Injector Study via VOF:
Emphasis on Vapor Condensation
due to Spray
As presented at: ILASS–Americas, 23rd Annual Conference on Liquid Atomization and Spray Systems,
Ventura, CA, May 2011
W. Kalata*, K. J. Brown, and R. J. Schick
Spray Analysis and Research Services
Spraying Systems Co.
Wheaton, IL 60187 USA
Abstract
Condensation and absorption are used in gas scrubbing
applications and industrial scale production of chemicals.
Various processes that depend on condensation
techniques require the usage of liquid injection such as
jets and sprays. The mass transfer efficiency of these
techniques depends on ability of liquid to disperse into
vapor and interact in a controlled manner. Computation
Fluid Dynamics (CFD) can be used to aid or verify a design
of certain class of spray injectors within condensing
processes.
Volume of Fluid (VOF) technique was used to investigate
condensing steam due to cooling by atomized liquid. Two
types of hollow cone injectors varying by design and
size were investigated at moderate delivery pressure
conditions. Initially, both injectors’ spray angles were
validated empirically at standard conditions. In this
study, the VOF model approaches condensation and
evaporation via the Hertz-Knudsen relation. The CFD
results revealed a trend that the spray angle decreases as
the rate of condensation increases. The increase of the
condensation rate was partially dependent on the inverse
of characteristic diameter which further was accounted in
the VOF mass transfer model.
*Corresponding author
Experts in Spray Technology
Spray
Nozzles
Spray
Control
Spray
Analysis
Spray
Fabrication
Injector Study via VOF: Emphasis on Vapor Condensation
due to Spray
Introduction
Mass transfer of dispersed liquid has proven to be
extremely useful in many industrial applications
starting with evaporative flue gas conditioning
inside high temperature flow conduits ending with
condensing and absorptive systems for production of
chemicals. In today’s world, many industrial systems
are designed or upgraded to optimize production
efficiency with beneficial operating costs. In mass
transfer, spray technology provides solutions to many
complex problems.
more environmentally friendly. While experiments
usually can only provide focused point information
reliably, CFD can give detailed information of the full
computational domain, especially in environments
that are difficult to reproduce experimentally.
The focus of this study was to investigate spray
condensation properties of two differently sized
hollow cone nozzles (shown in Figure 1) spraying
liquid into condensing vapor. Only a single fluid in its
liquid and vapor states were investigated.
Presently, Computational Fluid Dynamics (CFD)
has been widely adopted in many disciplines that
involve critical assessment of fluids in motion. As
technological advancements in numerical simulation
have developed, fluid motion is often coupled with
complex heat and mass transfer. Currently, simulation
tools are becoming more available and cost effective
in engineering applications. The computational
sciences have become an integral part of engineering
research and design.
Figure 1. Spraying Systems Co. pressure swirl type spray nozzles
(small capacity – left, large capacity – right).
Compared with empirical testing, numerical
simulation is becoming more cost effective and
METHODS
Swirling Nozzle Simulations
The CFD simulations were performed with ANSYS
FLUENT version 12.1. The CFD models were
reproduced according to the internal geometry inside
swirling chambers and orifices for two injectors that
are shown in Figure 1. The biggest difference was the
spray nozzle capacity. The orifice of the large capacity
injector was two orders of magnitude larger than the
small capacity nozzle. In some instances, geometry
was simplified to reduce geometrical complexities in
3D CAD model (Figure 2).
Figure 2. Swirling injector chambers used in CFD.
Meshing was performed within ANSYS Workbench
13. Initially each unstructured grid was composed of
about 4.0–4.5 million of mixed cells which employed
boundary layer type inflation at all walls. Inside
FLUENT, each mesh was converted into polyhedral
grid while the boundary layer mesh remained. The
grids were reduced to 0.8–1.2 million polyhedral cells.
Dense mesh was incorporated in vicinity of orifices.
Size functions were used to focus smaller grid sizes
on geometries such as whirling chambers or orifices.
