High Resolution LES of cavitating 2-phase Ethanol Gasoline blends

Special Issue Article

International J of Engine Research14(6) 578589 IMechE 2013Reprints and permissions:sagepub.co.uk/journalsPermissions.navDOI: 10.1177/1468087413501824jer.sagepub.com

High-resolution large eddy simulationsof cavitating gasolineethanol blends

Daniel J Duke1,2, David P Schmidt3, Kshitij Neroorkar3,Alan L Kastengren4 and Christopher F Powell1

AbstractCavitation plays an important role in the formation of sprays in fuel injection systems. With the increasing use ofgasolineethanol blends, there is a need to understand how changes in fluid properties due to the use of these fuels canalter cavitation behavior. Gasolineethanol blends are azeotropic mixtures whose properties are difficult to model. Wehave tabulated the thermodynamic properties of gasolineethanol blends using a method developed for flash-boilingsimulations. The properties of neat gasoline and ethanol were obtained from National Institute of Standards andTechnology REFPROP data, and blends from 0% to 85% ethanol by mass have been tabulated. We have undertaken high-resolution three-dimensional numerical simulations of cavitating flow in a 500-mm-diameter submerged nozzle using thein-house HRMFoam homogeneous relaxation model constructed from the OpenFOAM toolkit. The simulations are con-ducted at 1 MPa inlet pressure and atmospheric outlet pressure, corresponding to a cavitation number range of1.0661.084 and a Reynolds number range of 15,00040,000. For the pure gasoline case, the numerical simulations arecompared with synchrotron X-ray radiography measurements. Despite significant variation in the fluid properties, thedistribution of cavitation vapor in the nozzle is relatively unaffected by the gasolineethanol ratio. The vapor remainsattached to the nozzle wall, resulting in an unstable annular two-phase jet in the outlet. Including turbulence at the condi-tions studied does not significantly change mixing behavior, because the thermal nonequilibrium at the vaporliquid inter-faces acts to low-pass filter the turbulent fluctuations in both the nozzle boundary layer and jet mixing layer.

KeywordsOpenFOAM, HRMFoam, gasoline, ethanol, X-ray radiography

Date received: 25 February 2013; accepted: 12 July 2013

Introduction

Cavitating channel flow is a complex fluid mechanicalphenomenon which has 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 producea spray. Cavitation leads to component wear and canmarkedly change the structure of the resulting liquidspray.2,3 These changes in spray structure can lead tochanges in engine performance, emissions, and effi-ciency.46

Gasolineethanol blends are becoming an importantfactor in injector design as their use increases and theethanol ratios also increase. A significant number ofstudies have been undertaken on the effects of ethanolblends on emissions.710 Experimental analysis of theeffects of gasolineethanol blend ratio on the spraystructure from simplified two-dimensional (2D) model

injectors reveals that the morphology of the spray isnot strongly affected by the quantity of ethanol.11

However, little work has been done on the effects ofgasolineethanol blend ratio on the internal flow ofcavitating nozzles. Gasolineethanol blends are azeo-tropic mixtures whose properties are difficult to model.

1Energy Systems Division, Argonne National Laboratory, Argonne, IL,

USA2Laboratory for Turbulence Research in Aerospace & Combustion,

Department of Mechanical & Aerospace Engineering, Monash University,

Melbourne, VIC, Australia3Department of Mechanical & Industrial Engineering, University of

Massachusetts, Amherst, MA, USA4X-Ray Science Division, Advanced Photon Source, Argonne National

Laboratory, Argonne, IL, USA

Corresponding author:

Daniel J Duke, Energy Systems Division, Argonne National Laboratory,

9700 South Cass Avenue, Argonne, IL 60439, USA.

Email: [email protected]

at City University Library on June 22, 2015jer.sagepub.comDownloaded from

Experimental approaches to measuring cavitationusing visible light are often limited to the analysis of2D nozzles and can only measure the outer structure ofcavitating regions.12,13 Recently, X-ray-based tech-niques have enabled measurements of the vapor frac-tion in three-dimensional (3D) cavitating flows.14

Synchrotron X-ray radiography methods which havebeen proven useful for measuring the mass distributionof fuel sprays15 are also being extended to measuringcavitation in model nozzles. However, X-ray propaga-tion techniques are only capable of measuring mass dis-tribution by attenuation (not velocity, pressure ortemperature). Numerical simulations are still essentialto understanding the fluid dynamics of cavitating noz-zles, and how they may be affected by variations influid properties.

