7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


Numerical simulation of optical diagnostics and comparisons to experiments


T. Mdnard*, S. Idlahcen*, J.B. Blaisot*, C. Roz6*, A. Berlemont*,

T. Girasole*, L. Meest
UMR 6614 CORIA, CNRS, Universit6 et INSA de Rouen, 76801 Saint-Etienne du Rouvray Cedex, France
t UMR 5509 CNRS, LMFA, Ecole central de Lyon, 69134 Ecully Cedex, France
tmenard@tcoria.fr
Keywords: jet atomization, optical diagnostic, level set, VOF




Abstract

Direct numerical simulations (DNS) of a high pressure liquid jet have been carried out, by using a coupled
LS/VOF/GF (Level Set/Volume of Fluid/Ghost Fluid) method with realistic physical parameters (pressure, velocity,
surface tension, viscosity, liquid and gas density). On the other hand, high resolution experimental images of the
liquid jet have been obtained, by using femtosecond laser beam. A direct comparison between DNS and experimental
images has been performed, by using the same analysis tools. This approach permits to introduce some criteria for the
validation of the numerical simulation. Finally simulation of light beam interaction with numerical results opens the
way of an improved analysis of optical signals that are obtained by interaction of a light beam with a liquid.


Nomenclature

Roman symbols
g gravitational constant (ms 1)
p pressure (Nm 2)
L, turbulent length scale (m)
'u' /U2 turbulent intensity
Greek symbols
p viscosity (kg/(m s)
p density (kg/(m3)
A laser wave length (kg/(m3)
Subscripts
g Gas
1 Liquid
i Injection
a Ambient


Introduction

Liquid jet atomization represents a key problem for
efficiency improvement of liquid fuel combustion en-
gines. Indeed, atomization governs the granulometry
of the fuel droplets and therefore the fuel/air gas mix-
ing through the evaporation of the droplets. The near
field of the injector nozzle is of primary importance: hy-


drodynamic instabilities, occurring in this region, play
an important role in the development of the liquid jet
and its break up into liquid elements like ligaments and
droplets. Experimental investigations in this zone are
particularly difficult due to the very short time-scale of
the phenomenon (injection time less than 1 ms for a high
pressure Diesel injector) and to the high liquid density
(limitations of classical optical diagnostics). Recent ex-
perimental tools tryed to extract some information from
the dense part of the spray. For example, X-ray imag-
ing (Wang (2i" '4); Ramirez et al (2009)) can give spatial
volume fraction distributions. Ballistic imaging (Gal-
land et al (1995); Idlahcen et al (2009); Linne et al
(2009)) improves ombroscopy techniques by selecting
the light that did not interact with the liquid from the
scattered light which scrambles the signal.
On the other hand, recent numerical developments
on direct numerical simulation (DNS) and the growing
computing power open new possibilities for numerical
simulations of Diesel injection. Indeed, classical simu-
lations (RANS, Lagrangian methods) transport statisti-
cal variables (volume fraction, interface density, mean
droplet diameter, etc.). They cannot provide knowledge
of the exact position of the liquid interface. On the con-
trary, DNS gives the position of the interface at each
time step. Thus, the simulated jet can be compared to
experimental results with the same procedures. The sta-
tistical variables are not the direct output of the compu-







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


station, but has to be evaluated from a set of simulated
jet samples, i.e. the same process than in the experimen-
tal analysis : samples are recorded and then statistical
characteristics computed.
For two-phase flow DNS, a lot of validation on
droplet collisions, droplets coalescences, bubble rising
and Rayleighjet were performed. Nevertheless, the abil-
ity of the simulation to reproduce the behaviour of the
liquid jet near the nozzle is still a question. The objec-
tive of this communication is to apply the same analy-
sis on a simulated liquid jet and on experimental data
to highlight the similarities and the differences between
numerical simulations and experiments. In this paper,
we first present the experimental set-up, and then we de-
scribe the numerical method and analysis tools. In the
last section, numerical simulations and experimental re-
sults are compared for similar configurations, with same
analysis tools. Results are discussed and perspectives
are proposed.


