Numerical Modeling of Diesel Spray Formation and Combustion C ...

Numerical Modeling of Diesel Spray Formation and Combustion
C. Bekdemir ∗ , L.M.T. Somers, L.P.H. de Goey
Mechanical Engineering, Eindhoven University of Technology, The Netherlands
www.combustion.tue.nl
Abstract
A study is presented on the modeling of fuel sprays in diesel engines. The objective of this study is in the first place to
accurately and efficiently model non-reacting diesel spray formation, and secondly to include ignition and combustion.
For that an efficient 1D Euler-Euler spray model [21] is implemented and applied in 3D CFD simulations. Concerning
combustion, a detailed chemistry tabulation approach, called FGM (Flamelet Generated Manifold), is adopted.
Results are compared with EHPC (Eindhoven High Pressure Cell) experiments, data from Sandia and IFP. The newly
created combination of the 1D spray model with 3D CFD gives a good overall performance in terms of spray length
and shape prediction, and also numerically it has advantages above Euler-Lagrange type models. Together with the
FGM, also auto-ignition and a flame lift-off length is achieved.
Introduction
Due to ever increasing demands from emission legislation
(NOx and soot), fuel economy (CO2) and fuel
flexibility (bio-fuels) diesel engines become more and
more complex. Therefore, conventional engine design approaches
that rely on prototype development become too
time-consuming and expensive. The development of predictive
and efficient computational tools would represent
a significant step forward in the ability to rapidly design
high efficiency, low emission engines [8].
Modern diesel engine technology unequivocally applies
liquid fuel injection with high pressure, that forms
a non-homogenous mixture leading to relatively high levels
of soot. This spray formation process may seem
straightforward, but in reality it is dauntingly complex.
Furthermore, combustion presents especially great challenges
[14]. For that reason, accurate and fast CFD is
needed. The objective of this study is to accurately and efficiently
model diesel spray formation, and capture autoignition
and flame lift-off by means of a tabulated chemistry
method called FGM (Flamelet Generated Manifold).
Spray formation and combustion modeling are described
in the following sections, respectively. Subsequently
some reacting spray results are presented. And finally
some conclusions and recommendations are given.
Spray Modeling
Fluent’s DPM model (Euler-Lagrange method) is extensively
used to model evaporating, but inert heptane
sprays. This is done with special attention for temperature
dependent material properties and for many different
setups, including various meshes, solver timesteps and
amount of parcels (groups of identical droplets). The results
are compared with a measurement on the EHPC and
experimental data from Sandia. From these comparisons
it is found that the DPM model gives unsatisfactory results
concerning spray and liquid lengths. From a numerical
point of view there are also major disadvantages. The
∗ Corresponding author: c.bekdemir@tue.nl
Proceedings of the European Combustion Meeting 2009
results are highly mesh and timestep dependent and often
convergence problems occur. Also the statistical approach
with parcels is a source of problems due to large
computing times when parcels accumulate in the domain.
Many authors tried to overcome these problems by fine
tuning the submodels for specific cases, but this is obviously
not the way to go due to the fundamental discrepancy
between, on one hand the limitation to cell sizes and
lack of parallelization possibilities, and on the other hand
solving in-cylinder velocity fields and turbulence with increasingly
finer meshes.
However, others also developed (semi) Euler-Euler
methods to model spray formation. One of them is the socalled
ICAS (Interactive Cross section Averaged Spray)
model [17, 22] that combines a 1D (Eulerian) spray model
with the existing Langrangian CFD model. The region
near the nozzle exit is then covered with the 1D spray
model and somewhere further downstream droplet source
terms are introduced to incorporate 3D spray formation
in the CFD environment. By introducing parcels anyway,
the influence of in-cylinder flow to spray formation would
still be captured [18], but to do so the Euler-Euler region
should be not more than a few millimeters from the nozzle
exit, because further downstream (behind the liquid
length) there are no droplets anymore. This makes complex,
adaptive meshes necessary, and the DPM model of
Fluent would still be needed. However, ideally the CFD
code should be used for gas phase calculations only in order
to circumvent the complex discrete phase interaction.
Therefore a 1D model that covers the complete spray region
is presented in this chapter. This model is coupled
to Fluent with appropriate source terms for mass (fuel vapor),
momentum and energy.
In the following, first the phenomenological spray
model proposed by Versaevel et al. [21] is introduced.
