ILASS Americas 28th Annual Conference on Liquid Atomization and Spray Systems, Dearborn, MI, May 2016

Direct Numerical Simulation of Aerated-Liquid Injection within ‘Out-In’ and ‘In-Out’

Nozzle Designs

Brett J. Bornhoft, Jack R. Edwards*,

Mechanical and Aerospace Engineering Department

North Carolina State University

Raleigh, NC 27695 USA

Susan Cox-Stouffer, Kuo-Cheng Lin

Taitech, Incorporated

Beavercreek, OH 45430 USA

Abstract

Direct numerical simulations of two-phase liquid water / gaseous nitrogen flow within prototype aerated-liquid in-

jectors being considered for cold-start fueling are presented in this paper. The aerated liquid injectors each consist

of a plenum chamber, a mixing chamber, and a nozzle but differ in how the aerating gas is introduced into the flow.

In the ‘out-in’ design, gas is injected through small orifices oriented along the perimeter of the mixing tube; in the

‘in-out’ design, gas is injected through a centrally-located perforated tube. A homogeneous mixture formulation of

the Navier-Stokes equations is solved using a sharp interface capturing method combined with a continuum surface

tension model. The ‘resolving power’ of the interface-capturing scheme is limited by a CFL condition. As a result,

the scheme cannot accurately capture structures smaller than about 50 µm for the present mesh sizes. For a gas-to-

liquid mass ratio (GLR) of 0.04, the aeration gas forces the liquid toward the walls of the nozzle, producing a thin

film that is deformed by aerodynamic shear forces in the highly-turbulent nozzle flow. Parcels of liquid are stripped

from the annular liquid sheet, populating the interior of the nozzle with liquid material. The ‘internal atomization’

process is more rapid for the ‘in-out’ design, as the rapid acceleration of the two-phase flow into the nozzle produces

a vena contracta that leads to very high velocities (< 250 m/s) in this region. The momentum flux of the exiting

two-phase flow is higher for the ‘out-in’ design. Comparisons with experimental line-of-sight density measure-

ments obtained using X-ray radiography for the in-out injectors show good agreement in the annular and mixing

regions. The calculations predict a higher liquid content in the exiting nozzle flow than evidenced in the experi-

mental measurements.

*Corresponding author: jredward@ncsu.edu

Introduction

The next generation of DoD scramjet combustors

will be designed to use only JP-class fuels. At low aer-

odynamic heating loads, the fuel will enter the combus-

tor as a liquid and it will undergo atomization before

vaporizing and burning. To accelerate the atomization

process, gas aeration is being considered as a means of

inducing primary breakup of the fuel within the injec-

tor. Aerated-liquid injection has been studied for sev-

eral years at AFRL. In [1], Lin, et al. compare charac-

teristics of sprays produced by aerated-liquid injectors

at various gas-to-liquid mass ratios (GLR) with that

produced by a pure liquid injector for water injection

into a supersonic crossflow. In a later study [2], X-ray

phase-contrast imaging techniques were used to probe

the outer portions of the spray. This study revealed that

small droplets with Sauter mean diameters of around 20

µm are formed as are larger bubbles. The spray cone

angle is a strong function of the nozzle shape, with a

converging-diverging nozzle leading to the largest cone

angle. Later studies [3,4] used X-ray radiography to

probe the ‘denser’ near-field parts of the spray. These

studies were able to determine regime maps that con-

nect the structures of the spray with aeration level, flow

rate, nozzle shape, and operating pressure. They con-

cluded that a core-annular two-phase flow structure is

the likely outcome of the internal aeration process. X-

ray fluorescence measurements were used in [5] to im-

age the (relative) density variation experienced within

the dense portion of the spray and from this, to distin-

guish specifically regions occupied by the aerating gas.

The results provide some indication of the degree of

kinematic non-equilibrium of the two-phase mixture as

it expands outside the nozzle.

All of the preceding studies focused on the spray

itself – no details of the internal processes that lead to

the formation of the spray were provided – and all ex-

cept [1] used a type of injector in which gas is injected

from a circular manifold into a straight tube containing

the liquid flow. This type of injector is termed an ‘out-

in’ design. More recently, X-ray radiography and fluo-

rescence line-of-sight measurements of the time-

averaged internal flow structure within another type of

injector, termed an ‘in-out’ design (see Figure 1), have

been taken.[6] In the ‘in-out’ design, aerating gas

flows through a perforated central tube into a co-

flowing, annular stream of liquid. The gas and liquid

interact within a ‘mixing chamber’ before flowing into

the nozzle and exiting the injector.

