Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 12.4.3 - Development of an Initial Drop-Size Distribution Model and Introduction in a CFD Code to Predict Spray Evolution
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 Material Information
Title: 12.4.3 - Development of an Initial Drop-Size Distribution Model and Introduction in a CFD Code to Predict Spray Evolution Computational Techniques for Multiphase Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Gapin, A.
Demoulin, F.-X.
Dumouchel, C.
Pajot, K.
Patte-Rouland, B.
Réveillon, J.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: liquid spray
drop-diameter distribution
CFD code
spray evolution
 Notes
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 drop-diameter distribution can be specified as initial condition. In the present approach, measurements of the initial drop-diameter distribution are performed with a Laser Diffraction Technique (LDT) which seems more appropriate to characterize sprays containing a non negligible proportion of the non-spherical droplets. A model of the initial drop-diameter distribution is developed. This model can substitute the missing primary atomization model in the CFD code. Comparisons between measured and calculated drop-diameter 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 drop-diameter 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 indentified 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.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Holding Location: University of Florida
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Resource Identifier: 1243-Gapin-ICMF2010.pdf

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Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Development of an Initial Drop-Size Distribution Model and Introduction in a CFD Code to
Predict Spray Evolution


Arnaud Gapin1'2, Frangois-Xavier Demoulin1, Christophe Dumouchel1, Karine Pajot2,
Beatrice Patte-Rouland', 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 Peugeot-Citroen Direction de la Recherche Centre Technique de Velizy Route de Gisy
78943 Velizy-Villacoublay Cedex, France

Snamea coria.fr

2karine.pajot@mpsa.com

Keywords: Liquid spray, Drop-diameter 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
drop-diameter distribution can be specified as initial condition. In the present approach, measurements of the initial
drop-diameter distribution are performed with a Laser Diffraction Technique (LDT) which seems more appropriate to
characterize sprays containing a non negligible proportion of the non-spherical droplets. A model of the initial drop-diameter
distribution is developed. This model can substitute the missing primary atomization model in the CFD code. Comparisons
between measured and calculated drop-diameter 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 drop-diameter
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 exhaust-gas 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
exhaust-gas after-treatment 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 drop-size distribution, i.e., the drop-size 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 drop-diameter
distribution obtained from measurements. This solution was
adopted by Birkhold et al. (2006) who used as initial
condition a drop-diameter 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 number-based
drop-diameter 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 drop-diameter distribution contains a
non negligible proportion of non-spherical big drops that
escape from the measurements.
To overcome this problem, we propose in the present work to
characterize the initial drop-diameter 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 volume-based drop-diameter
distribution.
The second objective of this work is to provide a model of the
initial drop-diameter 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 three-parameter generalized gamma function that
is known to provide a good representation of liquid spray
drop-diameter distribution (Lecompte and Dumouchel,
2008).
The second Section of this paper presents the experimental
set-up and diagnostic used. The modelization of the initial
drop-diameter 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) number-based drop diameter distribution (vtm 1)
f,(D) volume-based drop diameter distribution (vtm 1)
h distance from the injector (mm)
I Kullback-Leibler number (-)
pv volume-fraction distribution (-)
q parameter of the Generalized-Gamma distribution
(-)
V, average liquid jet velocity (m/s)
WeG gaseous Weber number (-)
Greek letters
a parameter of the Generalized-Gamma 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 number-based
v volume-based

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 30-June 4, 2010

spray consists in measuring the drop-diameter 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 set-up

A single liquid is used throughout the work. This liquid is
water whose physical properties are pL= 998 kg.m-3,
PL = 1.10- Pa.s and o= 73.10 N.m-1.
A single injector is used. It is a transient injection system
based on the low pressure gasoline technology (pintle-type
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 drop-size 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 Lorentz-Mie theory and the
system provides the volume-based drop-diameter
distribution of the set of spherical drops that would produce
the same diffraction pattern as the one recorded. The laser
diffraction is a line-of-sight 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, dash-lines: 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 particle-sizer are triggered by a pulse
generator according to the chronograph shown in Fig. 4.
The operating frequency of the particle-sizer 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 particle-sizer performed three


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

measurements for each injection and this was repeated on
40 consecutive injections. The measured volume-based
drop-diameter distributions presented hereafter are the
averages of these 120 measurements.


Figure 4: Chronograph of injection and particle-sizer
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: Volume-based drop-size distribution for injection
pressure of 0.2 MPa to 0.5 MPa and h = 15 mm

Figure 5 presents the volume-based drop-diameter
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 particle-sizer 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 Weber-number 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 volume-based drop-diameter
distribution will not evolve with the downstream distance.
Indeed, as shown in Fig. 6, the volume-based drop-diameter
distribution evolves with the downstream position. As the
distance from the injector increases, the distribution
becomes clearly more and more bi-modal 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 non-negligible 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: Volume-based drop-size 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 30-June 4, 2010