The model is then implemented in Matlab and validated
with measurements of IFP [20] and Sandia [7][15]. Last
but not least, source terms are extracted from the 1D
model and put into Fluent via UDFs (User-Defined Function),
and the resulting 3D solutions are also compared
with measurements.

1D Euler-Euler Spray Model
The 1D quasi steady spray model of Versaevel et al.
[21] is an extension of the earlier efforts of Naber et al.
[11] and Siebers [15]. Naber and Siebers developed a 1D
model for non-vaporizing spray penetration first, and later
Siebers added some thermodynamics to distinguish liquid
penetration from vapor penetration. But Siebers’ contribution
is based on the assumption that only at the steady
liquid length position thermodynamic equilibrium exists.
This approach implies that no temperature information is
available, except at the liquid length position. Also the
composition of the spray volume between the nozzle exit
and liquid length is unknown. Versaevel et al. overcame
this shortcoming by introducing a void fraction m that
couples the mass, momentum and energy equations.
The model is based on five basic assumptions from
which the first four are the same as in the work of Naber
et al. [11] and Siebers [15].
⇒ no velocity slip between gas and liquid phases
⇒ whole system at constant pressure
⇒ uniform velocity, density and temperature profiles
⇒ constant spray angle
⇒ whole system at thermodynamic equilibrium
The last assumption is necessary to gain information
about the temperature and composition of the spray in
the entire 1D domain. The mass, momentum and energy
equations are derived by considering a control volume as
defined in Figure 1. The spray is described in one direction
due to the constant angle and the axisymmetry. The
figure shows that from fuel injection ( ˙mfl,0) into the xdirection
the spray diverges due to air entrainment ( ˙ma)
into the spray volume. Air entrainment is controlled by
the prescribed spray angle ( θ
2 ). For this purpose an experimental
dispersion relation is chosen. At the liquid length
just enough hot air is entrained into the spray to evaporate
all liquid fuel, so from that point on the fuel penetrates the
surrounding gas as a vapor.
The phenomenological spray model is implemented in
Matlab. The standard non-linear solver of Matlab is used
for this purpose. Material properties, except the liquid fuel
.
mfl,0
.
ma
.
ma
control volume
/2
d eff
gas and liquid gas only
Figure 1: Definition of the control volume used in the derivation
of the 1D model [21]
df
x
2
density, are temperature dependent, and are obtained from
the thermophysical database of DIPPR [6]. The calculated
spray length compares good with IFP measurements [20]
as shown in Figure 2, indicated with the solid en dotted
lines, respectively.
SL [mm]
50
45
40
35
30
25
20
15
case: IFP heptane
10
5
3D model
Fluent DPM
1D model
fit through IFP measurements
0
0 0.1 0.2 0.3 0.4 0.5
Time [ms]
0.6 0.7 0.8 0.9 1
Figure 2: Spray length as function of time with the Euler-Euler
3D model, compared to Fluent DPM, Euler-Euler 1D model and
IFP measurement
3D Spray Simulation
The 1D phenomenological spray model discussed in
the previous section is, in contrary to the earlier model of
Naber and Siebers, suitable to apply in combination with a
3D CFD code. To accomplish such an interaction, source
terms are extracted from the 1D model and are assigned
to the corresponding transport equations in Fluent (see [3]
for the details). Subsequently the combined model is validated
through spray length comparison with experimental
data. IFP [20] and Sandia [15][7] measurements are used
for validation purposes. These are all for single component
fuels that are well documented, so thermophysical
data needed for the numerical model is found in literature.
The implemented 3D model (circles) predicts the
spray length better than Fluent’s DPM model (stars), as is
shown in Figure 2. The correctness of the 3D model prediction
is best visualized with the contours of fuel mass
fraction at the spray cross-section shown in Figure 3. The
upper spray is a DPM simulation result and the other one
is gained with the 3D model, both at 1 ms. Apart from the
obvious spray length difference, the shape/width of the
sprays are also dissimilar. DPM gives too wide sprays,
since relatively large cells have to be used to meet the requirements
of the Lagrangian approach. In the 3D Euler-
Euler case one can refine the grid until the spray is resolved
sufficiently, without having discrete phase related
problems.
Summarizing, the better overall performance (spray
length and shape) and the proper mesh resolution behavior
(higher resolution gives better solutions) of the 3D
Euler-Euler model, together with the ability to parallelize
is a major advantage compared with Fluent’s DPM model.