This new data can serve as validation for computa-

tional approaches that attempt to capture the fine-scale

details of the aeration process. A successful validation

would pave the way for the use of numerical simula-

tions to determine how the aerating gas accelerates pri-

mary breakup and how the process depends on the pa-

rameters of interest, such as liquid flow rate, GLR, and

nozzle shape. The present study utilizes direct numeri-

cal simulation techniques to capture the two-phase mix-

ing process in a time-dependent fashion. The numeri-

cal methods employ interface-sharpening techniques

and continuum surface-force models to simulate the

interaction of aerating-gas pockets with the co-flowing

liquid stream. Earlier efforts at applying such tech-

niques to ‘out-in’ and ‘in-out’ injector configurations

have been presented in [7] and [8]. These simulations

were conducted for smaller injectors without nozzle

extensions and utilized smaller meshes. A more recent

study, focusing on an ‘out-in’ injector, was presented in

[9]. Selected results from this study are included in the

present work to highlight differences in the aeration

process as achieved through ‘out-in’ and ‘in-out’ de-

signs. The remainder of the paper discusses the numeri-

cal methods employed and describes results of simula-

tions of two-phase flow in ‘out-in’ and ‘in-out’ aerated-

liquid injectors at a liquid flow rate of 18.2 g/s and a

gas-to-liquid (GLR) mass ratio of 0.04.

Numerical Methods

REACTMB-INS

Flow simulations described in this work were con-

ducted using NCSU’s REACTMB-INS flow solver.

REACTMB-INS solves a weakly-compressible, iso-

thermal form of the Navier-Stokes equations using a

time-derivative preconditioning technique. [7] A dual-

time stepping method is used to solve an implicit dis-

cretization of the time-dependent equation system to a

prescribed tolerance at each physical time step. Two-

phase flow effects are accounted for by solving a conti-

nuity equation for the vapor phase, in addition to the

bulk continuity equation:

0)()(

j

jvv

x

u

t

(1) (1)

where is the gas-phase volume fraction. Closure of

the equation system is facilitated by the following rela-

tions:

)/()(

)1(

)1()(

RTpp

p

v

lv

lv

(2)

Liquid density and gas / liquid viscosities are consid-

ered constants.

Time advancement is facilitated by a precondition-

ing technique described in [7] for incompressible two-

phase flows. For the weakly-compressible flows con-

sidered herein, a transition to supersonic flow is possi-

ble. Eigenvalues of the preconditioned equation sys-

tem have the following form:

222

222

222

22222

3,2

1

/

))/||,,max(,min(

m/s 1500,,11

4)1()1(

aVM

pUuuaV

aRTaaaa

VnuMnuM

nu

RR

refR

lv

llvv

RRR

(3) (3)

In the calculations presented in this work, the reference

velocity ref

U is set to 60 m/s. The definition of 2

RV also

includes a term that is proportional to the local pressure

difference.

THINC-EM

The current work employs the Tangent Hyperbola

Interface Capturing (THINC) method [10] as a means

of resolving sharp liquid / vapor interfaces. The par-

ticular variant of the THINC scheme employed was

first described in [7] and was later improved in [11].

The basic idea is utilize a tangent hyperbola function as

the model for the variation of the volume fraction with-

in a mesh cell instead of the polynomial model em-

ployed in total variation diminishing (TVD) or piece-

wise parabolic methods (PPM). Complete details of the

method are given in [7], and only the most current im-

plementation is described in this paper. Given that the

index ‘i’ represents a particular mesh cell bounded by

interfaces ‘i+1/2’ and ‘i-1/2’, expressions for the vol-

ume-fraction reconstruction at each interface are as

follows:

]1)(2

exp[

1)cosh()tanh(

1

]1)(2

exp[

]1)([tanh)cosh(

1)tanh(

1

])sinh()log[cosh(1

])sinh()log[cosh(1

)1)((2

1

)1)((2

1

minmax

min2/1,

minmax

min2/1,

2

2/12/1

2/1

2/12/1

2/1

minmaxmin2/1,

minmaxmin2/1,

iR

iL

ii

i

ii

i

iR

iL

ST

TB

ST

TB

BCCC

G

BCCC

G

SG

SG

(4)

