Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Development of an Initial DropSize Distribution Model and Introduction in a CFD Code to
Predict Spray Evolution
Arnaud Gapin1'2, FrangoisXavier Demoulin1, Christophe Dumouchel1, Karine Pajot2,
Beatrice PatteRouland', Julien Reveillon'
'CNRS UMR 6614 CORIA, Universite et INSA de Rouen
Avenue de l'Universite BP. 12, 76801 Saint Etienne du Rouvray, France
2 PSA PeugeotCitroen Direction de la Recherche Centre Technique de Velizy Route de Gisy
78943 VelizyVillacoublay Cedex, France
Snamea coria.fr
2karine.pajot@mpsa.com
Keywords: Liquid spray, Dropdiameter distribution, CFD code, Spray evolution
Abstract
The work presented in this paper participates to the improvement of the spray evolution simulation. The liquid sprays considered
are those encountered in the Selective Catalytic Reduction (SRC) technology developed to reduce Diesel engine NOx emissions.
One of the characteristics of this application is the use of low injection pressure (not greater than 0.6 MPa) for which primary
atomization models required by CFD code such as FIRE (used here) are not available. To overcome this problem, measured
dropdiameter distribution can be specified as initial condition. In the present approach, measurements of the initial
dropdiameter distribution are performed with a Laser Diffraction Technique (LDT) which seems more appropriate to
characterize sprays containing a non negligible proportion of the nonspherical droplets. A model of the initial dropdiameter
distribution is developed. This model can substitute the missing primary atomization model in the CFD code. Comparisons
between measured and calculated dropdiameter distributions as a function of the distance from the SCR injector and of the
injection pressure show an acceptable agreement. They validate the whole approach as well as the use of the initial dropdiameter
distribution model. As far as this point is concerned it is pointed out that this model is required since the use of experimental
distribution as initial condition reports a very poor agreement. This problem has been identified to be due to the diameter class
width distribution imposed by the LDT and suggests that improvement of the simulations could be achieved by adjusting this
width distribution
Introduction
The European legislation imposes car manufacturers to
reduce nitrogen oxides emissions (NOx). One of the
solutions for this purpose is the Selective Catalytic Reduction
technology (SCR), which appeared in the early seventies in
petroleum refineries. It is developed today to reduce NOx
emitted by Diesel engines. The SCR consists in ejecting Urea
Water Solution (UWS) in the hot exhaustgas flow. This
injection, performed at an injection pressure that does not
exceed 0.6 MPa, induces the disintegration of the UWS jet
and the production of a spray. The heating up of the spray
droplets produces ammonia (NH3) that reacts with NOx in
the SCR catalyst to produce nitrogen and water vapor
(Koebel et al. 2000). As for any process involving a spray, the
efficiency of the SCR technique depends on the spray
characteristics. The development of numerical codes
allowing the spatial evolution of the liquid spray to be
predicted is therefore required in order to help this
exhaustgas aftertreatment technique to be investigated and
improved. This is the purpose of this contribution.
The Computational Fluid Dynamic (CFD) code FIRE is
commonly used to predict liquid spray evolution. This code
may take into account the secondary breakup and the
evaporation of the liquid droplets if required. Furthermore, it
is also equipped with an atomization model that predicts the
initial dropsize distribution, i.e., the dropsize distribution of
the spray resulting from the primary atomization process.
However, this primary atomization model was developed for
operating conditions that are different than those of the SCR
application, i.e., high injection pressures, high temperatures
and fuels. It is therefore not adapted for the present process.
The alternative to this problem consists in initializing the
calculation by specifying an initial dropdiameter
distribution obtained from measurements. This solution was
adopted by Birkhold et al. (2006) who used as initial
condition a dropdiameter distribution measured by a phase
Doppler instrument. This optical diagnostic whose principle
of working is described in Dodge et al. (1987) performs local
temporal sampling of the spray and returns a numberbased
dropdiameter distribution. One of the drawbacks of the
phase Doppler technique is that it measures spherical
droplets only. As pointed out by Birkhold et al. (2006) this
limitation is pejorative for the initial sprays in the SCR
application. Indeed, as mentioned above, the typical injection
pressure for this application is not greater than 0.6 MPa.
Paper No
Therefore, the initial dropdiameter distribution contains a
non negligible proportion of nonspherical big drops that
escape from the measurements.