Each CFD model was set up with liquid velocity
or mass flow inlet boundary condition (BC) with
temperature at 20ºC. The outlet pressure BC was
setup as constant zero pressure with standard 1 bar
operating pressure. The backflow temperature for
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Injector Study via VOF: Emphasis on Vapor Condensation
due to Spray
METHODS
the outlets was set as slightly above saturation
temperature (Tsat) (105ºC) with only vapor passing
through, which means that the liquid volume
fraction backflow (LVFBF) was set to zero. Injector
and other walls were set as rigid, with no-slip and
adiabatic conditions. All vapor material properties
were dependent on temperature. The density of the
vapor was solved through incompressible ideal gas
law, where pressure term is an operating pressure.
Throughout all simulations the following models were
included: k-e Realizable Turbulence Model, energy
enabled and Volume of Fluid (VOF) with inclusion of
mass transfer and temperature dependent surface
tension of liquid. The simulations were performed in
steady state mode. Table 1 shows the BC summary for
both injectors used in this study.
Nozzle
Dorifice
Prated*
Inlet BC
VIN
AIN
QIN
QIN
ṁIN
Dh
Re
TIN
Outlet BC
Type
POUT
TBF
LVFBF
TX-2
CRC-250
mm
barg
0.71
3.79
82.6
2.07
m/s
m2
m3/s
lpm
kg/s
m
–
°C
5.24
4.7054E-07
2.4656E-06
0.1479
0.002461
0.0007740
3.30E+04
20
6.48
0.004927
0.03193
1915.7
31.871
0.07921
4.18E+06
20
bara
°C
barg
Mass Transfer
L
kJ/kg
Tsat
°C
βqp**
Dq (SMD)*
μm
B
-
The VOF model used implicit scheme for volume
fraction in equation below (1) with modified version
of High Resolution Interface Capturing (HRIC)
discretization scheme [1].
(1)
𝛥𝛥𝛥𝛥
+
𝑓𝑓
= 𝑆𝑆𝛼𝛼 +
𝑛𝑛+1
𝜌𝜌𝑞𝑞𝑛𝑛+1 𝑈𝑈𝑓𝑓𝑛𝑛+1 𝛼𝛼𝑞𝑞,𝑓𝑓
=
𝑛𝑛
𝑝𝑝=1
𝑚𝑚𝑝𝑝𝑝𝑝 − 𝑚𝑚𝑞𝑞𝑞𝑞
In VOF scheme equation (1) above, ṁqp is the mass
transfer from phase q to phase p and ṁpq is the mass
transfer from phase p to phase q. By default, the mass
source term on the right-hand side of Equation (1) Sα,
is zero, but you can specify a constant or user-defined
mass source for each phase. Uf, ρq, ρp, αq,f , Δt, V, f, and
n are volume flux through face, density of phase q and
p fluid, face value of phase volume fraction, time step
(or iteration step if steady), volume of cell, cell face
index, and computational stepping index [1].
In this study, right side from equation (1) was
employed to assess mainly condensation effects
within the vicinity of sprayed liquid phase. The mass
transfer was conditional with respect to the saturation
temperature (Tsat) that was an input by a user. In
most cases, for water liquid and vapor, Tsat was set at
100°C since operating pressure was set at standard
conditions. In higher pressure applications, Tsat would
have to be determined based operating pressure for
particular fluid that is being analyzed. Additionally,
volumetric heat source (Sh) was included in energy
computations. It was computed based on calculated
mass transfer for a particular phase (ṁpq) and fluid’s
latent heat (L) as shown in equation (2) below.
Constant Pressure
1
1
105
150
0
0
2257
100
0.01
1620
48.2
𝛼𝛼𝑞𝑞𝑛𝑛+1 𝜌𝜌𝑞𝑞𝑛𝑛+1 − 𝛼𝛼𝑞𝑞𝑛𝑛 𝜌𝜌𝑞𝑞𝑛𝑛
(2)
2270
100
0.01
78
1002
̇
*laboratory measurement
**Hagen et al. [7]
Table 1. Boundary conditions summary
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Injector Study via VOF: Emphasis on Vapor Condensation
due to Spray
METHODS
Mass Transfer Considerations
(9)
The mass transfer model (MTM) used in VOF
simulations was based on supplying evaporation
and condensation constants (A and B respectively)
in mass transfer equations shown in (3) and (4) [1].