A range of approaches have been used to modelcavitating flow. Many cavitation models simplify thetwo-fluid problem by assuming that the two-phase mix-ture can be approximated as a single fluid with varyingsound speed and density, with either compressible orincompressible mass conservation.1618 In a 3D simula-tion, interface velocity slip does not need to be modeledas long as the discretization is fine enough.19 Single-fluid models are often preferred over a full compressibletwo-phase calculation, since the time and length scalesbecome so small in the full compressible approach thatcomputational cost can become prohibitive, especiallyif a transient solution is desired over a reasonable time-span in a large domain. The use of a single-fluid modeloften leads to the assumption that the vapor and liquidphases are in instantaneous local equilibrium. In somemodels, a constant empirical time scale for homogeni-zation to local equilibrium has been used, with the con-tinued assumption of thermal equilibrium.20 However,such assumptions are not valid in cavitating flash-boiling flows which experience significant nonequili-brium in both phase change rate and temperature. Thehomogeneous relaxation model (HRM) used in thisstudy allows a variable relaxation time for both phasechange rate and temperature, which depends on thelocal pressure and void fraction.21

The modeling of fluid properties is also an importantfactor in considering how ethanol blending may affect acavitating nozzle flow. Many cavitation models handlefluid properties via an equation of state. A barotropicmodel is often used so that the density field can be cal-culated from the pressure field using predefined empiri-cal constants. However, when considering the effects offluid properties, a more accurate model of the fluidproperties may be desired. An alternative approach isto precompute a lookup table of fluid properties overthe desired pressure and temperature range.19 Sincelookup tables more accurately capture slight variationsin fluid properties, this approach is ideally suited to aninvestigation of the effects of various fuel blends.Previous experiments on the effect of fuel viscosity anddensity on nozzle discharge coefficient suggest a

significant sensitivity to viscosity at megapascal pres-sures, but little sensitivity to density variation.22

Neroorkar and Schmidt23 have used the HRM tomodel the cavitating and flash-boiling of fuel in a 3Dmultihole fuel injector nozzle with a range of fluids,including n-hexane, n-octane, and E60 and E85 ethanolblends. The fluid properties were obtained from lookuptables.24 They found that the E60 blend generated morevapor and a wider spray cone angle. These calculationsassumed a laminar flow, so the question remains as tohow the inclusion of turbulence may affect the mixingof vapor and liquid. Other questions which need inves-tigation are how the flow may be affected by a widerrange of ethanol blends, and how well the simulationresults might compare with experimental data in acanonical geometry.

Although previous studies have often neglected tur-bulence, it is known that it can have a significant effecton a cavitating flow.25 Where turbulence modeling isimplemented, the most popular approach is k2e, whichperforms well for free shear flows at modest pressuregradients, is computationally efficient, and permits sim-ple analysis of grid convergence.17,18,20,26 Som et al.27

investigated fluid properties by simulating the effects ofdiesel and biodiesel fuels, where the effects of turbu-lence were included using realizable k2e in both achannel flow and an axisymmetric injector geometry.They found that the local strain rate due to turbulentmixing was an important factor in cavitation inception.The largest turbulent features in nozzle flow are there-fore likely to strongly interact with cavitation features.This behavior can be more accurately captured usinglarge eddy simulation (LES), which is not as frequentlyimplemented.

In this article, we have undertaken high-resolution,3D LESs of cavitating flow in a canonical nozzle geo-metry at fixed pressure boundary conditions using thesingle-fluid HRM.21 The fluid properties have beenmodeled using precalculated lookup tables.24,28

Variations in cavitation behavior between a range ofgasolineethanol blends from E0 to E85 have beeninvestigated. For the pure gasoline case, the numericalsimulations are compared against synchrotron X-rayradiography measurements of the local void fraction.

Method

The canonical nozzle geometry used in the followingsimulations is a submerged nozzle with a throat dia-meter of D = 0.5 mm, and an expansioncontractionratio of 5. The nozzle length is 5D (2.5 mm), and thecontraction and expansion have hemispherical profiles.The inlet boundary condition is a fixed pressure of1.034 MPa and a temperature of 300 K, with zero velo-city gradient. The outlet boundary condition is a fixedpressure of 0.1 MPa, with zero velocity gradient. Thegeometry and boundary conditions were chosen tomatch those used in the X-ray experiments.