To overcome this problem, we propose in the present work to
characterize the initial dropdiameter distribution with a laser
diffraction technique (LDT). Contrary to the phase Doppler
technique, LDT considers all the droplets that go through the
measurement volume and this, whatever their shape. This
instrument reports a volumebased dropdiameter
distribution.
The second objective of this work is to provide a model of the
initial dropdiameter distribution. Such a model could
substitute the missing primary atomization model in the code
and allow calculations to be performed at operating
conditions not experimentally explored. This model makes
use of the threeparameter generalized gamma function that
is known to provide a good representation of liquid spray
dropdiameter distribution (Lecompte and Dumouchel,
2008).
The second Section of this paper presents the experimental
setup and diagnostic used. The modelization of the initial
dropdiameter distribution is described in Section 3 and the
CFD code is introduced in Section 4. All the results of this
investigation are presented and discussed in Section 5.
Nomenclature
do, discharge orifice diameter (unm)
D drop diameter (ptm)
Dmn mean diameter series (vtm)
f,(D) numberbased drop diameter distribution (vtm 1)
f,(D) volumebased drop diameter distribution (vtm 1)
h distance from the injector (mm)
I KullbackLeibler number ()
pv volumefraction distribution ()
q parameter of the GeneralizedGamma distribution
()
V, average liquid jet velocity (m/s)
WeG gaseous Weber number ()
Greek letters
a parameter of the GeneralizedGamma distribution
()
AP, injection pressure (MPa)
PG gas density (kg/m3)
PL liquid density (kg/m3)
IUL liquid dynamic viscosity (Pa.s)
r Gamma function ()
a surface tension coefficient (N/m)
Subsripts
e experimental
i diameter class index
j distribution component index
n numberbased
v volumebased
Experimental setup and measurements
The test bench is set in order to measure the characteristics
of the spray produced by the injector under atmospheric
conditions. Injections are performed in air at rest under
atmospheric pressure and temperature. Furthermore, the
spray evolution is free of any confinement that would be
caused by the presence of walls. The characterization of the
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
spray consists in measuring the dropdiameter distribution.
The experimental setup is shown in Fig. 1. The liquid is
stored in a pressurized tank (2) whose internal pressure is
imposed by a compressed air system. The internal pressure
in the tank is maintained constant thanks to the reducing
valve (1). The injection pressure used as reference in the
work is measured by the pressure gauge (3) that is located
just upstream the injector (4).
1 Reducing valve U
2 Pressuredtank
3 Pressure gaugeii 
4 Injector
5 Control unit
6 Particle sier
7 Computer
Figure 1: Experimental setup
A single liquid is used throughout the work. This liquid is
water whose physical properties are pL= 998 kg.m3,
PL = 1.10 Pa.s and o= 73.10 N.m1.
A single injector is used. It is a transient injection system
based on the low pressure gasoline technology (pintletype
injector). The injector has three discharging holes whose
diameter is of the order of 100 vtm. The nominal operating
pressure of this injector is AP, = 0.5 MPa. In the present
work, this parameter is varied from 0.2 to 0.5 MPa.
The injection time is set to 90 ms and the injection
frequency to 4 Hz. Measurements of the liquid mass
injected per injection were performed for injection times
ranging from 5 ms to 225 ms. The results reported a linear
relationship between the mass injected per injection and the
injection time indicating a negligible percentage of mass
injected during the injection transient phases, i.e., during the
opening and the closing of the injector. This result agrees
with Cousin et al. (1996). For a similar injector, they
pointed out that the liquid mass injected during the transient
injection phases is negligible when the injection time is
greater than 2 ms.
Furthermore, the liquid mass measurement allowed an
average liquid jet velocity V, to be calculated. This velocity
was used to evaluate the gaseous Weber number of the
liquid jet, i.e., WeG = pGoV2dor/ Considering the greatest
velocity, i.e., the one measured at 0.5 MPa, and taking
PG = 1.2 kg/m3, we obtain that the liquid jet gaseous Weber
number never exceeds 1.12. As reported by many
references (see Sterling and Sleicher (1975) for instance),
this value is low enough to indicate the negligible action of
the aerodynamic forces on the jet primary atomization
process.
The spray dropsize distributions are measured with a laser
diffraction technique (Malvern Spraytec 97). The principle
of working of this instrument can be found in many
references (see Dodge et al. 1987, for instance). The
measurement volume is defined as the intersection of a
collimated laser beam and a particle field. The light
forwardly scattered by the particles falls on a Fourier lens
that focuses this light on a set of diodes positioned at the
lens focal plane. The light scattering pattern recorded by the
Paper No
diodes is analyzed by the LorentzMie theory and the
system provides the volumebased dropdiameter
distribution of the set of spherical drops that would produce
the same diffraction pattern as the one recorded. The laser
diffraction is a lineofsight technique. It performs a spatial
sampling of the spray, i.e., it registers a signal proportional
to drop spatial frequency.
