstrated. The raster scan radiography experiments achieve a spatial resolution of 5 micron and atemporal resolution of 3.6 microseconds. The projected vapor distributions indicate a very rapid migrationof vapor from the wall into the core of the flow. The vapor distributions are also found to be very steady;time resolved measurements indicate that RMS fluctuations are not more than 1% of the mean. The spectralcontent of cavitation is concentrated at small Strouhal Numbers on the order of 0.001 to 0.1, suggesting asteady cavitation inception and mixing process without any large-scale fluctuations in the vapor distribution.

∗Corresponding Author: dduke@anl.gov

1 IntroductionCavitating pipe flow is a complex fluid mechani-

cal phenomenon found in many applications and hasbeen studied in detail for some time[1]. In particular,cavitation is a problem in fuel injection for internalcombustion engines, where the fuel travels through asmall nozzle under a large pressure gradient to pro-duce a spray. Cavitation leads to component wearand can markedly change the structure of the result-ing spray[2, 3]. Changes in spray structure can leadto changes in engine performance, emissions and ef-ficiency [4, 5, 6].

Quantitatively measuring the distribution ofcavitation vapor in a nozzle is a particularly chal-lenging experimental problem. To obtain opticalaccess, nozzles have been modified with transpar-ent windows and transparent scale models have beenmade to allow observation of cavitation structures[7,8]. The outer morphology of large cavitating struc-tures such as solid vapor films, bubbly clouds andstrings can be observed, revealing new physicaldetails[9, 10, 11]. However, the phase interface be-tween liquid and gas scatters visible-wavelength lightstrongly, which can obscure three-dimensional fea-tures.

Recently, x-ray sources have been used to pro-vide useful quantitative measurements of the localvoid fraction in cavitating flows. Tube source x-rayswith relatively low photon fluxes are moderately ab-sorbed by the liquid phase, with weak scattering andgood penetration. The void fraction intercepted bya fan of x-rays passing through a two-dimensionalchannel flow with transparent walls can be quanti-tatively measured[12, 13]. Recent experiments us-ing intensified detectors such as those of Aeschli-mann et al. are now capable of several kHz timeresolution[14]. However, tube source x-rays have alarge source size and a divergent beam, leading toa trade-off between temporal and spatial resolution.High spatial resolution can be obtained over long in-tegration times and time-resolved measurements canbe made at low spatial resolution, but it is difficultto satisfy both requirements.

Due to these resolution limits, x-ray measure-ments of cavitation have often been performed inscaled-up models [15]. In cavitating venturis, it hasbeen shown that cavitation effects do not necessar-ily scale with turbulence, such that a rescaled flowat the same non-dimensional conditions (ReynoldsNumber, Cavitation Number) will not always showthe same cavitation behavior[16]. Therefore, tech-niques capable of measuring cavitation vapor distri-bution at scales closer to those of production fuelinjectors become important when considering how

Ø2.5mm

Ø0.5mm

9.0 mm

flow

R1.19

2.5mm

Figure 1: Schematic of cavitating nozzle understudy.

well-mixed the vapor and liquid phases may be atthe nozzle outlet.

We have undertaken measurements of cavitationvapor in a 500 µm diameter nozzle using focused syn-chrotron x-rays. The measurements are line-of-sightprojections which can be used to quantify the to-tal amount of vapor in the flow. Vapor productioncan also be determined by integrating across mul-tiple nozzle planes. Synchrotron x-ray radiographyis demonstrated as a versatile tool for the measure-ment of cavitation at small scales.