Duke et al. 579


The application of appropriate wall boundary condi-tions in LES remains an open research question. In thisstudy, we have applied the standard set of wall bound-ary conditions used in the OpenFOAM solver. Velocityis assumed zero at the wall, and density gradient isassumed to be zero. The flow is assumed isenthalpic, sono boundary conditions for the energy terms (such asthermal diffusivity) are required. For the LES modelterms, the subgrid scale viscosity uses the Spalding wallfunction for mSGS and k has zero gradient.

Gasolineethanol blend modeling

In order to obtain the properties of gasoline, a fuel sur-rogate was employed consisting of four components:15% isopentane, 20% hexane, 45% isooctane, and20% decane by mass. This surrogate was used byStyron et al.29 and was designed to match the distilla-tion curve of a California Phase II gasoline. The fluidproperty lookup tables required by the HRMFoamflow solver were generated by creating mixtures of theabove-mentioned surrogate with ethanol using theREFPROP fluid property program.28 The REFPROPprogram uses equations of states to calculate the ther-modynamic and transport properties of fluids andmixtures.

To confirm that the modeling procedure is accurate,experimental data from Takeshita et al.30 were used tocompare the distillation curves for the different ethanolblends in Figure 1. To predict the distillation curvesusing the REFPROP code, a subroutine was obtainedfrom EW Lemmon (April 2012, personal communica-tion). This subroutine solves the vaporliquid equili-brium for the surrogate to calculate the number ofmoles lost in the form of vapor during the distillationprocess, and consequently the volume of liquidobtained from the condensation of the vapor. The ratioof volume condensed to the original liquid volumegives the evaporated volume fraction.

The saturation pressure, density, viscosity, andsound speed of the gasolineethanol blend models at

the boundary conditions are shown in Figure 2. It canbe seen that, consistent with the observations of Karet al.,31 the REFPROP code predicts that the gasolineethanol blends show azeotropic behavior and the vaporpressure trend is nonlinear. The sound speed and visc-osity are at a minimum around 20% ethanol by vol-ume. The change in properties is relatively large overthe range of blends considered; the saturated liquidpressure decreases by around 50% and the liquid den-sity by 13% from E0 to E85.

HRMFoam solver

The solver used in the following study is the HRM(HRMFoam) for cavitating and flash-boiling flows,which is an in-house code running on the OpenFOAMtoolkit.32 A complete description of the solver is givenby Neroorkar et al.;21 a brief summary of which is givenhere. The HRM relates the substantial derivative of thevapor mass fraction (x) to the nonequilibrium timescale u

dx

dt=

x xu

1

where x is the equilibrium vapor mass fraction over thetime u. The value of x is calculated based on a flashingprocess, as implemented in REFPROP.33

The physical concept behind equation (1) is that thevapor fraction will return to an equilibrium value overa time u according to a complicated function which canbe linearized.34 The instantaneous mass fraction is cal-culated from the vapor volume fraction, density, andvapor density as x=arv=r, where the vapor volumefraction is defined as

a=rl rrl rv

2

The time scale u is calculated via an empirical rela-tion proposed by Downar-Zapolski et al.35

u= u0a0:54c1:76 3

c=Psat PPsat Pcrit 4

where the empirical constant u0 =3:843107s.21,23 Togeneralize their expression to multicomponent mix-tures, we use the bubble point pressure in place of Psat.In practice, the mass fraction of vapor in any given cellis almost always small; consequently, the bubble pointis a good representation of the pressure during phasechange. The mass, momentum, and energy conserva-tion equations are expressed in terms of mass fluxf= ru

r

t+r f=0 5

ru

t+r fu = rP+rt 6

300 320 340 360 380 400 420 440 460 480

0 0.2 0.4 0.6 0.8 1

Tem

pera

ture

, K

Evaporated Volume Fraction

E10E20E40E60E10E20E40E60

Figure 1. Distillation curves for several gasolineethanolblends calculated using the REFPROP model (lines), as comparedto the experimental data of Takeshita et al.30 (markers).