Figure 2: Positioning of the laser beam in the spray (circles:
laser beam, dashlines: spray)
The collecting lens used here has a focal length equal to
200 mm and the collimated laser beam diameter is equal to
10 mm. The distance between the spray and the Fourier lens
is fixed equal to 150 mm in order to avoid the vignetting
phenomena. The center of the laser beam is positioned at
several downstream distances from the injector. This
distance varies from 15 to 65 mm from the nozzle exit.
15 mm is the closest position at which measurements could
be performed. At this distance the laser beam is wider that
the spray and the measurement concerns the all spray (see
Fig. 2). Furthermore, in order to ensure the best possible
drop spatial distribution in the measurement volume, we
adjusted the injector as shown in Fig. 3.
As the distance between the injector and the nozzle
increases, the spray becomes wider than the laser beam
diameter. Thus, at 65 mm, the central part of the spray is
measured only (see Fig. 2).
La erbeam mijector
Figure 3: Orientation of the injector versus the laser beam
(dash lines represent the laser beam)
The injector and the particlesizer are triggered by a pulse
generator according to the chronograph shown in Fig. 4.
The operating frequency of the particlesizer is set equal to
50 Hz (20 ms). As said above, the injection frequency is set
equal to 4 Hz (250 ms) and the injection time is equal to
90 ms. Although the transient injection stages carry a
negligible amount of liquid, we decided to avoid measuring
the drop produced during them. To achieve this, the
measurements last 60 ms only during the 90 ms injection
time (see Fig. 4). Thus, the particlesizer performed three
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
measurements for each injection and this was repeated on
40 consecutive injections. The measured volumebased
dropdiameter distributions presented hereafter are the
averages of these 120 measurements.
Figure 4: Chronograph of injection and particlesizer
acquisition
f0. D) (1/pm)
0.008 1
0.006
0.004
0.002
0.000
cs v *
Ha^7 0
17
V 0
* 0.2 MPa
v 0.3 MPa
* 0.4 MPa
0 0.5 MPa
h 15 mm
0
, ^
0 100 200 300 400
D (gm)
Figure 5: Volumebased dropsize distribution for injection
pressure of 0.2 MPa to 0.5 MPa and h = 15 mm
Figure 5 presents the volumebased dropdiameter
distributions measured at 15 mm from the injector as a
function of the injection pressure. This figure shows that the
proportion of volume fraction contained in the small
droplets increases with the injection pressure. This behavior
is the one expected. As explained above, the primary
atomization process of the jets produced by the injector is
not influenced by the aerodynamic forces. Therefore, the
increase of the small drop proportion with the injection
pressure shown in Fig. 5 is by no mean related to the
increase of these forces. However, it is believed that this
behavior is due to the increase of the liquid jet turbulence.
Injection at low Weber numbers is very sensitive to the
liquid flow turbulence level that controls the initial
perturbation of the liquid jets issuing from the injector and
favors the production of small drops as it increases, i.e.,
when the injection pressure increases (Dumouche et al.
2005).
The distributions presented in Fig. 5 allow the gaseous
Weber number of the initial drops to be estimated. This
Test time = 10 s
 t (ms)
Chronograph of injection
   t (ms)
ograph of particlesizer acquisition
 t(ms)
Paper No
number, defined as WeG = pGV2D/a, gives information on a
possible secondary atomization of the droplets measured at
15 mm from the injector. Considering the greatest drop
diameter (D 350 vtm) as well as the greatest average
velocity (VF, 23 m/s), the greatest droplet gaseous Weber
number was estimated equal to 3.2. Shraiber et al. (1996)
reported that the smallest possible Weber number of a liquid
droplet above which secondary atomization may occur is
equal to 4. In other references (Birkhold et al. (2006) for
instance) the drop critical Webernumber above which
secondary atomization occurs is taken equal to 12. Thus, in
the present experimental situation it appears reasonable to
assume the absence of any secondary atomization process.
This does not mean that the volumebased dropdiameter
distribution will not evolve with the downstream distance.