2 Method2.1 Experiment Setup

The test geometry was a polycarbonate noz-zle with a throat diameter of D=0.5 mm, alength/diameter ratio of L/D = 5 and an in-let/outlet diameter ratio of 5, as per Figure 1. Fuelwas delivered to the nozzle via a piston-accumulatorsystem pressurised with inert gas (see Figure 2). Thefluid temperature and pressure were monitored im-mediately upstream and downstream of the nozzle,and a turbine flowmeter monitored the mass flowrate. The upstream and downstream pressures P1

and P2 were varied independently to produce a de-sired flow rate, such that the two key independentvariables are the Reynolds number and cavitationnumber (σ or K);

ReD =4m

πρlνlD, (1)

σ =P1 − P2

P2 − Pvap, (2)

K =P1 − Pvap

P1 − P2, (3)

where Pvap is the vapor pressure of the fuel, whichwas measured by an isoteniscope test. The work-

2

11L, 3000psi piston

accumulator

Regulated N2

Capture Pressure Vessel

Regulated N2

VacuumPump

Cavitation Fixture

Magnetic Turbine

Flowmeter

P1, T1 P2, T2

Refill Valve

Figure 2: Schematic of fuel delivery system.

ing fluid was a commercial gasoline surrogate witha vapor pressure of approximately 580 Pa at 25 ◦C.It should be noted that in this study, no effort wasmade to remove dissolved gases from the fuel.

The 7-BM beamline of the Advanced PhotonSource (APS) at Argonne National Laboratory wasused to make the x-ray measurements presented inthis paper. The facility is specifically designed tomake time-resolved radiographic measurements ofmultiphase flows, and is described in detail by Kas-tengren et al[17]. A simplified schematic of the keybeamline components is shown in Figure 3. X-raysfrom the APS bending magnet are reflected off awater-cooled double-multilayer monochromator[18]tuned to a mean energy of 8keV, which generatesa monochromatic beam of x-rays with a bandpass of1.4% FWHM and a flux of approximately 2.5× 1011

ph/s/mm2. The monochromatic beam is focused toa spot size of 5 × 6 µm FWHM with a pair of 300mm, Rh-coated Kirkpatrick-Baez mirrors. The fo-cused beam acts as a microprobe, allowing the voidfraction over a small area to be probed along a lineof sight. The experiment is traversed through thefixed beam in a raster-scan pattern to develop a two-dimensional representation of the x-ray transmission(see Fig. 6a).

The beamline can also be configured in a conven-tional x-ray imaging setup by removing the focusingmirrors from the beam path to allow the x-ray beamto pass directly through the experiment. The x-rayimages are taken in this configuration with 150 µmLYSO:Ce scintillator which converts the x-ray inten-sity to visible light, which is imaged with a mirror,

microscope objective and a CCD camera.Before the beam interacts with the experiment,

it passes through a thin Ti foil, which absorbs asmall fraction of the beam energy and emits floures-ence photons which are captured by a photodiodearray. This signal is used to normalize out tempo-ral fluctuations in the incomimg beam. The beampasses through the experiment, and is collected by a300 µm thick PIN diode. The experiment is placed36.5m downstream from the source; the PIN diode isapproximately 5cm downstream of the experiment.

For time-average measurements, the intensitymonitor and PIN diode are sampled for δt = 0.5s. For time-resolved measurements, the PIN diodeis sampled at 5 MHz with a 1 MHz analog low-passfilter for δt = 5 s. The time-resolved signal is in-tegrated over each synchrotron orbit period, whichreduces the effective sampling rate to 271.554 kHz,giving a temporal resolution of ±3.68 µs.

The rationale for the choice of 8keV photon en-ergy is explained by Figure 4. The cavitation con-trast is expressed as the measurable change in trans-mission due to 0.5 mm of liquid octane vs vaporoctane[19, 20], as a fraction of the total signal. Thereis a trade-off between contrast in the liquid andvapor phases and overall transmission through thenozzle. At low energies, absorption in the liquid isgood but poor transmission through the polycabon-ate nozzle wall and surrounding air reduces the over-all contrast. At high energies, the beam penetratesthe nozzle easily but absorption in the liquid phase isweak. The theoretical contrast peaks around 10keV,but 8keV was found to be the optimum choice basedon the actual absorption of the fuel and nozzle walls,which differed slightly from the estimated values.