These equations represent mass rate per volume
(kg/s•m3) transferred through gas-liquid interface.
When setting p to be gas phase and q liquid
phase, ṁqp becomes mass rate from liquid to vapor
(evaporation), ṁpq represents mass rate from gas to
liquid (condensation), αp and αq are volume fractions
for gas and liquid, and ρp and ρq are densities for gas
and liquid.
(3)
(4)
̇
(
(
(8)
(7)
)
( ⁄
)
( )(
)√
⁄
)
(11)
(
(
)
(10)
β, M, R, Tsat, Psat, and P* are accommodation
coefficient, molecular weight, universal gas constant,
saturation temperature and pressure, and partial
pressure at the interface, respectively. When
assuming that pressure and temperature (P* and
T *) are close to saturation condition, a combination
of (5) with Clasius Clapeyron relation (6) and
accommodation for interfacial area within cell volume
(7), resulted with derivation for equations (3) or (4),
where A or B coefficients take form of equations (8)
and (9).
(6)
(
In various scientific literatures, theoretical and
experimental values for evaporation or condensation
accommodation coefficients (βqp and βpq respectively)
can be found. There, accommodation coefficients
are further modified to equations (10) and (11) shown
below where Ke and Kc are known as evaporation and
condensation constants [4-7].
As ANSYS FLUENT documentation points out, A and B
need to be fine-tuned accordingly to fluids’ properties
while Hertz-Knudsen relation (5) is considered. This
formula gives evaporation-condensation flux (F) based
on kinetic theory [2-5].
√
)√
L, A i, Dp and Dq are latent heat, interfacial area
density, volume fraction of fluid, and representative
diameters for both condensation and evaporation,
respectively. By quick examination, it can be noticed
that density term can make A larger than B by 2 or 3
orders of magnitude, depending on fluid and operating
conditions which may vary saturation temperature.
Also Dp and Dq could be assumed based on SauterMean Diameter (SMD, D32) measured at that specific
flow rate at standard laboratory conditions. As it
can be noticed in equations (8) and (9), A and B are
proportional to an inverse of SMD.
̇
(5)
( )(
In studies with whirling injectors, water and steam
were used to determine injector’s performance when
condensation effects are involved. Condensation
and evaporation constants for water were available
in literature where these constants were obtained
through various experimentally and theoretically
[4-7]. The value for condensation accommodation
coefficient was 0.01 which was chosen based on
Hagen et al. [7].
The simulations were performed first without and
then with MTM to capture effects of condensation
with respect to non-condensing environment. A
comparative study was performed indicating spray
performance differences.
)
)
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Injector Study via VOF: Emphasis on Vapor Condensation
due to Spray
METHODS
Backflow Study
Large capacity pressure swirl type of nozzle (see
Figures 1 and 2) was used in studying an injector
outflow in various liquid volume fraction backflow
conditions ranging from 0.0 to 0.05. This backflow was
a part of constant pressure outlet BC setup. Overall
schematic of the flow problem is shown in Figure 3. In
this study, the level of liquid volume fraction (LVF) that
advances into swirling core inside the nozzle chamber
was varied until the spray collapse. The advancement
is due to negative pressure caused by swirling fluid
inside and below the nozzle. A toxic fluid mainly
composed of trioxin (Metaformaldehye) ~50%, water
~25% and additional toxic chemicals was used in
cases with inlet gas velocity BC of 4 and 8 m/s. Mass
exchange model described above was enabled.
Figure 3. CFD setup schematic for LVF backflow study.
RESULTS & DISCUSSION
angle resulted in ~90 degrees for both cases with and
without MTM.
Swirling Nozzle Simulations
The summary of results for low capacity injector
simulation with mass transfer is shown in Figure 5
below. The results show partial collapse of the spray
plume as compared to the simulation performed
without MTM (see Figure 6). Initially, in the case
without condensation, the simulation resulted with
~66 degrees. When condensation was included, the
temperature of vapor advancing up from the bottom
towards the orifice had a temperature drop over a
longer span, therefore cooling it earlier (Figure 6 top).
The spray angle resulted in ~47 degrees (Figure 7
bottom).