580 International J of Engine Research 14(6)


rh

t+r fh = P

t+ u rP 7

where t is the shear stress tensor. For a single-phaseflow, equations (5) and (6) can be closed to form apressure equation. However, due to phase change,equations (5)(7) are not closed, so equations (1)(4)are implemented to deal with the additional terms. Theoff-diagonal terms are represented by H(u) and thediagonal terms by a, such that ajuj=H u rP.34The derivation is described in full by Neroorkar andSchmidt23 The implicit solution for the pressure equa-tion is expressed in its final form as

1

r

r

P

x, h

rP

t+rrPfv

+ r

H(u)

aj

rr 1ajrP+ P

x

P, h

dx

dt=0

8

The first two terms concern the transmission of pres-sure waves and are neglected since they result in anasymmetric linear system for pressure. Such systemscost more to solve and produce less robust solutions.Past tests19 found that these compressibility terms hadnegligible impact on the predicted flowfield. The incom-pressible liquid assumption has previously been shownto yield reasonable results.21,23,25 The pressure equationis solved using a pressure-implicit split-operator (PISO)predictor-corrector algorithm with 10 iterations.36

Turbulence is modeled in this study using LES, with asingle-equation subgrid scale model.32,37 This allows usto investigate the instantaneous interactions betweenturbulent mixing and cavitation at large scales. The dis-cretization schemes are second order, using gamma dif-ferencing for the r, P, h, and u divergence terms and

upwind differencing for the turbulent effective k and edivergences. The Laplacian terms are discretized usingsecond-order central differencing. The pressure field issolved using the fast simplified diagonal-based incom-plete Cholesky preconditioner and a generalizedgeometric-algebraic multigrid solver for the final step,with under-relaxation. The r, h, k, e, and u fields aresolved using a simplified diagonal-based incompleteLU preconditioner and a preconditioned biconjugategradient method for the final step, with under-relaxa-tion. The solution is calculated on a cluster computer atArgonne National Laboratory, with OpenFOAMsimplementation of Message Passing Interface (MPI)parallelization over 96 CPUs. The time-steppingscheme is Courant number limited such that the localCourant number does not exceed 0.8 at any cell.

Mesh development and resolution study

The mesh used in the following simulations is a 3Dunstructured hex mesh with 8.4 million cells, as shownin Figure 3. The mesh is successively refined in thethroat region; the mean cell size relative to the throatdiameter is D=d50.

In order to determine the rate of convergence of thesolution with increasing mesh resolution, three succes-sively refined meshes with cell sizes of D=d=25,D=d=34, and D=d=50 have been solved out to asimulation time of 2 ms with neat gasoline as the work-ing fluid. Profiles of the steady-state, time-averagedvapor volume fraction, velocity, turbulent energy, andpressure are shown in Figure 4, along a streamwise vec-tor which passes near the throat wall where the flow isstrongly cavitating (at a radial position of r=R=0:96).

10 15 20 25 30 35 40

0 0.2 0.4 0.6 0.8 1Sa

tura

tion

Pres

sure

(kPa

)

Ethanol fraction

Current StudyKar et al

960

1000

1040

1080

1120

0 0.2 0.4 0.6 0.8

Soun

d sp

eed,

m/s

Ethanol fraction

Inlet conditionsOutlet conditions

2x10-4

4x10-4

6x10-4

8x10-4

1x10-3

0 0.2 0.4 0.6 0.8

Dyn

amic

Vis

osity

, Pa-

s

Ethanol fraction


660 680 700 720 740 760 780

0 0.2 0.4 0.6 0.8

Den

sity

, kg/

m3

Ethanol fraction


Figure 2. Calculated properties of gasolineethanol blends at the boundary conditions (inlet pressure 1 MPa, outlet pressure 0.1MPa). Vapor pressure reference data are from Kar et al.31

Duke et al. 581


The three time-averaged solutions have been used toperform a Richardson extrapolation to determine howclose the D=d=50 mesh is to a converged solution.The sum square error in the centerline pressure is0.04% with respect to the converged solution since it ispinned by the boundary conditions. The velocity mag-nitude is within 0.12%, and the density is within 0.66%.

The turbulent energy and vapor fraction are within1.2% of convergence. Given that the Richardson extra-polate of three successively refined meshes may not rep-resent the true converged solution, a series expansionerror contribution of order O(dkn+1) is included in theabove error values, where kn is the convergence rate ofthe extrapolation.

Figure 4. Convergence of time-averaged vapor volume fraction, velocity magnitude, turbulent energy, and pressure with increasinggrid resolution, plotted along a streamwise vector near the nozzle wall, at a radial position of r=R= 0:96.