2.2 X-ray Radiography Theory and UncertaintyAnalysis

Data are collected by both the beam intensitymonitor (I0) and the PIN diode (I1) over an inte-gration area δA = 30 µm2 along a line of sight δzat a particular point of interest through the nozzle.The experiment is then repeated at a non-cavitatingcondition where the nozzle is filled with liquid atthe same inlet pressure, but over a very small pres-sure gradient where there is no cavitation (denotedI ′). The presence of cavitation vapor in the nozzleresults in an increase in the transmitted beam inten-sity due to a reduction in the number of absorbersin the beam path. The only change in the trans-mitted intensity is due to absorption in the sampleand a small degree of scattering. As a result, theprojected density of fluid in the interrogation region

3

Figure 3: Monochromatic radiography microprobe setup at Sector 7-BM. The diagram is not to scale; thedistance from the source to the experiment is 35.5m. The beam is focused to a 5×6 µm spot where it passesthrough the nozzle.

0

0.005

0.01

0.015

0.02

0 5 10 15 20 0

0.2

0.4

0.6

0.8

1

Liq

uid

/ V

apor

Contr

ast

X-r

ay T

ransm

issi

on

Photon energy, keV

ContrastTransmission

Figure 4: Theoretical transmission of x-rays throughthe nozzle, and contrast of 0.5 mm of vapor in thenozzle, computed vs photon energy. Experimentswere conducted at 8keV (indicated).

δAδz is defined by the Lambert-Beer law;

I1/I0I ′1/I

′0

= e−µl(Ml−M ′l). (4)

(Ml −M ′l ) is the mass of displaced liquid per unitarea between the experiment I1/I0 and the referencecase I ′1/I

′0 due to the presence of cavitation vapor.

µl is the attenuation coefficient of the working fluid(units m2/kg.). M is normalized by the known den-sity of the liquid phase to convert mass per unit areato a path length δzv which represents the projecteddepth of vapor in the path of the beam:

δzv =−1µlρl

loge

(I1/I0I ′1/I

′0

). (5)

Normalizing against a known geometric path lengthδz allows the mean depth-integrated vapor frac-tion α = δzv/δz to be recovered. A depth-integrated vapor fraction α is sensible in relativelytwo-dimensional flows[14], but may be misleadingin a highly three-dimensional or axisymmetric flow,

since the beam passes through regions which mayrepresent a solid vapor film, a bubbly cavitationcloud, and solid liquid at a single position. We thusexpress the quantity of vapor as the total path lengthof vapor δzv in the following analysis. This is moreconsistent with the fact that the measurement is aprojection of the total vapor in the beam.

The attenuation coefficient µl is measured byfilling capillary tubes with the working fluid, wa-ter, and air, and measuring the x-ray transmissionthrough the tubes. Using the known attenuation co-efficients of water and air at the same x-ray energy,the x-ray attenuation of the working fluid can bedetermined. The attenuation coefficient of the liq-uid fuel was determined to be µlρl ≈ 0.3124 mm−1.We have neglected the vapor phase attenuation co-efficient from Eqns. 4-5, since it is very small.The vapor phase attenuation coefficient can be es-timated using tabulated x-ray data[19] at µvρv ≈3.6 × 10−4 mm−1. This value is very small due tothe low density of the vapor phase; µv is smallerthan the uncertainty in µl.

An error propagation calculation[21] has beenundertaken to determine the measurement uncer-tainty in the projected vapor measurement (δzv).The contribution to error from photon shot noise isdetermined by the photon flux at the detector; 1010

ph/δt at the PIN diode and several orders of magni-tude less for the intensity monitor. The photon shotnoise contributes an error of 0.007% for the beam in-tensity monitor and 0.001% for the PIN diode overa sampling time of δt = 0.5 s. Signal processing andelectronic noise contribute an additional 0.11% er-ror. The error in the attenuation coefficient in turndepends on the uncertainty in the PIN diode duringthe calibration process, the non-uniformity of thecapillary tubes and the number of averages, and iscalculated at 0.28% (including error due to assum-ing µv → 0). The uncertainty in the time-averagemeasurement δzv is thus determined mainly by thecontrast (I/I ′), and is expressed in Equation 6.