Indeed, as shown in Fig. 6, the volumebased dropdiameter
distribution evolves with the downstream position. As the
distance from the injector increases, the distribution
becomes clearly more and more bimodal with an increase
of the proportion of the small drop population where the
distribution main peak develops. Similar evolutions were
obtained for the other injection pressures. The behavior
reported in Fig. 6 is due to two factors. First, as the distance
increases, a nonnegligible proportion of the spray is lost as
shown in Fig. 2. Each of the three spray plumes contains
rather big droplets in their central region and small one at
the periphery. At 65 mm from the injector, the big droplets
carried by the left and right jets escape from the
measurement as they do not cross the laser beam. However,
a part of the small drops in the outskirt of these two jets will
participate to the measurement. Therefore, the proportion of
small droplets in the measuring volume increases.
Second, as the distance increases, the liquid drop velocity
decreases due to air drag. The small droplets are those for
which this reduction starts first. As a consequence, the small
droplets get closer and closer as the distance from the nozzle
increases and accumulate in the measuring volume. This
behavior, detailed by Risk and Lefebvre (1984), leads to an
increase of the small drop proportion with the distance as
the one reported in Fig. 6.
0.010f(D) (1 /inm)
0.010
0 15 mm
0.008 A^ v 25 mm
*0A E 35 mm
%<>A 0 45 mm
0.006 55 mm
65 mm
0.004 ** AP1 =0.5 MPa
f I
0.002
0.000 I
0 50 100 150 200 250 300
D (pm)
Figure 6: Volumebased dropsize distribution for distances
of 15 mm to 65 mm and AP, = 0.5 MPa
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Initial dropdiameter distribution model
The objective of the initial dropdiameter distribution
model is to provide a mathematical expression for the
dropdiameter distribution of the initial spray as a function
of the working condition, i.e., the injection pressure, and to
use this mathematical distribution as initial condition in the
CFD code that calculates the spray evolution. The initial
dropdiameter distribution model is obtained by fitting the
measured distributions with a mathematical function. We
suggest using the threeparameter GeneralizedGamma
function that has been demonstrated to be the solution of the
Maximum Entropy Formalism (MEF) applied to
atomization processes (Dumouchel, 2006). The
threeparameter GeneralizedGamma function is identical
to the empirical NukiyamaTanasawa distribution
established to fit dropdiameter distribution of air assisted
sprays (Nukiyama and Tanasawa, 1939). Since then, it has
been demonstrated that the NukiyamaTanasawa
distribution is among the best function for representing
liquidspray dropdiameter distributions (Paloposki, 1994).
Therefore, there is no doubt that the threeparameter
GeneralizedGamma function will succeed in fitting
experimental spray dropdiameter distributions. This has
been recently evidenced by Lecompte and Dumouchel
( 2i ",) who reported the high capability of this function to
reproduce dropdiameter distribution of sprays produced by
very different mechanisms and measured by different
diagnostics.
Another advantage of the threeparameter
GeneralizedGamma function is that it allows mathematical
manipulations to be performed. The MEF reports the
following solution:
f D~a_ q crl D er D }q
f, (D) D exp _ D
jaJq) Dqo q DOoJ
q
This numberbased drop diameter distribution, equivalent to
a threeparameter GeneralizedGamma function and to the
NukiyamaTansawa distribution, introduces three
parameters, namely, q, a and Doo. q and a are parameters
that have no dimension. Dqo is a drop diameter, called the
constraint diameter, that belongs to the mean drop diameter
series D,, standardized by Mugele and Evans (1951). It can
be demonstrated that the mean dropdiameter series of the
numberbased distribution given by Eq. (1) is given by:
Dm,,
(Note that for m = q and n = 0, Eq. (2) reports Dn = Dqo.)
The mean diameter series is helpful to calculate other
dropdiameter distributions. For instance, the relationship
between the numberbased and the volumebased
dropdiameter distributions is:
Paper No
f.(D)= f,(D) (3)
D30
The combination of Eqs. (1), (2) and (3) allows the
expression of the volumebased dropdiameter distribution
to be obtained. It comes:
,+3 q
fv(D) q aq Daexp+2 p a D (4)
a+3j Dq q qo
The determination of the mathematical model is performed
on the volumebased dropdiameter distribution because the
laser diffraction technique reports this type of distribution.