Since the DPM model uses only one CPU to do all discrete

Figure 3: Case: IFP heptane. Contours of fuel mass fraction
gained with Fluent’s DPM model and the implemented 3D spray
model. Note the minimum/maximum values between the brackets
at the right hand side, the colorbar is scaled for each separately
phase calculations no matter how many CPUs are available.
The consequence is large computation times despite
the relatively small amount of cells.
Possible improvements to the 1D/3D spray model for
the future may be the following:
⇒ Make 3D spray model pressure dependent in order to
simulate spray formation in a variabele volume combustion
chamber.
⇒ Sound spray angle prediction. Not really an improvement
to the model itself, but spray angle prediction
certainly has a large effect on the final results. Therefore
the quest for proper and generic angle prediction
methods/relations should be promoted.
Combustion Modeling
In the preceding chapters a 3D Euler-Euler spray
model is implemented and validated for evaporating inert
fuel sprays. This model is mesh and solver timestep
independent, and is suitable for parallel simulations. So,
regarding the status of modeling the mixing process, additional
modeling features, which may require fine spatial
and time resolutions, can be included. In this chapter an
attempt is made to add combustion, more specific, the emphasis
is on the application of FGMs (Flamelet Generated
Manifolds) in modeling of the turbulent combustion of a
transient igniting spray.
In the following, first the principle of flamelets and its
use for modeling combustion with tabulated chemistry is
shortly mentioned. Then, the procedure of a FGM generation
is shown. Subsequently, its implementation into
Fluent is described.
FGM Approach
Detailed models can be very accurate, but unfortunately
also computationally very expensive. To overcome
3
the impractical computing times, while solving the combustion
process still with high detail (depends on used reaction
scheme), an approach with tabulated chemistry is
applied. This so-called FGM approach is developed by
van Oijen [19] for laminar premixed flames, and makes
use of 1D laminar flamelet data to tabulate composition,
density, temperature etc. as function of local control
variables. However, the flamelet concept views a turbulent
flame as an ensemble of thin, laminar, locally 1D
flames, called flamelets, embedded within the turbulent
flow field. Furthermore, the concept is based on the assumption
that the smallest turbulent time and length scales
are much larger than the chemical ones, and there exists a
locally undisturbed sheet where chemical reactions occur
[16]. So, later Ramaekers [13] extended the application to
turbulent partially-premixed combustion by choosing one
control variable describing non-premixed (mixture fraction
Z) and one describing premixed (reaction progress
variable P V ) combustion, and by PDF (Probability Density
Function) integration to account for turbulence.
In this study non-premixed flamelets for a counterflow
setup are solved with CHEM1D [1], which is a specialized
one-dimensional laminar flame code developed at the
Eindhoven University of Technology. A heptane flamelet
database at constant pressure is calculated, making use of
a reduced n-heptane mechanism [12].
In non-premixed combustion it is common practice to
introduce the mixture fraction Z, here the definition of
Bilger [4] is adopted:
Z =
2 YC−YC,2
MC
2 YC,1−YC,2
MC
1 +
YH −YH,2 (YO−YO,2)
2 − MH
MO
+ 1 YH,1−YH,2
2 − MH
YO,1−YO,2
MO
, (1)
where Y stands for mass fraction, M is the molar mass
and the subscripts C, H and O indicate the quantities
for the elements carbon, hydrogen and oxygen, respectively.
The subscripts 1 and 2 refer to the constant mass
fraction in the original fuel and oxidizer streams, respectively.
In the fuel stream the mixture fraction is equal to
unity and monotonically decreases to zero at the oxidizer
stream. An additional control variable, called the reaction
progress variable P V , is introduced to parameterize the
progress of the irreversible combustion process. In this
study a combination of CO2, CO and CH2O mass fractions
is chosen as a reaction progress variable:
P V = YCO2
MCO2
+ YCO
+
MCO
YCH2O
. (2)
MCH2O
The succes of this concept is related to the fact that
all occurring compositions tend to have a common,
low-dimensional, attractor in composition space, a socalled
intrinsic low-dimensional manifold (ILDM) [9].
Hence, the complex chemistry is reduced and completely
described by the mixture fraction Z and the reaction
progress variable P V .