4

εδzv= δzv

√√√√(εµl

µl

)2

+(ερl

ρl

)2

+ 2

((εI1I1

)2

+(εI0I0

)2)(

loge

(I1/I0I ′1/I

′0

))−2

. (6)

The contrast in the intensity (I/I ′) varies from1 to 1.06 in the present experiment, giving an un-certainty in the time-average measurement εδzv

of±3.5µm of vapor, which is 0.7% of the nozzle diam-eter or 2% of the peak value in a typical measure-ment. The fractional uncertainty is slightly smallerthan those reported by Stutz et al[13] and Baueret al[15] for x-ray tube sources, but at much higherspatial & temporal resolution.

For the time-resolved signal analysis, the rawPIN diode voltage signal is numerically integratedover each synchrotron orbit period (3.6 µs). A 1MHzanalog low-pass filter eliminates any aliasing in the 5MHz digitized signal. Assuming a Poisson distribu-tion for the photon shot noise and including signalprocessing errors as above, the uncertainty at anysample point over the orbit time is ±0.38%. Thedigitized time series is convolved with a sliding Hannwindow and the resulting spectrum is the average of1.1× 106 Fast Fourier Transforms, with a frequencyresolution of ±33 Hz and a bandwidth of 136 kHz.

3 Results and Discussion3.1 Time-average vapor distribution

A flat-field time-average x-ray image of the noz-zle inlet is shown in Figure 5a, taken with a conven-tional x-ray imaging setup. The presence of localcavitation vapor (Fig. 5b) results in an increase inthe image intensity. Cavitation vapor can be seenstarting at small machining defects in the nozzlewall near the inlet. A conventional x-ray imagingconfiguration is useful for revealing the morphologyof strongly cavitating regions, however the changesin intensity due to cavitation are at maximum 5-6%of the overall image intensity, only a few gray lev-els. This makes quantitative measurements difficultwith a conventional imaging setup. Phase contrasteffects (manifesting as dark and bright bands at thenozzle wall) and background intensity variations dueto the incoming x-ray beam (manifesting as horizon-tal striping) can be at the same order of magnitudeto the absorption due to cavitation and make quan-titative measurements difficult. The focused beammicroprobe technique overcomes these problems dueto a higher photon flux and by normalizing the beamintensity, and has much higher sensitivity at muchhigher time resolution.

Microprobe measurements were conducted atfour conditions, as shown in Table 1. The effect of

varying both Re and σ / K have been investigated.At each case, measurements were taken over a rasterscan grid as shown in Figure 6a, at 8 keV photonenergy. 100 transverse positions (y) were measuredat 19 streamwise (x) locations. The time-averagedvalues δzv are interpolated onto a series of contourplots in Figs. 6b-6e. The data have been linearlyinterpolated in x.

In all cases, qualitatively similar cavitation fea-tures are observed. Cavitation vapor is generatednear the sharp nozzle inlet (as evidenced by Figs.5b and 6). Shortly thereafter, the vapor separatesfrom the wall and mixes with the flow as it trav-els further downstream. The vapor distribution isasymmetric at the nozzle inlet owing to nucleationfrom small machining defects, as seen in Figure 5a.The maximum measured projected vapor values atthe wall near the inlet are consistent with vapor frac-tions near to 100%, and represent a film or annularbubble of vapor attached the wall. There is alsoa substantial accumulation of vapor in the centerof the flow several diameters downstream, which isconsistent with the measurements of Bauer et al.[15]In this region, the depth-averaged vapor fraction istypically 10-30%. Given that the vapor is likely con-centrated in a bubbly cloud at the center of the noz-zle rather than evenly spread along the line of sight,the local vapor fraction in these regions is likely tobe approximately twice this value (ie. up to 60%).

The vapor distribution, particularly the accu-mulation of vapor along the centerline, is differentto the canonical vapor distribution in a channel ofsimilar size, such as the two-dimensional throttle ex-periments of Winklhofer[22]. The lift-off of vaporfrom the wall is similar, but the accumulation of va-por along the centerline is distinctly different. If theentrainment of vapor into the center of the nozzleis caused by a radial pressure gradient, it may notoccur as strongly in rectangular channels.