Experimental set-up

Experimental set-up consists of a Diesel injection bench
and a imagery setup composed of a pulsed laser and
a camera. The Ti:Sa amplified laser system (800 nm,
1 kHz, 1 mJ) generates 100-femtosecond pulses. The
camera, the injector activation and the laser are synchro-
nized at a repetition rate of 1 Hz. The beam profile is
approximately Gaussian with a 5 mm full width at half
maximum (FWHM) and has a low divergence. It illu-
minates the jet and a lens forms the image of the spray
directly onto the sensor of a camera. The focal length is
chosen to obtain the magnification adapted to the image
processing to be applied. To produce some images, the
basic wavelenght of the laser is transform from 800nm
to 400nm by second harmonic generation in BBO cristal.
An illumniation at A = 400nm may reduced the diffrac-
tion effects and increase the optical system resolution
(11 pm for 800nm and 7 pm for 400nm). The injector is
located in an injection chamber and mounted on a XYZ
translation. All image are recorded at atmospheric pres-
sure (pa = 1 bar), allowing the use of thin optical win-
dows, which do not perturb the light propagation. The
chamber is maintained at room temperature. Injection
pressure may be adjusted from 400 bars to 1000 bars, by
a high-pressure pump though an accumulator (a com-
mon rail). Two single-hole injectors have been used:
D1 = 200 pm (injector 1) and D2 = 113 pm (injec-
tor 2). The fluid (NormaFluid) is a calibration fuel with
properties similar to Diesel with precisely controlled vis-
cosity and density specifications (see table 1). Activa-
tion duration is fixed at 1 ms for injector 1 and 400 ps
for injector 2. Effective injection duration of injector 1
varies from 500 ps at 400 bars to 1110 ps at 1000 bars.


i- C'


(a) (b)


(d) (e)


Figure 1: Images of the jet for different delays from the
start of injection (A 800nm) : (a) 0 ps, (b) 20 ps,
(c) 30 ps, (d) 40 ps, (e) 50 ps, (f) 200 ps Injection
pressure is pi 400 bar and hole diameter is D1
200pm.


Examples of images for injector 1 are shown on fig-
ure 1, for different delays from the start of injection. As
the system is unable to produce several images over a
unique injection, each experimental image corresponds
to a different injection. It must be stressed that the jitter
between the electronic trigger command and the effec-
tive ejection of liquid may be important, so that delays
given in figure 1 may be subject to large variations. Nev-
ertheless, it can be considered that images of the figure 1
are statistically representative.


Numerical method

Our numerical code (called ARCHER) has been devel-
oped to describe the dynamic of liquid/gas interface.
The Level Set method is used to capture the interface
motion. Resolution of Level Set transport equation is
coupled with the resolution of incompressible Navier-
Stokes equations and Ghost Fluid method is applied to
take into account jump conditions at the liquid/gas inter-
face. This approach was successfully applied on droplet
collisions, Rayleigh jet atomization and droplet evapo-
ration.
The Level Set method suffers from mass loss which be-
comes problematic in situation with strong stretching
near interface. We so develop the CLSVOF method
(Coupled Level Set and Volume Of Fluid) introduced
by Sussman and Puckett (2000). This method couples
Levet Set and Volume Of Fluid approaches. Information







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


given by volume fraction enforces the mass conservation
and the Level Set function ensures accurate topological
information and volume fraction transport. In addition
specific care has been devoted to improve simulation ca-
pabilities with MPI parallelization.
Applications of such method on high speed liquid jet
have been already performed by some author. The VOF
was applied by De Villier (21' 14), a conservative Level
Set method was recently applied by Desjardin (2008),
and we have applied ourselves the CLSVOF method
(M6nard et al (2007); Lebas et al (2009)). Some dif-
ficulties are encountered in such simulations. The first
one is to obtain a realistic inlet flow with good turbulent
characteristics. The second one is to capture accurately
the process of droplets formation. We have shown (Md-
nard et al (2007)) that the droplet diameter distribution
formed by such computations has a mesh dependence,
with a poor influence on some statistical variables, but
a significant influence, for instance, on interface den-
sity variable. Concerning inlet turbulent characteristics,
we have adopted the method developed by Klein et al
(2003), which imposes a turbulent intensity and a tur-
bulent length scale. Figure 2 presents a comparison be-
tween two simulations with similar parameters (M6nard
et al (2007)), but with different mesh size, and illustres
previous remarks. Main problem of such simulations is
to capture all structures of the interface. A same remark
applies to the turbulent scales.
Nevertheless, simulations present a satisfying visual be-
haviour and can from now be compared with experi-
mental results, by using some statistical tools. Param-
eters used in following computations are given by table
1 and 2. Mesh dimension is 128 x 128 x 1024 on 16
processors, and the domain is 3D1,2 x 3D1,2 x 24D1,2
(A = 4.7pm).