Backflow Study
At gas velocity approaching a spray at 4 m/s, the
spray collapsed at backflow LVF value of 0.05 (Figure
9 top). With gas velocity at 8 m/s, the spray collapsed
partially at LVFBF value of 0.04 (Figure 9 bottom).
Discussion
In low capacity injector study, an inlet BC and injector
geometry was set up according to work by Bade et.
al. The difference between the reported study by
Bade et al. and current study without condensation
was the gaseous phase which was water vapor
instead of air at laboratory conditions and thermal
effects were added with vapor properties varying
with temperature. The case without condensation
showed some differences in dynamics as compared
to Bade et al. work. The spray angle was 66 degrees
as compared to 77 degrees reported by Bade et al.
Taking account that injector is spraying into less
dense gas and with higher viscosity, it experienced
The summary of results for high capacity injector
simulation with MTM is shown in Figure 7 below.
The results show no collapse of the spray plume
with respect to the simulation performed without
mass exchange (see Figure 8). Slight variations in
temperature were noticed in the swirling core inside
the nozzle chamber and in the bottom portion of the
spray. Temperature profiles of fluid mixture were
slightly higher with MTM where condensing process
added heat to the mixture via latent heat. The spray
5
www.sprayconsultants.com
intuitive scenario where nozzle performance depends
on both heat and mass transfer which are directly
coupled.
In the large capacity injector case, interaction dynamics are significantly different. There is a significant
swirling core inside the nozzle chamber and its size has
remained the same when comparing cases with or without MTM. There were slight temperature effects due to
condensation heat sources but the overall dynamics
remained almost identical.
The additional study showed that liquid volume
fraction would have to be higher than 0.04 or 0.05 inside the core to decrease the spray angle or even colcases
withspray
or without
There
were slight
lapse the
plume.MTM.
For this
to occur,
there needs to
temperature
effects
due
to
condensation
be either a high condensation rate inside theheat
core, which
sources
the overall
almost
is rather but
unlikely
due todynamics
the natureremained
of the spray,
or high
enough LVF advanced due to suction of the swirling
identical.
action.
The additional
studyforshowed
that liquid
volume
There is room
improvement
in this
model. The
fraction
be higher
than 0.04 ordiameter
0.05 as
MTM atwould
some have
point to
relies
on characteristic
inside
core to decrease
the. spray
evenwas
shownthe
in equations
(8) and (9)
In thisangle
studyor
SMD
used for the
the spray
characteristic
diameter.
It wasthere
based on
collapse
plume. For
this to occur,
laboratory
the spray at rate
the inside
same flow
needs
to bemeasurement
either a high of
condensation
the
rate but
in standard
conditions.
TheofSMD
core,
which
is rather laboratory
unlikely due
to the nature
the
changes
and throughout
the temporal
evolution
spray,
or spatially
high enough
LVF advanced
due to suction
of
of
the
spray.
Also
droplet
growth
is
not
accounted
for
the swirling action.
in MTM. It is likely that mass and heat sources will
decrease
as droplets
experience growth.
There
is room
for improvement
in this model. The
Discussion
In low capacity injector study, an inlet BC and injector geometry was set up according to work by Bade
et. al. The difference between the reported study by
Bade et al. and current study without condensation was
the gaseous phase which was water vapor instead of air
at laboratory conditions and thermal effects were added
with vapor properties varying with temperature. The
case without condensation showed some differences in
dynamics as compared to Bade et al. work. The spray
RESULTS
& DISCUSSION
angle was
66 degrees as compared to 77 degrees reported by Bade et al. Taking account that injector is
spraying into less dense gas and with higher viscosity, it
a resistance awhich
posedwhich
a result
that ais result
somewhat
experienced
resistance
posed
that is
counter
intuitive
(density
and
dynamic
viscosity
somewhat counter intuitive (density and dynamic vis3
and 1.25e-5
N·s/m
of steam
105°Catis105°C
0.58 kg/m
1.25e-5
cosity
of atsteam
is 30.58
kg/m3 and
3
respectively
and air and
density
and at
viscosity
N·s/m
respectively
and air density
viscosity
20°C is at
3
3
3
and N·s/m
1.79e-5
N·s/m3 respective20°C
is and
and 1.21
kg/m1.21
andkg/m
1.79e-5
respectively).
ly).