Bauer et al proposed that the weak accumula-tion of vapor they observed along the centerline of alarge cavitating pipe flow (using water) may be anisolated nucleation event caused by the low pressurein this region[15]. In case 1 of the present experi-ment, the area reduction for the core liquid flow isapproximately 30%, since the vapor bubble attachedto the wall forms a vena contracta[23]. The areafraction of the vena contracta was determined by

5

Case Inlet Pressure P1 Outlet Pressure P2 Fuel flow rate(kPa abs.) (kPa abs.) (L/hr) Re σ K

1 1060± 20 87± 2 26.8± 0.24 1.58× 104 11.2 1.092 1020± 50 312± 4 26.5± 0.57 1.57× 104 2.3 1.443 1050± 50 19± 6 26.7± 0.55 1.58× 104 58.6 1.024 290± 10 25± 3 14.1± 0.35 8.36× 103 10.7 1.09

Table 1: Experiment conditions.

nonlinearly fitting an annular vapor distribution tothe projected vapor quantities. An increase in veloc-ity due to a reduction in flow area would not cause asufficient pressure gradient in x to reach Pvap, whichis quite low due to the nature of the gasoline surro-gate used in these experiments. Conversely, trans-port of vapor from the wall to the centerline due toa change in pressure is more likely.

It is possible that dissolved gases in the fuelcould also cause the centerline vapor accumulationwe observe. The fuel’s saturation capacity is esti-mated at 10−2 mole fraction at the inlet conditionsand 10−3 mole fraction at the outlet conditions usingexperimental data for N2 dissolved in n-octane[24].This corresponds to a mass fraction of 2.5× 10−3 atthe inlet, dropping to 2.5× 10−4 at the outlet. Thischange is sufficient to produce a measurable quan-tity of gas, assuming that the fuel is almost saturatedwith gas and is well-mixed.

If the accumulation of vapor at the nozzle cen-terline is either due to cavitation or dissolved gasescoming out of phase in the fuel, the total quantity ofvapor integrated over the nozzle cross-section wouldbe expected to change with x in a manner that cor-relates with the location of these features. However,if the centerline vapor is merely caused by transportfrom the walls, no net change in the total quantityof vapor with x would be expected. To investigatethis hypothesis, we have performed a conservationanalysis on the total quantity of vapor in the nozzleas a function of x to determine the net rate of phasechange as the flow evolves. Since the projected x-raydata captures all the vapor in the path of the beam,we have numerically integrated the total area frac-tion of vapor across slices of the nozzle for a rangeof streamwise (x) positions. The results are shownin Figure 7. For x/L > 0.1, the total quantity of va-por remains relatively constant for all cases until theflow approaches the expansion, after which the vaporquantity drops as the bubbles collapse due to the de-celeration of the flow. This suggests that most phasechange occurs due to cavitation from the sharp noz-zle inlet. The vapor accumulation at the centerline

which occurs over 0.1 < x/L < 1 is either transportof vapor from the wall to the core of the flow viaan entrainment mechanism, or the production rateof vapor in the core is almost exactly equal to thevolume rate of cavitation bubble collapse, which isunlikely.

In cases 2 and 3, σ is varied over an order of mag-nitude and the Reynolds number is kept relativelyconstant. At σ = 2.3, (case 2), the vapor lifts fromthe wall very quickly and the projected quantity ofvapor along the nozzle centerline reaches its maxi-mum value at x/D ≈ 4. From σ = 11.2 to σ = 58.6,the lifting of the vapor from the wall is stretchedover a longer spatial extent, and the location of thecenterline peak remains relatively constant near thenozzle outlet. It is likely that the mechanism respon-sible for the mixing of vapor into the freestream issaturated in cases 1 and 3.

In case 4, Re is halved and σ kept approximatelyconstant with respect to case 1. Between cases 1 & 4the spatial extent of cavitation features is relativelyconstant but the vapor fractions are proportionatelyreduced across most of the domain by approximately20%. This is mostly due to increased static pres-sure, due to lower flow rates. Otherwise, the effectof halving Re does not change the distribution ofvapor in the nozzle significantly, given that the min-imum pressure remains below Pvap and cavitationnucleation still occurs. This suggests that withinthe range of Re investigated, turbulent mixing playsa less important role in the entrainment of vapor intothe freestream than the pressure gradient. This rein-forces the hypothesis that the accumulation of vaporalong the centerline is pressure-gradient driven.