In this, is a sharpening factor. A value of 3.5 is

used in this work, which means that mesh-aligned inter-

faces are captured with at most one interior cell. The

following definitions bound the reconstructed volume

fractions at the cell interfaces to lie within the range

spanned by volume fractions at2/1, iR

and 2/1, iL

)sgn(

),max(

),min(

2/1,2/1,

2/1,2/1,max

2/1,2/1,min

iLiR

iLiR

iLiR

S

(5)

In this formulation, an initial monotone reconstruc-

tion of the volume fraction distribution is needed as a

basis for the sharpening strategy. In the present work,

we use a first-order reconstruction for the majority of

the calculations:

iiR

iiL

2/1,

2/1,

(6) (

A TVD-type reconstruction is also used for certain cas-

es:

),(minmod2

1

),(minmod2

1

112/1,

112/1,

iiiiiiR

iiiiiiL

(7)

The response of THINC-EM is affected by the rate

at which the volume fraction discontinuity propagates

across the cell. The following definitions of a local

CFL number control this rate.

),min(),,max(

))||

)(,1max(,1min(

2/12/12/12/1

2/12/1

2/12/1

2/1

iiii

ii

ii

i

CCCC

nx

tnuC

(8)

If the local CFL number (in magnitude) reaches or ex-

ceeds one, the reconstruction model sets the corre-

sponding left or right state for the volume fraction to

the local cell-interface values 2/1,2/1,

, iLiR

determined

from the initial monotone reconstruction. In the above

expressions, is a small number (10-12) that is used to

avoid division-by-zero errors where the volume fraction

is zero.

The THINC-EM scheme’s ‘resolving power’ de-

pends directly on the choice of the interface CFL,

which itself depends on the time step. Optimal inter-

face-capturing performance occurs when the local CFL

is small, and it is possible in some cases to simply set

2/1iC to zero. However, for the injector configurations

discussed next, the two-phase flow accelerates rapidly

prior to exiting the nozzle, and local CFL numbers can

easily reach or exceed unity. Setting 2/1i

C to zero in

these cases can lead to an unphysical rate of transfer of

mass across the cell interface and the appearance of

pockets of unresolved fluid, termed ‘flotsam’ and ‘jet-

sam’ in the literature. Mass ‘leakage’ from vapor to

liquid phases is a common consequence, as is numerical

instability. The alternative of including the CFL de-

pendence leads to the loss of resolving power but ena-

bles good vapor and liquid mass conservation.

Interfacial Tension Modeling

REACTMB utilizes a continuum conservative for-

mulation of interfacial tension effects first presented in

[12]. The specific form of the interfacial force vector

is

|~|/~~

)~~(|~|

curvatureonlocalizati

,

ii

jjiij

A

is

xn

dAnnnF

(9) (7)

As shown, the force term consists of an interface

localization component and a curvature component.

To compute the latter accurately, it is necessary to uti-

lize a mollified (or smoothed) volume-fraction function.

In this work, we use a few steps of a Jacobi method to

compute the smoothed volume-fraction field.

Experiments

The focus of the present study is toward predicting

the effects of gas aeration in accelerating jet breakup.

Attention is focused on an injector configuration

sketched in Figure 1. This configuration is referred to

as an ‘in-out’ design, as aerating gas enters from a per-

forated tube into a co-flowing annular stream of liquid.

An earlier design, termed an ‘out-in’ configuration,

involves gas injection from an outer plenum into a dis-

charge tube. The ‘in-out’ design is simpler to machine

and offers the additional advantage of being able to

achieve a choked-flow condition when operating using

vaporous fuel. The injector geometry was machined

from beryllium by virtue of its low X-ray absorption

properties. X-ray radiography and fluorescence line-of

sight measurements were recorded for two ‘in-out’ con-

figurations, one containing two rows with two orifices

per row (Case 2) and the other containing ten rows with

two orifices per row (Case 5). (See Figure 1). Liquid

water mass flows were held at 18.2 g/s while the gas-to-

liquid mass ratio (GLR) was fixed at 4% for each case.

The aerating gas is nitrogen. The data available con-

sists of time-averaged line-of-sight measurements of

liquid-phase density )1( l

extracted at different

locations within the injector. The extracted points can

be combined to create a contour map of liquid density

within the annulus region, mixing region, and nozzle

regions of the injector (see Figure 1). Details regard-

ing the experiments may be found in [6].