Statistical morphological analysis

The morphological analysis is based on the application
of morphological opening and closing operations over a
two level picture of the jet. Dispersed liquid phase el-
ements (droplets) are removed from the image and the
liquid and the surrounding are represented in black and
in white respectively. This analysis was developed to
analyze the complex interfacial structure of atomizing
Diesel jets (Yon and Blaisot (2003)). Radial and lon-
gitudinal segments of one pixel width are used as struc-
turing elements. The analysis consists in calculating the
length distribution of segments included in a ROI (Re-
gion Of Interest) over the entire picture series. In the
present study, the ROI width was fixed to half the initial
jet diameter. Black and white segments, oriented either
radially or longitudinally are considered and five groups
of segments are defined:


Figure 2: Comparison of high speed jet simulations with
two different mesh size (left : Ax 1.17 pm, right :
Ax 2.36 pm)


IVB : radial black segments that cross the jet axis.

EVB : radial black segments that do not cross the
jet axis, i.e. segments belonging to ligaments.

VW : radial white segments enclosed between
black segments.

HW : longitudinal white segment enclosed between
black segments.

HB : longitudinal black segments that do not inter-
cept the picture sides.

The variation of three parameters, constructed from the
distributions of segments, are presented here. The dense
core diameter Dc is computed from the surface cor-
responding to the dense part of the jet. This surface
is defined as the total jet surface (IVB + EVB) mi-
nus the mean surface of the disintegrating part of it :







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


Table 1: Summary of liquid and gas characteristics used
in computations and experiments.
Variable Value Units

pi 821. kg/(m3)
P9 1.22 kg/(m3)
P 3.2-10-3 kg/(mns)
p 1..10-5 kg/(m s)
a 0.02547 N/m


Table 2: Geometric and flow properties used in compu-
tations and experiments.
Variable Value Units
D1 200. /pm
D2 113. /in
pi 400. bar
Pa 1. bar
Ua 200. m/s
u'u'/U2 0.05
L, 0.lxD1,2 /rn
Rel 10262.
Wel 257872.


(HB+EVB)/2. The ligament thickness tl is the mean
length of EVB distribution, i.e. the ratio between the
area of EVB and the number of segments that make up
the EVB surface. The ligament number nl corresponds
to the mean total length of the ligaments found in the
ROI, divided by width of the ROI, i.e. the mean number
of ligament that can be seen on the side of the jet.


IVB + (EVB HB)/2
D (1)
WROI
EVB
ti (EVB) (2)

.1. (EVB)
nl = (3)
WROI


Comparisons between experiments and
simulations

Sequences of 90 simulated images corresponding to 90
time-step (100ns) of computation and of 100 experimen-
tal images corresponding to 100 different injections are
used for the statistical morphological analysis. The fig-
ure 3 presents an example of image for the experimental
jet (before and after processing) and for the numerical
jet. Results for experimental and numerical jets along
the first millimetre from the nozzle exit are presented
in figure 4-6. The core jet diameter Dc increases more


(a) (b)


(c) (d)

Figure 3: Experimental jet (D1 200pm, A=400 nm)
: (a) before processing, (b) after processing ; numerical
jet: (c) before processing, (c) after processing.