3.2 Time-resolved measurementsTime-resolved measurements were taken at se-

lected positions of interest at the wall, in the en-trainment region, and in the freestream. The largestRMS magnitudes in the time-resolved signal were0.95% of the mean projected vapor quantity. Thus,the time-average measurements shown in Fig. 6 areindicative of a steady-state cavitation process thatdoes not exhibit any large-scale unsteady cavitation

6

(a) No cavitation (b) Cavitating case 1 (P1=1060 kPa, P2=87 kPa, σ=11.2,K=1.09.)

Figure 5: Time-integrated x-ray images of nozzle inlet, taken with an unfocused X-ray monochromatic X-raybeam.

(a) Measurement grid. (b) Case 1. Re =1.58× 104, σ = 11.2,K = 1.09

(c) Case 2. Re =1.57 × 104, σ = 2.3,K = 1.44

(d) Case 3. Re =1.58× 104, σ = 58.6,K = 1.02

(e) Case 4. Re = 8.36×103,σ = 10.7, K = 1.09

Figure 6: Raster-scan grid and interpolated contour plots of time-averaged vapor projection δzv. Verticallines indicate the walls. Flow is from bottom to top.

7

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4x/L

0.00

0.05

0.10

0.15

0.20

Vapor area fraction

Case 1Case 2Case 3Case 4

Figure 7: Experimentally measured total volumefraction of vapor in slices across the nozzle, for cases1-4. Error bars indicate the uncertainty in the totalintegral.

separation.The spectral content of these small fluctuations

was investigated using a sliding fast Fourier trans-form of the raw (unnormalized) signal from the PINdiode, and the results at several important probepoints are shown in Figure 8. Much of the con-tribution to the power spectrum occurs at low fre-quencies due to variations in the incoming beam andsources other than cavitation and turbulence. How-ever, variations in the spectra between the cavita-tion and non-cavitating conditions at certain probelocations are clearly visible. At the wall (Fig 8a),no change in the power spectrum is observed, asexpected. The frequency peaks which appear inboth cavitating and non-cavitating cases are due tothe x-ray source and other small mechanical vibra-tions, rather than being due to cavitation. All of thefrequency peaks above 10kHz can be attributed tothe synchrotron source, as they remain in the spec-trum when the experiment is removed from the beampath. In the freestream (Fig. 8c), a broadband in-crease in spectral energy is observed during cavitat-ing conditions. In the entrainment region where thevapor at the wall mixes with the freestream liquidflow (Fig. 8b), addition frequency components ap-pear around 4kHz (St = fD/U ≈ 0.04) which maybe characteristic of the mechanism which transportsvapor from the wall into the center of the flow. Sincethe time-averaged vapor distributions (Fig. 6) donot show any steady connection between the walland core vapor, the transport mechanism is likely tobe transient.

Power spectra were calculated along a series ofraster scan points at x/D = 0.8 and 1.2. The ratioof power spectral density between the non-cavitatingcase and cavitating case 1 is calculated, leaving only

the spectral contributions due to variations in thefluid density. The results are shown in frequency-space domain in Figure 9. It should be noted thatthese spectrographs have been interpolated over 15points in the horizontal axis.

The increase in spectral power due to cavita-tion is concentrated between 10−3 ≤ St ≤ 10−1.These results are notably different to cavitation mea-surements in other geometries. The lifting of a va-por cloud from the wall on a cavitating hydrofoilis known to be caused by an unsteady re-entrantjet mechanism[25]; cloudy cavitation is shed with St≈ 0.2. However, the cavitating nozzle in this studyshows no such large-scale fluctuations, and the smallfluctuations that do exist are at much lower St. Thissuggests that the mixing process in the cavitatingnozzle is very different in nature to two-dimensionalflows, being much steadier. The concentration ofspectral power at small St suggest that the char-acteristic time scales of cavitation clouds sheddingfrom the wall into the freestream are much slowerand steadier than those observed in two-dimensionalflows[26, 22].