Figure 3. Mesh of cavitating nozzle: (a) centerline slice, cropped around the nozzle throat and (b) oblique view.



Results and discussion

The solution is run until the net momentum and massflux reach a steady state, which occurs after approxi-mately 0.8 ms. The solution is then run out to at least 1ms. Figure 5 shows the evolution of the minimum andmaximum density and the maximum velocity withrespect to simulation time. The minimum density is agood marker of cavitation inception; phase changebegins about 0.4 ms after start of injection at the givenpressure gradient and reaches a steady state after 0.5ms. The maximum velocity magnitude reaches a steadystate very close to the Bernoulli velocity UB=2

DP

p=r,

as expected.16 The selected boundary conditionsand fluid properties result in a Reynolds numberrange of ReD=UD=nl2 (1:53104,4:03104) and a cavi-tation number range of K= P1Pvap

= P1P2 2

(1:066,1:084). Both Re and K vary due to the change indensity, viscosity, and vapor pressure of the varyingblends, while the pressure and geometry remain con-stant (see Figure 2). The bulk velocity U is the meancenterline pressure in the nozzle throat, which is closeto the Bernoulli velocity.

Most cavitation vapor is generated at the sharp inletto the nozzle. The vapor in the computations sticks tothe wall through the nozzle since nearly all the pressuredrop happens in the inlet region and the pressure gradi-ent along the nozzle throat is flat. Centerline slices ofvapor volume fraction in the nozzle for each of theblends studied are shown in Figure 6. An annular jet ofvapor is generated at the nozzle outlet. This unstableconfiguration rapidly breaks down and the vaporjet mixes with the surrounding liquid, as shown inFigure 7. A reasonable fraction of the vapor does notcondense but is convected through the outlet. Very lit-tle change in the vapor distribution is observed acrossthe different blends investigated; this is a surprisingresult given the significant change in fluid properties.

In the application of cavitating nozzles to fuel injec-tion systems, the main location of interest is the nozzleexit plane, where the mass flow rate, velocity profile,and vapor distribution will have an impact on sprayformation.3 The time-averaged steady-state velocity

distribution over the outlet plane has been azimuthallyaveraged to generate a mean radial profile, as shown inFigure 8. The velocity magnitude (Figure 8(a)) has awell-developed profile which does not vary significantlywith ethanol blend. The spanwise velocity components

Figure 6. Centerline slices of vapor volume fraction at 1 msafter start of injection. The nozzle outlet is submerged. (a) E0(neat gasoline), (b) E10 (10% ethanol, 90% gasoline), (c) E20(20% ethanol, 80% gasoline), (d) E40 (40% ethanol, 60%gasoline), (e) E60 (60% ethanol, 40% gasoline), and (f) E85 (85%ethanol, 15% gasoline).

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1

|U| m

ax /

UB

Time, ms

E0E10E20E40E60E85

-1000

100200300400500600700800900

0 0.2 0.4 0.6 0.8 1

Den

sity

, kg/

m3

Time, ms

E0E10E20E40E60E85

Figure 5. Evolution of density extremes and maximum velocity (normalized by the Bernoulli velocity) in transient solution.

Duke et al. 583


indicate that the flow becomes slightly more divergentnear the wall as the ethanol ratio increases. The totalmass flux in the outlet plane is shown in Figure 9(a),normalized as a discharge coefficient

CD=_m

A

1 b42rDP

s9

where b=0:2 is the nozzle diameter contraction ratioand _m=

rUdA. For a round nozzle, Nurick1 predicts

a discharge coefficient of CD=CCK

p, where the coef-

ficient CC0:61 for a sharp-edged nozzle with b! 0.16Figure 9(a) indicates that Nuricks relation tracks

reasonably well with the simulation results. UsingCC=0:61, Nuricks relation underpredicts the massflux by about 5%. In addition to the effect of the non-zero b, the hemispherical inlet profile to the nozzle willcause an increase in CC similar in effect to an obtuseinlet angle, which would explain the underprediction.However, the effect of b is known to be very small; CDvaries with b as

1 b4

p0:9992 in this geometry.38

The best fit value for the results is CC0:63, whichagrees reasonably well with previous simulations of theeffects inlet angle.16

The vapor mass flux weighted by the total massflux is calculated as _mv=

xrUdA and is shown in

Figure 9(b). The vapor flux decreases by a factor of 3from E0 to E85 blends, peaking for the E40 blend. Anincrease in vapor flux corresponds to a reduction inCD. Given that the vapor volume fraction and its spa-tial extent do not significantly change (Figure 6), thissuggests that the discharge coefficient is not varyingdue to area occlusion, but rather due to changes in den-sity caused by variation in fluid properties.