rapidly for the experiment than for the numerical sim-
ulation. This difference leads to a cone angle for the
simulated jet that is half the cone angle of the experi-
mental jet. However, the characteristics of ligaments are
in good agreement. The number of ligaments increases
with the distance from the nozzle with the approximative
same slope in the experimental cases than in the numer-
ical one. Also, the ligaments thickness have the same
order of magnitude for the two cases.
The previous quantitative comparisons show a good
behaviour of numerical simulation. But a lot of struc-
tures presented on the experimental liquid jet are not
captured by simulation. For example, one can see that
the simulation does not generate filaments ejected hori-
zontally as seen on experimental images. This is prob-
ably due to the incomplete knowledge of the inlet con-
ditions. Further tests will be conducted to understand
these differences, taking into account the spatial distri-
bution of turbulent length scale in the inlet condition of
simulations, or inlet velocity. For that, the technique of
Klein et al (2003) may be modified, or the internal flow
in the injector may be computed, to obtain more realistic
simulations.
As an illustration, the jet penetration length mea-
sured experimentally at the very beginning of injection
is shown on 7 : the mean initial jet velocity is around
50 m.s 1, whereas the velocity at the nozzle used for the








7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


05,


Exp 1


- Exp 1
Exp 2
Num


Figure 4: Jet diameter Dc versus downstream position z
for the simulated jet and for the experimental jet at two
different times after start of injection.


0016
0014
0012
001


0 002


Figure 5: Mean ligament thickness tl of the jet versus
downstream position z for the simulated jet and for the
experimental jet at two different times after start of in-
jection.



simulations is constant and equal to 200 m.s 1 during
all the injection, i.e. the value for an established regime.
Tests show that it may explain the difference between the
experimental and the simulated cone angle, but does not
lead to the creation of horizontal structures. On the con-
trary, when the spatial velocity profile is changed from a
flat one to a profile with thick boundary layers, some ex-
perimental behaviours may be qualitatively reproduced
(figure 8).
Extensive tests show that some experimental be-
haviours cannot be reproduced by only changing the
maximum velocity and/or the spatial velocity profile.
For example, at the beginning of the injection, shapes
like those shown on figures 9a, 9c may be observed. The
only possibility to obtain such shapes is to apply a time
modulation of the injection velocity. In other words,


Figure 6: Number of ligaments ni of the jet versus
downstream position z for the simulated jet and for the
experimental jet at two different times after start of in-
jection.


E2000-
.=c
tM 1500-
a,
C 1000-
0

500-

0)


20 30
Time(ps)


Figure 7: Length of the experimental jet.


the liquid undergoes acceleration and deceleration dur-
ing injection. When applying a temporal velocity pro-
file, very similar behaviours may be obtained with the
simulation (figure 9b, 9d).
We can have some confidence for the future develop-
ments because the numerical tools already allow to sim-
ulate particular jet shapes in the near field of the nozzle
by using accelerations and decelerations, as shown in
figure 9.


Conclusions

Validation of numerical simulation in the dense zone of
the spray is a necessary step. Some parameters have
been presented to estimate quantitatively the differences
between experimental and numerical jets. Even if the


x







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


-it.


Figure 8: Influence of spatial velocity profiles on spray
(left : with boundary layer, right : flat profile).


U




(b)


(c) (d)


Figure 9: Comparisons between experimental jets
(D2 113pm, A 800nm) (a and c) and numerical
ones (b and d) at two different times just after the begin-
ning of injection.


morphological analysis show that the statistical proper-
ties of the experimental images are similar to the simu-
lated ones, some liquid structures shapes do not appear
in the simulated jets. Tests lead to the conclusion that a
specific attention on inlet conditions is essential to have
a good behaviour of simulations.
More generally, it has been demonstrated that the
DNS allows to apply the same analysis tools on the com-
puted data and on the experimental ones. It open the
way to completely reproduce optical diagnostics using
numerical results. In this case, the key factor is the sim-
ulation of light propagation through the liquid jet. A
ray tracing technique may be used: it consists on send-
ing light bundles (called photons) and to compute their
trajectory through the liquid interfaces. At each inter-
section with an interface, the Snell-Descartes laws are
used to compute the new direction of the photon. When
the photon hits a surface modelling a camera, its coordi-


Figure 10: Simulation of the light propagation through a
computed liquid jet. (A = 800nm)


nates are recorded. The liquid surface being computed
on a mesh by the DNS, it must be smoothed for the pur-
pose of light propagation simulation. The 3D interpo-
lation technique of Lekien and Marsden (2005) is used
in our computations. An image of the interaction of a
light beam with a DNS liquid jet has been simulated, and
shown in figure 10. Even if interference and diffraction
is not taken into account, the transmitted light is observ-
able. If this computation is made at different injection
time, an optical signal may be simulated. It may help the
interpretation of some experimental optical techniques,
like VLC (Velocimetry Laser Correlation) (Hespel et al
(2006)).