Computational Meshes and Boundary Conditions

Computational Meshes

Meshes generated for the simulations described

herein encompass the annular region, the gas plenum

chamber, the injection ports, the main mixing chamber,

and the nozzle. GridPro (Program Development Com-

pany) was used for mesh generation. Figure 2 shows

side views of the Case 2 geometry. Inset figures show

details of the mesh resolution near the injector ports and

within the nozzle. The average mesh spacing in the

nozzle tube is around 17 µm. Considering that the in-

terface-sharpening methods generally include one inte-

rior zone when capturing an interface, this means that

structures no smaller than about 50 µm can be effec-

tively resolved. The mesh for Case 2 contains 34.4 M

cells, while the mesh for Case 5 contains 36.7 M cells.

The ‘out-in’ geometry utilized as a point of comparison

contains 35.1 M Cells.

Boundary Conditions

In simulations involving pressure-driven flow

through manifold-type geometries, the pressure differ-

ential that produces a specified mass flow rate is rarely

known precisely. One must specify either the pressure

differential or the mass flow rate. We have had better

success in imposing the pressure differential by specify-

ing stagnation pressures at the inflow of the mixing

tube (pure liquid) and the inflow of the plenum cham-

ber (pure vapor). Given the stagnation pressure and

flow direction, the static pressure at the inflow can be

determined from Bernoulli’s principle if the velocity

magnitude is extrapolated from the interior. With this

strategy, there is no way to simultaneously specify the

volume flow rates and thus no way to maintain a speci-

fied GLR. To overcome this problem, the stagnation

pressures are updated at each time step according to an

ad hoc rate law that depends on the difference between

the actual mass flow rate at a given inflow and a target

value:

)()(

)()(

1

target,2

target,

,

1

,

1

target,2

target,

,

1

,

n

vapvap

vapvap

vapn

vapo

n

vapo

n

liqliq

liqliq

liqn

liqo

n

liqo

mmA

mpp

mmA

mpp

(10) (10)

Here, liq

A and vap

A are the cross-section areas of the

entrance tubes for the liquid and vapor, respectively

This procedure is effective in forcing the flow rates to

remain near their target values after enough time has

elapsed.

Results

Out-in injector

Reference [9] describes results obtained for an

‘out-in’ geometry operating at 18.2 g/s liquid flow rate

at a GLR of 0.04. A few of these results are repeated

here to anchor comparisons between the ‘out-in’ injec-

tor design and the ‘in-out’ injector design. Figure 3

shows a snapshot of density evolution along an X-Y

centerplane within the out-in injector along with an

inset view that focuses on the mixing / nozzle region. A

3D view of the 50% volume fraction iso-surface super-

imposed onto a rendering of the injector geometry (Fig-

ure 4) shows that the two-phase mixture fills almost the

entire volume of the mixing tube and the nozzle. The

pressure differential between the plenum and the dis-

charge tube initiates the formation of gas plumes, which

penetrate deep into the tube core flow. Liquid flows

around the base of each plume, increasing the interfa-

cial surface area. The gaseous plumes are unstable, and

eventually parcels of vapor separate from the plumes

and form irregularly-shaped bubbles under the influ-

ences of surface tension. These bubbles migrate into

the nozzle where they elongate and merge, stripping

away parcels of liquid in the process. The gas forces

the liquid toward the surfaces of the tube, leading to a

thin film of intact liquid from which small droplets

might be shed due to aerodynamic forces. Due to the

general decrease in resolving power due to higher local

CFL numbers, spherical droplets and bubbles are not

resolved very well in the nozzle. Elongated parcels of

vapor and liquid are captured instead.

Figure 5 shows average centerline mixture density

and pressure distributions for the out-in configuration.

The ‘averages’ were taken over only 46 frames of an

animation sequence and are noisy as a result. The large

drop in mixture density at the nozzle inflow results

from the passage of the gaseous bubbles into the nozzle.

Axial velocity and Mach number distributions are

shown in Figure 6. A choked-flow state of the mixture

is realized at the exit of the nozzle, and the velocity

accelerates to nearly 100 m/s. The results show the

primary advantage of gas aeration – the momentum flux

of the exiting two-phase mixture is ~5.5 times the value

that would be achieved for a pure liquid jet at the same

conditions.

