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: [email protected]
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.
References
1. Lin, K.-C., Kennedy, P.J., and Jackson, T.A.
“Structures of Water Jets in a Mach 1.94 Superson-
ic Crossflow”, AIAA 2004-0971.
2. Lin, K.-C., Rajnicek, C., McCall, J., Fischer, B.,
Carter, c., and Fezzaa, K. “Structures of Aerated-
Liquid Jets Injected from Various Nozzle Con-
tours”, AIAA 2011-0232.
3. Lin, K.-C., Carter, C., Smith, S., and Kastengren,
A. “Exploration of Aerated-Liquid Jets Using X-
Ray Radiography”, AIAA 2012-0347.
4. Lin, K.-C., Carter, C., Smith, S., Kastengren, A.
“Exploration of Near-Field Plume Properties for
Aerated-Liquid Jets using X-Ray Radiography”,
AIAA 2014-1183.
5. Lin, K.-C., Carter, C., Smith, S., Kastengren, A.
“Characterization of Aerated-Liquid Jets Using
Simulataneous X-Ray Radiography and X-Ray
Fluorescence Measurements” ILASS Americas 26h
Annual Conference on Liquid Atomization and
Spray Systems, Portland, Oregon, 2014
6. Peltier, S., Lin, K.-C., Carter, C., and Kastengren,
A., “Characterization of Flow Structures Inside and
Aerated-Liquid Jet Using X-Ray Diagnostics”
ILASS Americas 27th Annual Conference on Liquid
Atomization and Spray Systems, Raleigh, NC
2015.
7. Cassidy, D.A., Edwards, J.R., and Tian, M. “An
Investigation of Interface-Sharpening Schemes for
Multiphase Mixture Flows”, Journal of Computa-
tional Physics, Vol. 228, No. 16, 2009, pp. 5628-
5649.
8. Cassidy, D.A., Choi, J.-I., Tian, M., Edwards, J.R.,
Lin, K.-C., and Jackson, T.J. “Numerical Simula-
tion of Two-Phase Flow within an Aerated-Liquid
Injector” AIAA Paper 2010-98.
9. Bornhoft, B.J., Edwards, J.R., Cox-Stouffer, S.,
and Lin, K.-C., JANNAF 46th CS / 34th APS /
34th EPSS / 28th PSHS Joint Subcommittee Meet-
ing, Albuquerque, NM, 2014.
10. Xiao, F., Honma, Y., and Kono, T. “A Simple Al-
gebraic Interface Capturing Scheme using Hyper-
bolic Tangent Function”, International Journal for
Numerical Methods in Fluids, Vol. 48, 2005, pp.
1023-1040.
11. Shyue, K.-M. and Xiao, F. “An Eulerian Interface
Sharpening Algorithm for Compressible Two-
Phase Flow: The Algebraic THINC Approach”
Journal of Computational Physics, Vol. 268, 2014,
pp. 326-354.
12. Lafaurie, B., Nardone, C., Scardovelli, R., Zaleski,
S., and Zanetti, G. “Modelling Merging and Frag-
mentation in Multiphase Flows with SURFER”.
Journal of Computational Physics, Vol. 113, 1994,
pp. 134-147.
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