A quick
studystudy
was was
performed
where
steam
A quick
performed
where
steam tempertemperature
was increased
consequently
decreasing
ature
was increased
consequently
decreasing
the steam
density
butdensity
increasing
dynamicthe
viscosity
and further
the steam
but the
increasing
dynamic
causing
of spray
angle.
The plot
below angle.
(Figviscosityreduction
and further
causing
reduction
of spray
ure
shows
that
the spray
anglethat
decrease
and angle
corresThe4)
plot
below
(Figure
4) shows
the spray
ponding
kinematic vapor/air
viscosity kinematic
increase with
decreasevapor/air
and corresponding
increasing
temperature.
viscosity increase with increasing temperature.
Injector Study via VOF: Emphasis on Vapor Condensation
due to Spray
MTM at some point relies on characteristic diameter
Conclusions
as
shown in equations (8) and (9). In this study SMD
In this
the performance
of pressure
was used
forstudy,
the characteristic
diameter.
It was swirl
atomizers in condensing fluid were investigated. Two
based on laboratory measurement of the spray at the
hollow cone spray nozzles with significant variations in
same
flowcapacity)
rate but inwere
standard
laboratory
conditions.
size (and
simulated
and compared
with
The
SMD changes
spatially and throughout the
non-condensing
scenarios.
temporal
evolution
of thenozzle
spray.was
Also
dropletbygrowth
The small
capacity
affected
the conisdensation
not accounted
MTM. angle
It is likely
that mass
and
where for
itsinspray
partially
collapsed
heat
sources
will
decrease
as droplets
(Figures
6 and
10).
The large
capacityexperience
spray was not
affected directly by condensation (Figures 8 and 10).
growth.
However when liquid volume fraction was introduced
into swirling core inside the nozzle chamber, the spray
Conclusions
Figure
Spray
angleangle
and kinematic
viscosity viscosity
with varyingwith
Figure4. 4.
Spray
and kinematic
temperature.
varying temperature.
plume was affected and even collapsed at LVF of 0.05
In
this study,
(Figure
9). the performance of pressure swirl
The mass
transfer model
reliedinvestigated.
on fluid properties
atomizers
in condensing
fluid were
Two
and
on
the
characteristic
diameter
that
was
based
hollow cone spray nozzles with significant variationson
The coefficient
for the condensation
was
inSMD
size values.
(and capacity)
were simulated
and compared
proportional
to
the
inverse
of
the
characteristic
diamewith non-condensing scenarios.
MTMMTM
was was
not included.
Steam
density
was was
calculated
not included.
Steam
density
calcuwith
ideal
gas
law
shown
in
equation
(12).
lated with ideal gas law shown in equation (12).
(12)
 
 
 
ter; therefore theoretically the smaller the drop size, the
(12)
better
the capacity
condensation
rate.
The
small
nozzle
was affected by the
condensation where its spray angle partially
Nomenclature
collapsed
(Figures 6 and 10). The large capacity spray
was not affected directly by condensation (Figures
face index
8f and 10).cell
However
when liquid volume fraction
n
computational stepping index
was introduced into swirling core inside the nozzle
inlet mass transfer flow rate

chamber,
the spray
plume
affected
and peven
mass
transfer
fromwas
phase
q to phase

collapsed at LVF of 0.05 (Figure 9).
As condensation
waswas
included
thethe
spray
angle
As condensation
included
spray
angle colcollapsed
even
further
as
shown
in
Figure
5. When
lapsed even further as shown in Figure 5. When
kinekinematic
viscosity
of mixture
the mixture
investigated
matic
viscosity
of the
was was
investigated
around
around
the local
orifice,
local kinematic
wasdue
lower
the
orifice,
kinematic
viscosityviscosity
was lower
to
condensed
vapor. vapor.
This isThis
a reversed
situation
as comdue to condensed
is a reversed
situation
pared
to non-condensing
scenario.
It poses
nonas compared
to non-condensing
scenario.
It poses
nonintuitive scenario where nozzle performance
depends on both heat and mass transfer which are
directly coupled.