X-ray radiography measurements

In order to provide experimental comparison of thesimulation results, X-ray radiography measurements ofa cavitating flow in a nozzle of the same nominal

0.6

0.62

0.64

0.66

0.68

0.7

0 0.2 0.4 0.6 0.8

CD

Ethanol Fraction

SimulationsNurick, CC =0.61Nurick, CC =0.63

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6 0.8

Ethanol Fraction

SimulationsX-ray Experiment

(a) (b)

Figure 9. Time-averaged fluxes at the nozzle outlet plane, for (a) total mass flux as a discharge coefficient and (b) weighted vapormass flux versus blend ratio.

0

10

20

30

40

50

60

-1 -0.5 0 0.5 1

Vel

ocity

mag

nitu

de (m

/s)

r/R

E0E10E20E40E60E85

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

-1 -0.5 0 0.5 1

Span

wis

e ve

loci

ty (m

/s)

r/R

E0E10E20E40E60E85

(a) (b)

Figure 8. Time-averaged and azimuthally averaged radial velocity profiles in the nozzle outlet plane, for (a) the streamwisecomponent of velocity and (b) the total spanwise component for the different blends considered.

Figure 7. Iso-contours of cavitation vapor distribution for E20blend, 1 ms after start of injection.



geometry as that used in the simulations have beenundertaken using a commercial gasoline surrogate whoseproperties are close to the E0 model. Measurements wereperformed at the 7-BM beamline of the AdvancedPhoton Source (APS) at Argonne NationalLaboratory.39 A schematic of the experiment is given inFigure 10(a). The X-ray beam is monochromatic, with amean energy of 8 keV, a bandwidth of 1.4% full widthat half maximum (FWHM), and a flux of approximately2:531011ph=s. The beam is focused to a spot size of536mm FWHM with a pair of KirkpatrickBaez mir-rors. The focused beam acts as a microprobe, allowingthe cavitation vapor fraction over a small area to beprobed along a line of sight. The incoming X-ray inten-sity is normalized and the transmitted X-rays are col-lected by a 300-mm-thick PIN diode. The experiment isplaced 36.5 m downstream from the source; the PINdiode is approximately 5 cm downstream of the experi-ment. The normalized PIN diode reading is sampled fordt=0:5 s at each sample point.

The quantity of cavitation vapor is measured alonga line of sight dz at some point of interest. The experi-ment is then repeated at a noncavitating conditionwhere the nozzle is filled with liquid at the same inletpressure, but over a very small pressure gradient wherethere is no cavitation (denoted by prime). The presenceof vapor results in a relative increase in transmissiondue to a reduction in the absorbing mass in the beampath. The X-ray attenuation through the sample can be

described by the LambertBeer Law. The known den-sity of the liquid phase is used to convert mass per unitarea measurements from radiography to a path lengthdzv, which represents the projected depth of vapor inthe path of the beam

dzv=1mlrl

loge

I1I0I91I90

!10

The quantity of vapor is expressed as the total pathlength of vapor dzv in the beam, rather than an averagevapor fraction since the vapor is not evenly distributedalong the line of sight. An example of a typical mea-surement is given in Figure 10(b); the X-ray beam inter-acts with both the vapor near the wall and the liquid inthe core of the flow, and the resulting measurement isintegrated along the beam path.

The attenuation coefficient ml is measured by fillingcapillary tubes with the working fluid, water, and air,and measuring the X-ray transmission through thetubes. It was found that mlrl0:3124mm

1. We haveneglected the vapor phase attenuation coefficient sincerv rl. The uncertainty in the time-averaged projectedvapor quantity is determined by error propagation cal-culations to be edzv63:5mm of vapor (0.007 D), whichis 2% of the maximum path length of vapor in a typicalmeasurement.