It consists in finding the set of parameters that allows the
mathematical distribution to best reproduce the measured
distribution. As noticed in the previous section, the
measured distributions show two peaks. However, the
mathematical distribution given by Eq. (4) is a single peak
distribution. Thus, we suggest fitting the measured
distributions by a combination of two mathematical
distributions, namely, the distributions are going to be fitted
by a function of the form:
f (D)= fvfvi(D)+ (1 f )fv2(D) (5)
Such an approach was successfully used by
Yongyingsakthavom et al. (2 i"i ). In Eq.(5), fvl(D) and
fv2(D) represent the small and big drop population,
respectively. Each of these distributions introduces three
parameters, namely, qj, a and Do,. The parameter f, in Eq.
(5) may vary from 0 to 1 and represents the volume fraction
of the small drop population. Therefore, the mathematical
distribution given by Eq. (5) introduces seven parameters.
The determination of these parameters is performed by
using the protocol established by Lecompte and Dumouchel
(2'" i). It is based on the minimization of the
KullbackLeibler number I. This number measures the
closeness of two distributions: it is equal to zero when the
distributions are identical. Following Lecompte and
Dumouchel (2'" ') recommendations, I is given the
following modified form:
I= EP, 1n( K V + Y Pv, Inp' 2 (6)
t ,ve I pvi,
where the index i refers to the diameter class, p,, is the
mathematical volumefraction distribution and pve, the
experimental volumefraction distribution. These
distributions are given by:
PV,
P,, '*
fM (DJAD,
D,+AD, 2
f f(D)dD
D, AD, /2
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
positive values for the parameters q, and o (Lecompte and
Dumouchel, 2008), only positive values were considered in
the present application. Furthermore, following
Dumouchel's (2006) recommendations, the parameters a
were maintained strictly greater than 2. This precaution is
indispensable to ensure physically representative
numberbased distribution to be recovered from the
volumebased distribution.
The procedure to determine mathematical distribution was
applied on the dropdiameter distributions that were
measured close to the nozzle (h = 15 mm) and for each
injection pressure. The following set of coefficients was
obtained:
q = 0.52
a, = 2.07
Dqo1 = 13.8AP,027
q2 = 2.48
a2 = 2.54
Dq2 = 114.3AP,016
p, = 1.158AP,06
We note that the parameters q, and a, are not dependent on
the injection pressure. Such behavior was often reported
(Lecompte and Dumouchel 2008, Yongyingsakthavom et al.
2008). It is believed that these two parameters are
characteristics of the atomization mechanism and that they
don't vary much if the physical phenomena responsible for
the droplet production are unchanged. Note that the
parameters a are always greater than 2. The other
parameters, namely, Dqoi, Dqo2 and fi, are functions of the
injection pressure in an expected way. Indeed, an increase
of the injection pressure induces a decrease of the diameters
Dqoi and Dqo2 as well as an increase of the volumefraction
contained in the small drop population.
Figure 7 shows the comparison between the measured and
the mathematical volumebased dropsize distributions. For
each injection pressure, the agreement is acceptable: the
main peak diameter is well positioned and the distribution
tails are well reproduced. It is also instructive to compare
the first order moment of the mathematical and measured
distributions. Since volumebased distributions are
considered, this moment is the mean diameter D43 (Sowa,
1992). Figure 8 shows that these mean diameters are in
close agreement.
Using Eqs. (5) and (8) the initial volumebased
dropdiameter distribution is fully modelized as a function
of the injection pressure. However, the CFD code requires a
numberbased dropdiameter distribution as initial
condition. Thus, this distribution fL(D) must be obtained
from the mathematical volumebased distribution fi(D).
Two approaches can be suggested.
The first approach consists in using Eq. (3) to calculate
f.(D) fromf/(D), i.e.,
f, (D) = D30 /f (D)
D)
The set of parameters that minimizes the number I (Eq. (6))
is determined with the software Scilab. Despite the fact that
the mathematical distributions can accept negative or
where D30 is calculated from the analyticalfv(D).
Paper No
0.008
0.006
0.004
0.002
0.000
f, (1/gm)
200 400 600
D (gm)
Figure 7: Comparison between the measured and the
mathematical volumebased drop diameter distributions.
Influence of the injection pressure (h = 15 mm)
50 100 150 200
Measured D43 (inm)
Figure 8: Comparison between the calculated and
measured D43 (h = 15 mm)
The second approach suggests that, as for the volumebased
distribution, the numberbased dropdiameter distribution
can be written as a combination of two single peak
distributions, i.e.:
where the components fj(D) are given by Eq. (1). In Eq.
(10), the blending parameter iA represents the
numberfraction of the small drop population. To use Eq.