Acknowledgements

Simulation were carried out at CRIHAN (Centre de
Ressources Informatiques de Haute Normandie) and
IDRIS (Institut de D6veloppement et des Ressources
en Informatique Scientifique), a computer center of the
CNRS.

References

Wang J., X-ray vision of fuel spray. J. Synchrotron Rad.,
Vol. 12, pp. 197-207, 2004.

Ramirez A.I., Som S., Aggarwal S.K., Kastengren A.L.,
El-Hannouny E.M., Longman D.E., Powell C.F., Quan-











titative X-ray measurements of high-pressure fuel sprays
from a production heavy duty diesel injector, Exp. Flu-
ids, Vol. 47, pp. 119-134, 2009.

Galland P.A., Liang X., Wang L., Breisacher K., Liou
L., Ho P.P., Alfano R.R. Time-resolved optical imaging
of jet sprays and droplets in highly scattering medium.
Proc. Am. Soc. Mech. Eng., HTD-321, pp. 585-588,
1995.

Idlahcen S., M&s L., Roz6 C., Girasole T, Blaisot J.B.
Time gate, optical layout, and wavelength effects on bal-
listic imaging. J Opt Soc Am A, Vol. 26, pp. 1995-2004,
2009.

Linne M.A., Paciaroni M., Berrocal E., Sedarsky D.
Ballistic imaging of liquid breakup processes in dense
sprays. Proceedings of the Combustion Institute, Vol. 32,
pp. 2147-2161, 2009.

Yon J., Blaisot J.B. Morphological analysis of the diesel
jet at the nozzle outlet. ICLASS-2003, Jul. 2003, Sor-
rento, Italy.

Sussman M., E.G. Puckett, A coupled level set and vol-
ume of fluid method for computing 3D and axisymmet-
ric incompressible two-phase flows. J. Comp. Phys.,Vol.
162, pp. 301-337, 2000

De Villier E., Gosman A. and Weller H., Large eddy
simulation of primary Diesel spray atomisation, SAE in-
ternationnal (2004-01-0100), 2004

Desjardins O., Moureau V, Pitsch H., An accurate con-
servative level set/ghost fluid method for simulating tur-
bulent atomization, Journal of Computational Physics,
Volume 227, Issue 18, pp. 8395-8416, 2008

M6nard T, Tanguy S., Berlemont A., Coupling level
set/VOF/ghost fluid methods: Validation and application
to 3D simulation of the primary break-up of a liquid jet.
International Journal of Multiphase Flow, Volume 33, Is-
sue 5,pp 510-524, 2007

M6nard T., Demoulin F.X., Berlemont A., 3D simulation
of the primary break-up of a liquid jet by coupling Leve
Set/ VOF/ Ghost Fluid methods, ICMF 2007

Lebas R., Menard T, Beau PA., Berlemont A., De-
moulin EX., Numerical simulation of primary break-
up and atomization: DNS and modelling study Interna-
tional Journal of Multiphase Flow, Volume 35, Issue 3,
pp 247-260, 2009

Klein M., Sadiki A., Janicka J., A digital filter based
generation of inflow data for spatially developing direct
numerical or large eddy simulations. Journal of Com-
putational Physics, Volume 186, Issue 2, pp. 652-665,
2003


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


F. Lekien, J.E. Marsden, Tricubic Interpolation in Three
Dimensions, International Journal for Numerical Meth-
ods in Engineering, Volume 63, Issue 3, pp 455-471,
2005

Hespel C., Blaisot J.B., Samson E., Gouesbet G. et
Gr6han G., Mesure de la vitesse en sortie d'injecteur
haute pression, Congris Francophone de Techniques
Laser, CFTL 2006, Toulouse, France, 19-22 sept 2006