4 ConclusionsIn this paper, we have undertaken measure-

ments of cavitation in a 500 µm diameter nozzle us-ing focused synchrotron x-rays. The time-averagemeasurements of vapor quantity achieve an uncer-tainty of 2%, similar to previously reported x-rayexperiments, but at several orders of magnitudesmaller spatial and temporal resolution. Vapor isobserved to separate from the wall and accumulatealong the nozzle centerline, similar to the CT exper-iments of Bauer et al[15]. The effect is even morepronounced in these smaller nozzles. A vapor vol-ume fraction conservation analysis suggests that thethe centerline vapor accumulation can be explainedby transport from the walls rather than an isolatedcavitation event, or dissolved gases in the fuel com-ing out of phase, since no net generation of vaporis observed in the region where significant vaporaccumulates along the nozzle centreline. Further-more, the acceleration of the fluid through the venacontracta[23] does not sufficiently drop the pressureto initiate cavitation. The centerline accumulationof vapor can most likely be explained by transportfrom the walls. If this is the case, it would explainwhy such an accumulation of vapor has not been ob-served in two-dimensional models, since a rectangu-lar nozzle would behave very diffrently to a circularone.

Spectral analysis in strongly cavitating regionsreveals that the spectral variations attributable to

8

102 103 104 105

Frequency, Hz

10-10

Power sp

ectral density, V2/H

zCavitationNo Cavitation

(a) x/D = 1.2, /y/R = 1. Power spectra at the wall.

102 103 104 105

Frequency, Hz

10-10

10-9

Power sp

ectral density, V2/Hz

CavitationNo Cavitation

(b) x/D = 1.2, /y/R = 0.9. Power spectra in the entrain-ment layer.

102 103 104 105

Frequency, Hz

10-10

10-9

Power sp

ectral density, V2/H

z

CavitationNo Cavitation

(c) x/D = 1.2, /y/R = 0. Power spectra in thefreestream.

Figure 8: Power spectra for cavitating nozzle. Both cavitating (case 1) and non-cavitating conditions areshown.

(a) x/D = 0.8. (b) x/D = 1.2.

Figure 9: Power spectral density map vs. Strouhal Number (vertical axis) and transverse co-ordinate (hori-zontal axis) at two streamwise co-ordinates in the cavitating nozzle. Dark regions indicate a proportionallylarger power spectral density at cavitating case 1 as compared to a non-cavitating condition.

9

cavitation occur in the range 10−3 ≤ St ≤ 10−1

and at very low power densities, in contrast to thelarger St values and RMS fluctuations which char-acterize the vapor shedding observed in cavitatinghydrofoils. This suggests that the transient vaporentrainment mechanism which is drawing vapor intothe freestream in this arrangement is occurring atmuch shorter length scales and longer time scales,resulting in a steadier flow than might be predictedin two-dimensional geometries[25, 22, 26].

Another important observation is that the at-tached vapor film at the wall separates less than onediameter downstream, so the nozzle L/D ratio doesnot have to be very large before significant mixingoccurs in the outlet. In practical terms, a fuel in-jector will have a very well-mixed vapor distributionby the time the fuel leaves the nozzle; this may haveimplications for the physics of spray breakup, sincetwo-dimensional channel visualisations of cavitatingspray nozzles[26] have not revealed this kind of mix-ing behavior.

AcknowledgmentsThis research was performed at the 7-BM beam-

line of the APS at Argonne National Laboratory.Use of the APS is supported by the U.S. Departmentof Energy (DOE) under Contract No. DE-AC02-06CH11357. The fuel spray research is sponsoredby the DOE Vehicle Technologies Program. The au-thors wish to thank Team Leader Gurpreet Singhfor his support of this work. We also acknowledgeProfessor David Schmidt and Dr Kshitij Neroorkarof the Department of Mechanical & Industrial Engi-neering at the University of Massachusetts, Amhest,for their substantial contribution to numerical sim-ulations which are not included in this paper butthat nevertheless informed the design and analysisof the experiment. We gratefully acknowledge thecomputing resources provided on “Fusion,” a 320-node computing cluster operated by the LaboratoryComputing Resource Center at Argonne NationalLaboratory.

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