(10), the triplet of parameters of each component must be
known as well as the parameter A. As a first approach, we
assume here that the parameters of the componentf,(D) are
the same as those of the component fv,(D). Then, the
parameter A, can be calculated by using the following
relation:
where the mean diameters Dio and D1io are calculated from
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
f,(D) and the componentf,,(D), respectively. The parameter
A, calculated with Eq. (11) reports the following
dependency with the injection pressure:
Note the slight dependence of A, with the injection pressure
as well as the fact for an injection pressure corresponding to
the present working conditions, i.e. [0.2 MPa; 0.5 MPa], ,,
is always greater than 0.92.
The resulting numberbased dropdiameter distributions
f,(D) obtained by the first approach (Eq. (9)) and the second
approach (Eq.(10) with the parameters given by Eq. (8)
except for/, that is given by Eq. (12)) are compared in Fig.
9 as a function of the injection pressure.
f/(D) (1/nm)
D (gm)
Figure 9: Comparison of the numberbased dropdiameter
distributions calculated from Eq. (9) and Eq. (10)
(h = 15 mm)
It can be seen in Fig. 9 that the two approaches presented
above to determine the numberbased distribution report the
same solution. Therefore, assuming that the components
fj(D) and f,,(D) have the same parameters is acceptable.
Note in Fig. 9 that the numberbased distribution appears far
less bimodal than the corresponding volumebased
distribution (Fig. 7). This comes from the fact that, as noted
above, the blending parameter A, is always very close to 1.
The initial numberbased distribution introduced in the CFD
code in the following is the one calculated with Eq. (10).
The CFD code
A professional CFD code for simulations in engines: AVL
Fire v2008.2 is used to simulate the transported liquid phase
as well as the gaseous flow induced by the spray. The
numerical description of the continuous phase (the gas) is
based on a conservative finite volume approach. The
turbulence modeling is addressed thanks to a Reynolds
Average NavierStokes (RANS) methodology. Effects of
turbulence on the flow are modeled by the standard
kepsilon model with the original coefficients given in
Jones and Launder (1972). The numerical description of the
spray is based on the Discrete Droplet Method (DDM)
proposed in Dukowicz (1980). This method is not suitable
0 2 MPa, Eq (9)
S 0 3 MPa, Eq (9)
S 0 4 MPa, Eq (9)
O 05 MPa, Eq (9)
0 2 MPa, Eq (10)
 03 MPa, Eq (10)
 03 MPa, Eq (10)
 3 MPa, Eq (10)
h = 15 mm
hBSaa
, = 1.o01A/ ,05
f (D) = Xnf, (D)+ (1 Xn )f2 (D)
DIo = ADlo, + (1 J)Do2,
Paper No
to describe the primary breakup of the jet at the exit of the
injector, since it supposed those droplets are already formed.
Though methods have been proposed to tackle this problem
(Lebas et al., 2009) they are not yet proved to be realistic for
this kind of injector. Consequently the more appropriate
approach consists in measuring the characteristic of the
spray very close to the injector tip and to initial the
calculation with these spray characteristics. Then, stochastic
parcels representing a class of droplet are transported in a
Lagrangian fashion interacting with the gaseous phase with
a two way coupling.
In the present work, the initial numberbased dropdiameter
distribution specified in the calculation is the one obtained
in the previous section. Furthermore, as mentioned in
Section 2, the drops at 15 mm from the injector are not
expected to experience supplementary disintegration. In
consequence, no secondary atomization model is introduced
in the CFD code. However, the code includes an
evaporation model that relies on the classic film theory
developed by Abramzon and Sirignano (1988), as well as
the turbulent dispersion model due to Gosman and loannidis
(1981).
Besides the initial dropdiameter distribution, the initiation
of the calculation requires the position and diameter of the
three discharge orifices, the direction of injection of each
orifice and the angle of the spray plumes as well as the
average liquid velocity. Each of these parameters are
specified.
Results
This section presents the comparisons between the
measured dropsize distributions and those obtained by the
CFD code as a function of the injection pressure and of the
distance from the injector. As explained above, the
modelized numberbased dropdiameter distribution (Eq.
(10)) is used as initial condition in the code. This
distribution is built using constant diameter class width
equal to 2 vtm. However, since the measurements are
performed with a laser diffraction technique, which reports
volumebased dropdiameter distribution, the comparison
must be performed on this type of distribution. Furthermore,
in order to conduct relevant comparisons, the volumebased
dropdiameter distribution built from the CFD code select
the droplets that are located in the measurement volume
delimited by the laser beam. This distribution is established
by using a constant diameter class width equal to the class
width of the initial dropdiameter distribution, namely,
2 [tm.