In-out injector: Case 2

A time history of volume-fraction contours at the

X-Y center plane for the Case 2 in-out injector is shown

in Figure 7. Sharp phase interfaces are captured in the

annular and mixing regions, where the flow speeds are

low, but the resolving power of the scheme reduces as

the two-phase flow passes into the nozzle region. The

degree of vapor blockage in the nozzle varies over time,

but at no time is there a distinct ‘slugging’ mode of

operation, characterized by the passage of large discon-

nected regions of vapor and liquid through the nozzle.

The flow speeds are too high for this mode to occur,

and a core-annular structure dominates as it does in the

out-in configuration.

Figure 8 shows an iso-surface of 50% vapor vol-

ume fraction superimposed onto a rendering of the in-

jector geometry along with density contours at the X-Y

centerplane. The injection ports are much larger for the

in-out configuration compared with the out-in configu-

ration – as a result, the gas bubbles remain attached to

the surface of the perforated tube and do not interact as

strongly with the co-flowing liquid. The bubbles re-

main mostly intact while migrating into the mixing re-

gion, filling the volume within and forcing the core

liquid fluid to the outer edges of the injector. Upon

entering the constant-area nozzle, the aerating gas ac-

celerates through a vena contracta formed by the still-

intact liquid sheet, reaching speeds of upwards of 250

m/s in this region. It then expands and slows, stripping

away parcels of liquid from the sheet that begins to

form on the outer surfaces of the nozzle. This process

is seen more clearly in the close-up view of the nozzle.

A comparison of line-of-sight liquid density pre-

dictions with X-ray radiography measurements is

shown in Figure 9 for Case 2. Agreement with exper-

iment is generally good in the annulus region, though

the experimental results indicate more jet penetration

from the furthest upstream injector ports. In the mixing

region prior to the nozzle, the calculation indicates that

aerating gas tends to remain trapped (on the average) in

the low-momentum region behind the tip of the perfo-

rated tube. The experimental measurements indicate

that liquid entrainment into this region is more proba-

ble, which could be a consequence of a more asymmet-

ric mixing response that predicted in the computation.

Statistics were taken over only 0.01 s in the calculation,

compared with 1 s in the experiment, and it is also pos-

sible that a different structure might emerge in a longer-

time average. Within the nozzle, both experiment and

calculation indicate the presence of a core-annular

structure with peak liquid density values in the annular

region of around 450 kg/m3. However, more liquid

content is predicted toward the core of the nozzle in the

calculation: ~280 kg/m3 versus ~200 kg/m3 near the

end of the measured region. It is possible that more

liquid is trapped near the walls (out of the range of the

interrogation region) in the experiment.

In-out injector: Case 5

The perforated tube used in the Case 5 injector has

more, smaller orifices for gas injection. Figure 10 pre-

sents a snapshot of the 50% vapor volume-fraction iso-

surface along with X-Y centerplane density contours

for this configuration. In general, the structure of the

flow is similar to that for Case 2 in that the gas plumes

merge and remain intact until they spill into the mixing

region. The vena contracta is again present, and the

liquid sheet rapidly breaks down downstream of this

region. Figure 11 compares predicted line-of-sight

density contours with experimental data. Trends are

similar to those evidenced in Case 2. The calculation

again over-predicts the amount of aerating gas trapped

in the wake of the perforated tube. Though a core-

annular structure is again predicted in the nozzle, liquid

content in the core of the nozzle is higher in the calcula-

tion than in the experiment.

Comparison of out-in and in-out injectors

It is clear from the preceding discussion that the

out-in and in-out injectors both produce a highly turbu-

lent, two-phase flow within the constant-area nozzles.

Volumetric expansion of the aerating gas within the

mixing regions of each injector displaces the core liquid

toward the surfaces, producing a thin liquid sheet. As

the aerating gas accelerates through the nozzle, it strips

liquid material from the sheet, populating the core of

the nozzle with liquid. The numerical method cannot

resolve the finer-scale structures that actually would

appear in the core, but it may be surmised that popula-

tions of small droplets (20 microns or less) would be

present. The means by which this internal atomization

takes place is somewhat different between the injectors,

as illustrated in time-averaged contours of liquid densi-

ty and liquid momentum flux extracted at the nozzle

exit for each case (Figures 12 and 13). The mixing

chamber cross-sectional area is much smaller for the

out-in injector, as the in-out design has to be large

enough to accommodate the sparging tube. As a result,

the aerating gas flows more smoothly into the out-in

nozzle and a vena contracta is not formed. Maximum

velocities occur at the nozzle exit, rather than at the

location of the vena contracta – the internal atomization

process is more gradual, and more of the annular sheet

persists to the end of the nozzle (Figure 12). The rapid

acceleration of the flow through the vena contracta

formed in the in-out designs leads to a more rapid dis-

appearance of the liquid sheet and more liquid content

in the nozzle core (Figure 12) The momentum flux

achieved in the out-in design is higher due primarily to

a higher average exit velocity in the core: ~103 m/s vs.