Initial drop-diameter distribution model

The objective of the initial drop-diameter distribution
model is to provide a mathematical expression for the
drop-diameter 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
drop-diameter distribution model is obtained by fitting the
measured distributions with a mathematical function. We
suggest using the three-parameter Generalized-Gamma
function that has been demonstrated to be the solution of the
Maximum Entropy Formalism (MEF) applied to
atomization processes (Dumouchel, 2006). The
three-parameter Generalized-Gamma function is identical
to the empirical Nukiyama-Tanasawa distribution
established to fit drop-diameter distribution of air assisted
sprays (Nukiyama and Tanasawa, 1939). Since then, it has
been demonstrated that the Nukiyama-Tanasawa
distribution is among the best function for representing
liquid-spray drop-diameter distributions (Paloposki, 1994).
Therefore, there is no doubt that the three-parameter
Generalized-Gamma function will succeed in fitting
experimental spray drop-diameter distributions. This has
been recently evidenced by Lecompte and Dumouchel
( 2i ",) who reported the high capability of this function to
reproduce drop-diameter distribution of sprays produced by
very different mechanisms and measured by different
diagnostics.
Another advantage of the three-parameter
Generalized-Gamma 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 number-based drop diameter distribution, equivalent to
a three-parameter Generalized-Gamma function and to the
Nukiyama-Tansawa 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 drop-diameter series of the
number-based 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
drop-diameter distributions. For instance, the relationship
between the number-based and the volume-based
drop-diameter distributions is:





Paper No


f.(D)= f,(D) (3)
D30

The combination of Eqs. (1), (2) and (3) allows the
expression of the volume-based drop-diameter 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 volume-based drop-diameter 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
Kullback-Leibler 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 volume-fraction distribution and pve, the
experimental volume-fraction 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 30-June 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
number-based distribution to be recovered from the
volume-based distribution.
The procedure to determine mathematical distribution was
applied on the drop-diameter 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 volume-fraction
contained in the small drop population.
Figure 7 shows the comparison between the measured and
the mathematical volume-based drop-size 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 volume-based 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 volume-based
drop-diameter distribution is fully modelized as a function
of the injection pressure. However, the CFD code requires a
number-based drop-diameter distribution as initial
condition. Thus, this distribution fL(D) must be obtained
from the mathematical volume-based 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 volume-based 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 volume-based
distribution, the number-based drop-diameter 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
number-fraction 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 30-June 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 number-based drop-diameter 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 number-based drop-diameter
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 number-based 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 number-based distribution appears far
less bimodal than the corresponding volume-based
distribution (Fig. 7). This comes from the fact that, as noted
above, the blending parameter A, is always very close to 1.
The initial number-based 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 Navier-Stokes (RANS) methodology. Effects of
turbulence on the flow are modeled by the standard
k-epsilon 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 number-based drop-diameter
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 drop-diameter 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 drop-size 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 number-based drop-diameter 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
volume-based drop-diameter distribution, the comparison
must be performed on this type of distribution. Furthermore,
in order to conduct relevant comparisons, the volume-based
drop-diameter 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 drop-diameter distribution, namely,
2 [tm.
The first result is presented in Figure 10 that compares the
measured and calculated volume-based drop-size
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 non-physical 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 30-June 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 volume-based 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 volume-based drop-size 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 volume-based drop-size 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 volume-based
drop-size 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 drop-diameter 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 drop-diameter 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 volume-based drop-size 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 30-June 4, 2010

number-based 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
number-based distribution is distributed in the diameter
space. To demonstrate this, we performed one calculation
by using as initial condition the number-based distribution
calculated from the measured volume-based distribution at
h= 15 mm using Eq. (9). Therefore, the resulting
number-based 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
volume-based 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 volume-based drop-size distribution
(zP, = 0.5 MPa, h = 65 mm). Case 1: Initial distribution =
experimental number-based distribution, Case 2: Initial
distribution = modelized number-based 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 number-based 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 number-based
13: Comparison between the measured and the distribution. The result of this case is also presented in Fig.
ited volume-based drop-size 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 number-based drop-diameter distribution as Therefore, we see that the modelized initial number-based
condition in the CFD code allows acceptable drop-diameter 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
drop-diameter distribution. At high Weber number injection
condition, primary atomization models can be used to
predict this initial drop-diameter distribution. However,
such models are not available at low Weber number
injection condition. In the present work, this problem is
overcome as follows.
Initial drop-diameter 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 non-spherical 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 drop-diameter distributions is established. It
makes use of the three-parameter Generalized Gamma
function that has been reported to correctly represent
drop-diameter 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 drop-diameter
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 drop-diameter distribution model allows a good
prediction of the initial drop-diameter distribution.
Then, this model is used to determine the initial distribution
required by the CFD code. The drop-diameter 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 drop-diameter 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 drop-diameter
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
drop-diameter distribution become very poor. This behavior
prevents using the measured initial drop-diameter
distribution as initial condition. The initial drop-diameter
distribution model allows this problem to be overcome and


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

this constitutes a valuable advantage. Indeed, as the initial
distribution is analytical, the diameter-class width can be
freely chosen. As far as this point is concerned, it is
mentioned here that this diameter-class 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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Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

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