In earlier X-ray experiments, a significant quantityof vapor was observed along the nozzle centerline that

PiNDiode

monochromaticx-ray source

Nozzle Wall

LiquidVapor

(a)

(b)

Figure 10. X-ray radiography experiment. (a) Monochromatic radiography microprobe setup at Sector 7-BM of the AdvancedPhoton Source. The diagram is not to scale; the distance from the source to the experiment is 35.5 m. The beam is focused to a 5 36 mm spot where it passes through the nozzle. (b) Example cross-section of submerged nozzle, showing the typical interaction ofthe X-ray beam with the flow.

Duke et al. 585


was not captured in the models. Such features were alsoobserved in the X-ray tomography experiments ofBauer et al.14 and were proposed to be related to cavi-tation phenomena; either migration of vapor awayfrom the wall or perhaps a string type along the nozzlecenterline. A recent numerical modeling study consid-ered the modeling of dissolved gas and cavitation inpure gasoline in the same submerged geometry40 andproposed that this centerline vapor may be due to dis-solved gas in the fuel coming out of solution, ratherthan cavitation. Since the X-ray radiography experi-ment is unable to distinguish between the two phenom-ena clearly, the experiment was repeated with the fueldegassed, and the results of this improved experimentare those shown in Figure 11. Once dissolved gas iscontrolled for, the experiment and model agree reason-ably well, although some asymmetry remains. The noz-zle wall was smoothed in the experiment to removemachining defects which may cause asymmetry. Theasymmetry that remains in Figure 11(b) is indicative ofthe fact that cavitation inception depends on localnucleation at the wall, and small machining defects canlead to large deviations of the vapor distribution fur-ther downstream, even in a very smooth nozzle.

In order to directly compare the X-ray data againstthe LES, simulated X-ray experiments are performedon the mesh by projecting several thousand raysthrough the domain and computing the projectedvapor distributions. The resulting measurements are avolume integral of the local vapor fraction normalizedover the X-ray beam cross-section, normalized to unitsof micrometers. The results are shown in Figure 11.Just downstream of the nozzle inlet in Figure 11(a),both experimental and simulated profiles take the formof an annular vapor distribution. The differencesbetween the experiment and the simulation for the puregasoline case are significantly larger than the variationsbetween the different gasolineethanol blends.

The variations between experiment and simulationare much more significant than the variations between

the different simulation cases, suggesting that ethanolblend does not strongly affect the distribution of vaporin the nozzle. Furthermore, the distribution of vaporcan be integrated in a plane to determine the total arearatio occluded by vapor, and by combining this withthe known mass flow rate of fuel (using a turbine flow-meter), the weighted vapor mass flux in the outlet planecan be estimated as _mv _m(Av=A)(rv=r), assuming thatthe slip velocity is not significant. The resulting vaporflux is shown in Figure 9(b) and agrees well with thesimulation results.

Influence of turbulence modeling

The effect of using LES for turbulence has also beeninvestigated. In addition to the HRMFoam cavitatingLES, the pure gasoline case has been simulated with alaminar assumption (phase change, but no turbulencemodel) and a single-phase incompressible LES using aPISO solver (turbulence modeled, but no phasechange). A comparison of the predicted velocity fieldsin centerline slices through the nozzle at 1.2 ms afterstart of injection is given in Figure 12. The single-phasesolution (Figure 12(a)) has a wide range of turbulentlength scales and a developing boundary layer in thethroat as expected of a turbulent liquid jet. Here, thereis no phase change nonequilibrium to impede turbulentmixing in the outlet.

The regions of high vapor fraction are also theregions of greatest shear (i.e. the nozzle throat bound-ary layer and jet mixing layer). As such, the nonequili-brium between vapor and liquid acts to eliminate mostof the boundary layer momentum deficit in the nozzlethroat and also acts to low-pass filter the smaller scalesof turbulence in the jet mixing layer. Thus, the single-phase model (Figure 12(a)) shows a higher turbulenceintensity than the cavitating cases (Figure 12(b)and (c)).

It is interesting to note that turbulence in the jetwake takes longer to develop in the LES case

(a) (b)

Figure 11. Projected vapor quantity dzv=R from X-ray measurements at two streamwise locations along the nozzle. The X-ray dataare compared against simulated projections from the numerical data, at 1 ms after start of injection: (a) x=L= 0:1 and (b) x=L= 0:7.