The mass transfer model relied on fluid properties
and on the characteristic diameter that was based
on SMD values. The coefficient for the condensation
was proportional to the inverse of the characteristic
diameter; therefore theoretically the smaller the drop
size, the better the condensation rate.
In the large capacity injector case, interaction
dynamics are significantly different. There is a
significant swirling core inside the nozzle chamber
and its size has remained the same when comparing
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Injector Study via VOF: Emphasis on Vapor Condensation
due to Spray
Nomenclature
Prated
Psat
Q IN
R
Re
pressure rated at certain flow rate
fluid saturation pressure
inlet volumetric flow rate
universal gas constant
Reynolds number
S α
mass source for energy equation
S h
volumetric heat source for energy equation
T temperature
T* partial temperature at the phase interface
T BF backflow temperature
T IN
inlet temperature
T sat fluid saturation temperature
U f
volume flux through face
V
volume of cell
V IN velocity for inlet BC
f
n
cell face index
computational stepping index
ṁIN inlet mass transfer flow rate
ṁqp mass transfer from phase q to phase p
ṁpq mass transfer from phase p to phase q
p
first phase (gas)
q
second phase (liquid)
A
A i
A IN
B
D32
D h
Dorifice
D p
D q
F
K c
K e
L
LVF BF
M
P*
POUT
evaporation constant
interfacial area density
inlet BC cross-sectional area
condensation constant
Sauter-Mean Diameter
hydraulic diameter
orifice diameter
representative diameter in phase p
representative diameter in phase q
evaporation-condensation flux
condensation constant
evaporation constant
fluid latent heat of vaporization
backflow liquid volume fraction
molecular weight
partial pressure at the phase interface
outlet pressure
αq,f
αp
αq
β
βpq
βqp
Δt
ρp ρq
face value of phase volume fraction
volume fraction of phase p
volume fraction of phase q
accommodation coefficient
accommodation coefficient for condensation
accommodation coefficient for evaporation
time step (or iteration step if steady)
density of phase p
density of phase q
References
1. ANSYS FLUENT 12.0 - Theory Guide, ANSYS, Inc., Canonsburg, PA, 2009.
2. Ythehus, T. and Ostmo, S., International Journal of Multiphase Flow, 22-1:133-155 (1996).
3. Wang, Z.-J., Chen, M. and Guo, Z.-Y., International Conference “Passive and LowEnergy Cooling for the Built
Environment:, Santorini, Greece, May 2005, pp. 543-547.
4. Tamir, A. and Hasson, D., The Chemical Engineering Journal , 2: 200-211 (1971).
5. Marek, R and Straub, J., International Journal of Heat and Mass Transfer, 44: 39-53 (2001).
6. Mills, A.F. and Seban, R.A., International Journal of Heat and Mass Transfer, 10: 1815-1827 (1967).
7. Hagen, D.E., Schmitt, J., Trueblood, M., Carstens, J., White, D.R. and Alofs, D.J., Journal of the Atmospheric
Sciences, 46-6:803-816 (1989).
8. Bade, K.M., Kalata, W. and Schick, R.J., ILASS Americas, 22nd Annual Conference on Liquid Atomization and
Spray Systems, Cincinnati, OH, May 2010.
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Injector Study via VOF: Emphasis on Vapor Condensation
due to Spray
Figure 5. Summary of CFD results for the small capacity injector.
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Injector Study via VOF: Emphasis on Vapor Condensation
due to Spray
Figure 6. Main differences between cases with and without mass transfer in the small capacity injector.
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Injector Study via VOF: Emphasis on Vapor Condensation
due to Spray
Figure 7. Summary of CFD results for a large capacity injector.
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Injector Study via VOF: Emphasis on Vapor Condensation
due to Spray
Figure 8. Noticeable differences between cases with and without mass transfer in a large capacity injector.
Figure 9. VOF results for backflow study. Effect of LVF backflow on the large whirling nozzle with two gas velocity modes.
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Injector Study via VOF: Emphasis on Vapor Condensation
due to Spray
Figure 10. Streamlines indicating swirling liquid motion inside and outside the nozzles.
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