~92 m/s for the in-out designs (Figure 13). One can

conclude that the current in-out design incurs more in-

ternal losses due primarily to the large mixing-area to

nozzle-area ratio, which leads to the formation of a ve-

na contracta that constricts the flow. Alternative noz-

zle shapes that reduce the degree of turning experienced

by the aerated liquid as it enters the constant-area noz-

zle or general reductions in the sparging tube and mix-

ing chamber sizes could improve the performance of

the in-out injector.

Conclusions

Direct numerical simulations of two-phase flow

within ‘out-in’ and ‘in-out’ aerated-liquid injectors test-

ed at AFRL have been described in this work. The in-

jectors consist of a plenum chamber, a mixing chamber,

and a constant-area nozzle. In the out-in design, gas is

injected through small ports placed along the circum-

ference of a mixing tube. In the in-out design, a cen-

trally-located sparging tube is used to inject aerating

gas into an annular stream of liquid. A homogeneous

mixture model for two-phase flow of the aerating gas

(nitrogen) and liquid water mixture has been employed.

The numerical methods employ variants of a Tangent

Hyperbola Interface Capturing method to resolve phase

interfaces sharply. Simulations have been conducted at

a gas-to-liquid (GLR) mass ratio of 0.04 and at a liquid

flow rate of 18.2 g/s. In both injector designs, the aerat-

ing gas displaces the liquid toward the walls of the in-

jector prior to entering the nozzle. Within the nozzle,

rapid acceleration of the aerating gas strips material

from the annular liquid sheet, populating the core of the

nozzle with liquid material. A core-annular structure

emerges for both injector designs. The acceleration of

the two-phase mixture in the nozzle is more gradual for

the out-in design. For the in-out injectors, a vena con-

tracta is formed at the entrance to the nozzle. Very

high velocities experienced as the flow passes through

the vena contracta hasten the internal atomization pro-

cess, producing an exit flow with more liquid content in

the core and a thinner liquid sheet. The momentum

flux of the exiting two-phase flow is less for the in-out

design than for the out-in design. Good agreement

with experimental line-of-sight density distributions

(obtained from X-ray radiography) is evidenced within

the annular and mixing regions of two in-out injector

designs. In the nozzle, the calculations predict more

liquid content within the core but a similar level of liq-

uid content in the annular region.

Acknowledgements

This work is supported by Taitech, Inc. under sub-

contract TS14-16-02-001 (prime: FA-8650-14-0-2316,

monitored by Steve Smith. Computer time has been

provided by the DoD’s High Performance Computing

Modernization Program.

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Figure 1. Details of ‘in-out’ injector (left: nomenclature and arrangement; right: Case 2 and Case 5 orifice pat-

terns)

Figure 2. Details of computational mesh used for Case 2 injector simulations.

Figure 3. Density contours in X-Y centerplane: out-in injector

Figure 4. 50% vapor-phase volume fraction isosurfaces for out-in injector (top: beginning of aeration region;

bottom: mixing and nozzle regions)

Figure 5. ‘Average’ centerline pressure and density distributions: out-in injector

Figure 6. ‘Average’ centerline velocity and Mach number distributions: out-in injector

Figure 7. Time evolution of centerplane volume fraction: Case 2 in-out injector

Figure 8. Vapor-phase volume fraction and density predictions for Case 2 in-out injector (top: 50% volume-

fraction iso-surfaces; middle: X-Y centerplane density contours; bottom: close-up of nozzle)

Figure 9. Line-of-sight average liquid density at different locations within the Case 2 injector

Figure 10. Vapor-phase volume fraction and density predictions for Case 5 in-out injector (top: 50% volume-

fraction iso-surfaces; middle: X-Y centerplane density contours; bottom: close-up of nozzle)

Figure 11. Line-of-sight average liquid density at different locations within the Case 5 injector

Figure 12. Time-averaged liquid density at nozzle exit

Figure 13. Time-averaged liquid momentum flux at nozzle exit