The first result is presented in Figure 10 that compares the
measured and calculated volumebased dropsize
distributions at 65 mm and for an injection pressure equal to
0.5 MPa.
Figure 10 shows a relative acceptable agreement: the tails of
the distribution including the minimum and maximum
diameters are well predicted as well as the position and
height of the distribution main peak. However, the
calculated distribution presents nonphysical high
frequencies. This behavior may result from an inappropriate
number of droplets per class. In other words, the diameter
class width, which has been fixed to 2 vtm, might be too low
to ensure a statistically number of droplets in each class. To
overcome this problem, the diameter classes of the
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
calculated distribution have been gathered by six leading to
a final diameter class width equal to 12 vtm. Furthermore,
the final distribution has been smoothed by applying a
sliding average on three consecutive classes. As it can be
seen in Fig. 11, the increase of the diameter class width and
the smoothing of the resulting volumebased distribution
considerably improve the agreement between the
measurement and the prediction. Therefore, the treatment
consisting in gathering the diameter classes by six and in
smoothing the resulting distribution is performed for each
condition.
f,(D) (1/gm)
0.012
Measured
0.010  Calculated
0.008 AP = 0.5 MPa
h = 65 mm
0.006
0.004
0.002 
0.000
0 100 200 300 400 500
D (gm)
Figure 10: Comparison between the measured and the
calculated volumebased dropsize distribution
(AP, = 0.5 MPa, h = 65 mm)
f0(D) (1/gm)
0.010
1 Measured
** Calculated
0.008
AP = 0.5 MPa
0.006 F h = 65 mm
0.004 s *
0.002
0.000 
0 100 200 300 400 500
D (gm)
Figure 11: Comparison between the measured and the
calculated volumebased dropsize distribution after
enlargement of the diameter classes and smoothing
(AP, = 0.5 MPa, h = 65 mm)
Figure 12 presents comparisons between measured and
calculated distributions at different distances from the
injector, namely, h = 25 and 45 mm for an injection pressure
equal to 0.5 MPa. We see in this figure that the numerical
code reports acceptable predictions of the volumebased
dropsize distribution. Note an average prediction of the
height of the main peak at 45 mm and this to the detrimental
of the distribution width which is slightly overestimated.
Paper No
However, despite this, the numerical code predicts a clear
increase of the proportion of small drops as the distance
from the injector increases.
Figure 13 shows the comparison between the measured and
the calculated dropdiameter distributions as a function of
the injection pressure at h = 65 mm. We see in this figure
that the numerical code has a tendency to overestimate the
width of the distribution for low injection pressures.
However, the overall agreement remains acceptable.
Furthermore, it must be pointed out that the numerical code
reports an evolution of the dropdiameter distribution with
the injection pressure which is similar to the one reported by
the measurements.
0.010
0.008
0.006
0.004
0.002
0.000
f,(D) (1/gm)
0 100 200 300 400
D (gm)
Figure 12: Comparison between the measured and the
calculated volumebased dropsize distribution. Influence
of the distance h from the injector (zP, = 0.5 MPa)
f(D) (1/gm)
0.012
Meas 02 MPa
0.010 V Meas 03 MPa
Meas 04 MPa
0.008 Calc 0 2 MPa
0.008 h  Calc 0 3 MPa
   Calc 0 4 MPa
0.006 h 65 mm
0.004 6
0.002
0.000
Figure
calcula
of the
The r
modeli
initial
predict
of the
press
one sh
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
numberbased distribution model. A first advantage is
evident: such a model allows situations that have not been
experimentally approached to be considered provided that
calculations are performed in the range of injection pressure
examined here. A second advantage lies in the fact that the
CFD code appears to be sensible to the way the initial
numberbased distribution is distributed in the diameter
space. To demonstrate this, we performed one calculation
by using as initial condition the numberbased distribution
calculated from the measured volumebased distribution at
h= 15 mm using Eq. (9). Therefore, the resulting
numberbased distribution is distributed in diameter classes
whose width follows a logarithm progression, i.e.,
ln(D,+I/D,) = Cte. Such a progression that indicates larger
and larger diameter class as the diameter increases is
imposed by the laser diffraction technique. The
volumebased distribution calculated with this initial
condition is compared in Fig. 14 with the measured
distribution (AP, = 0.5 MPa, h = 65 mm, Case 1).