(Figure 12(c)) than in the laminar case (Figure 12(b)).Initially, this seems counterintuitive because the LESmodel should show a more unsteady flow, as the effectsof subgrid scale turbulence are now being considered.However, when the damping effects of cavitation phasechange are considered, it becomes apparent that cavita-tion will deter turbulent mixing at the subgrid scaleequally effectively as at the cell scale. The result is arelative decrease in turbulence intensity as compared tothe noncavitating case, which results in an increasednumerical viscosity applied at the cell level when LES isimplemented. The effects of cavitation dominate turbu-lent effects near the wall where most turbulence is pro-duced, resulting in a slightly steadier flow. Conversely,a laminar simulation overpredicts the instability of theflow because the damping effects of phase change areonly applied at a cell level (i.e. at low wavenumbers),making the flow artificially more unstable. The imple-mentation of LES does not significantly alter the vaporproduction prediction, only the turbulent developmentlength of the jet wake.

Conclusion

A submerged nozzle of 500 mm diameter has been mod-eled using high-resolution LES and the HRMFoamcavitation and flash-boiling solver of Neroorkar etal.,21 using tabulated fluid properties. The purpose of

the simulations was to investigate the effect of varyinggasolineethanol blends on the vapor distribution in acanonical geometry. The simulations were also com-pared to an X-ray radiography measurement of fluiddensity.

Despite a significant variation in the fluid properties,the distribution of vapor does not vary much at all frompure gasoline up to 85% ethanol, with respect to vol-ume fraction and spatial extent. The vapor mass flux inthe nozzle exit plane varies by a factor of 3 from E0 toE85, peaking at E40. This occurs due to the variation influid density with ethanol ratio since the profile of thevena contracta does not vary between cases. Given thatK does not change much as the inlet pressure increasesand the nozzle is effectively choked, it is likely that theeffects of fluid properties such as vapor pressure aresaturated at lower cavitation numbers. Furthermore,laminar and single-phase solutions in the pure gasolinecase indicate that turbulence modeling with LES doesnot significantly alter the vapor fraction or velocityfields with respect to a laminar flow assumption; how-ever, it does act to damp instability in the jet wake. TheReynolds numbers achieved in the simulations are inthe range of 15,00040,000 depending on the viscosityand density of the fluids. In a fuel injector, the cavita-tion number is likely to be much higher due to thelarger pressure gradient, and the Reynolds number willbe similar. Therefore, it may be hypothesized that simi-lar sensitivity to the blend ratio would be observed in acavitating axial single-hole injector.

The X-ray cavitation measurement was found to behighly sensitive to the quantity of dissolved gas in thefuel, necessitating that the fuel be degassed prior to theexperiment. As such, prediction of the location ofvapor in the nozzle depends on the level of degassing. Itremains to be seen as to how factors not included in theHRM model such as transmission of pressure waves inthe liquid phase may affect the solution. The separationof vapor from the wall in the experiment which doesnot occur in the simulations is also a matter for furtherinvestigation. The simulations presented here suggestthat the cavitation vapor distribution in a nozzle of suf-ficiently large cavitation number will not be affected bygasolineethanol blend ratio.

Acknowledgements

The authors wish to acknowledge Dr Eric Lemmon ofthe National Institute of Standards and Technology(NIST) for his support in the fluid property modelingprocess described in section gasolineethanol blendmodeling. They also acknowledge the use of DrLemmons program code to generate the distillationcurves in Figure 1. They gratefully acknowledge thecomputing resources provided on Fusion, a 320-nodecomputing cluster operated by the LaboratoryComputing Resource Center at Argonne NationalLaboratory. The authors also acknowledge GeneralMotors Research Center, NASA, and the National

Figure 12. Centerline slices of velocity magnitude for E0 (neatgasoline) at 1.2 ms after start of injection. Contour units are m/s. (a) Single-phase PISO LES (no phase change); (b) HRMcavitation model with laminar, unsteady flow; and (c) HRMcavitation model with LES.

Duke et al. 587


Science Foundation for their support of the develop-ment of HRMFoam. The X-ray experiments presentedin this research were performed at the 7-BM beamlineof the APS at Argonne National Laboratory. Theauthors wish to thank Team Leader Gurpreet Singhfor his support on this work.

Declaration of conflicting interests

The authors declare that there is no conflict of interest.

Funding

Use of the APS is supported by the US Department ofEnergy (DOE) under Contract No. DE-AC02-06CH11357. The fuel spray research is sponsored bythe DOE Vehicle Technologies Program. D.J.D. wassupported by an ANSTO Fulbright Scholarship inNuclear Science & Technology during the research.

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