0.010
0.008
0.006
0.004
0.002
0.000
f(D) (1/gm)
0 100 200 300 400 500
D (gm)
Figure 14: Comparison between the measured and the
calculated volumebased dropsize distribution
(zP, = 0.5 MPa, h = 65 mm). Case 1: Initial distribution =
experimental numberbased distribution, Case 2: Initial
distribution = modelized numberbased distribution
distributed on diameter classes whose width follows a
logarithm progression
It can be noted that, in comparison with what was obtained
 in Fig. 11, the agreement is very poor. To demonstrate that
12 0 this agreement lost is related to the class width logarithm
progression and not the numberbased distribution itself, we
0 100 200 300 400 consider the case where the initial condition is the
modelized distribution (Eq. (10)) but distributed on the
D (gm) same class series as the experimental numberbased
13: Comparison between the measured and the distribution. The result of this case is also presented in Fig.
ited volumebased dropsize distribution. Influence 14 (Case 2) where it can be seen that it is exactly the same as
injection pressure (h = 65 mm) the one obtained in Case 1. This demonstrates that the result
provided by the CFD code is very dependent on the way the
results presented above show that the use of a initial distribution is organized in the diameter space.
zed numberbased dropdiameter distribution as Therefore, we see that the modelized initial numberbased
condition in the CFD code allows acceptable dropdiameter distribution allows this problem to be
ions of the evolution of the distribution as a function overcome since the distribution in the diameter space is not
distance from the injector and of the injection imposed as this is the case if the measured distributions are
re to be obtained. At this stage of the investigation, used as initial conditions. This point is important as it
would examine the advantage provided by the initial underlines that the initial distribution in the diameter space
Paper No
is a parameter of the problem that has to be taken into
account. As far as this very point is concerned, we wonder
whether this parameter could not be adjusted in order to
improve the results that have been presented in this work.
This aspect of the work is under consideration.
Conclusions
The investigation reported in this paper contributes to the
improvement of the use of a CDF code to simulate liquid
spray evolution. It concentrates more specifically on liquid
sprays produced at low injection pressure as those
encountered in the SCR application.
A major requirement of the CFD code to predict the spray
evolution is the knowledge of the initial spray
dropdiameter distribution. At high Weber number injection
condition, primary atomization models can be used to
predict this initial dropdiameter distribution. However,
such models are not available at low Weber number
injection condition. In the present work, this problem is
overcome as follows.
Initial dropdiameter distributions are measured with a
Laser Diffraction Technique (LDT) as a function of the
injection pressure. LDT has been preferred here because it
takes into account the nonspherical drops that are expected
to be numerous in low Weber number injection conditions.
The initial distributions are those measured as close as
possible to the injector, namely, at 15 mm. Then, a model
for these initial dropdiameter distributions is established. It
makes use of the threeparameter Generalized Gamma
function that has been reported to correctly represent
dropdiameter distribution in many different situations.
Because the measured distributions are bimodal, the model
is based on the combination of two Generalized Gamma
functions: the mathematical initial dropdiameter
distribution depends on seven parameters. Four of them
have been found independent of the injection pressure and
the three others reported a clear evolution with the injection
pressure and have been modelized in consequence. The
final initial dropdiameter distribution model allows a good
prediction of the initial dropdiameter distribution.
Then, this model is used to determine the initial distribution
required by the CFD code. The dropdiameter distributions
calculated by the CFD code at different distances from the
nozzle and for several injection pressures show a
satisfactory agreement with the measurements provided that
the comparison procedure is performed with precautions.
Thus, the initial dropdiameter distribution model is an
interesting alternative to the missing primary atomization
model. Of course, the application of this model is restricted
to the couple of injector and liquid for which it has been
established. However, the protocol to derive this model can
be easily reproduced for other operating conditions.
The results presented in this work demonstrate that the CFD
code is sensitive to the way the initial dropdiameter
distribution is specified. In particular, if the diameter class
width distribution in the diameter space follows a logarithm
progression as the one imposed by the LDT, the
comparisons between measured and calculated
dropdiameter distribution become very poor. This behavior
prevents using the measured initial dropdiameter
distribution as initial condition. The initial dropdiameter
distribution model allows this problem to be overcome and
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
this constitutes a valuable advantage. Indeed, as the initial
distribution is analytical, the diameterclass width can be
freely chosen. As far as this point is concerned, it is
mentioned here that this diameterclass width distribution
reports a non negligible influence of the calculated
distribution and could be therefore adjusted to improve the
results presented in this work. This very point is under
consideration.
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