FGM Construction and Implementation
FGMs can be generated in many ways. For stationary
flames, there is a classical way with steady flamelets only,

PV [−]
Flamelet database generation
igniting flamelet
extinguishing flamelet
igniting PSRs
0 0.1 0.2 0.3 0.4 0.5
Z [−]
0.6 0.7 0.8 0.9 1
Lowest strainrate
Steady solutions region
Highest non−quenching strainrate
Timedependently extinguishing or igniting flamelet
Perfectly Stirred Reactors (PSRs) before ignition
Figure 4: Ways to generate a ’full’ flamelet database
where a sequence of steady flames with strainrates varying
from a low value to the quenching value is computed.
An illustrative example is shown in Figure 4, see the gray
area between the solution for the lowest strainrate and the
solution at which the strainrate reached its maximum before
extinction.
But a spray event is unsteady and initially nonreacting,
so to cover the ignition process the table should
also contain information in the area beneath the quenching
strainrate solution. Several ways exist to fill this gap
in the Z-P V plane. One way is to solve a timedependent
flamelet with a higher strainrate than the highest possible
non-quenching strainrate, in this way forcing the flame to
extinguish and in the mean time sampling data to fill the
gap. Another approach, that is more appropriate for this
study, is solving timedependent flamelets from a mixed,
but non-reacting initial state. The ignition behavior is followed
in time until a steady flame is reached. The third
possibility is to reproduce ignition of mixtures covering
the entire Z-space with PSR (Perfectly Stirred Reactor)
auto-ignition calculations [10]. All three methods to fill
the Z-P V gap are depicted schematically in Figure 4.
The way(s) a FGM is constructed in this study is depicted
schematically in Figure 5.
Due to the unsteady nature of a diesel injection event,
ignition modeling is at least as important as combustion
modeling. Following the FGM approach, besides combustion,
ignition should be covered inherently. But not
surprisingly this depends on the way the FGM is generated.
The extinguishing flamelet approach is applied and
does not lead to ignition of the spray. Instead, only local
temperatures slightly above the initial ambient temperature
are found, and the source of the reaction progress
variable is not big enough to end in total ignition within
a few milliseconds. However, a FGM constructed with
4
an igniting flamelet database does result is auto-ignition
of the whole spray in short time. Therefore, in this paper
only the results of the igniting flamelet approach are
presented.
The turbulence-chemistry interaction is accounted for
by integrating the quantities ϕ in the 2D table with a β-
PDF function as follows:
˜ϕ =
1 1
0
0
ϕ(Z, P V ) ˜ P (Z) ˜ P (P V ) dZdP V. (3)
Note that this explicit formulation assumes that Z and
P V are statistically independent. The overtilde stands for
Favre (mass) averaged. Both control variables are from
then on described with a mean value ( ˜ Z, P V ) and a variance
(Z” 2 , P V ” 2 ), so a quantity is defined by the probability
of occurrence for several states instead of one fixed
state. The chemistry is in this way extended to a 4D lookup
table with the means and variances of the two control
variables as the parameters (look-up indices).
The 4D FGM combustion model is implemented in
Fluent, in order to do turbulent spray combustion simulations
in 3D space. The four scalars ( ˜ Z, P V , Z” 2 , P V ” 2 )
are solved with user-defined scalar transport equations, in
addition to the standard continuity, momentum and turbulence
equations. All species concentrations and corre-
quenching flame
Z-PV domain filled with
stationary loop over strainrates ,
and with timedependent
quenching flame
TRF mechanism
48 species
248 reactions
CHEM1D
solves:
flamelet equations
(constant pressure )
2D FGM
Z, PV – table
(laminar)
interpolated laminar flamelet data ρ,
sPV, Yi and T as function of
Z and PV
4D FGM
"2 "2
Z, Z , PV ,PV – table
(turbulence included )
2D data integrated with PDF
functions. ρ, sPVm,
"2
sPV ,sPV sPVv, Yi and T
as function of mmmmmmmm "2
, , "2
Z Z PV ,PV
Figure 5: FGM construction scheme
igniting flame
Z-PV domain filled with , from
initial pure mixing solution ,
igniting flame , using the
timedependent solver

sponding temperatures are in principle known from the
flamelet database for any mixture fraction and progress
variable combination.
Results and Discussion
The evolution from the early stage of ignition to further
combustion of the spray, injected from the left, is
shown at six moments in time in Figure 6. The upper half
of the plots represent the values of the progress variable
and the lower parts are contours of temperature. Several
interesting observations are done from this figure. First, at
the outer edge of the spray activity begins, here shown by
means of an increased (and still increasing) progress variable
and a corresponding increase in temperature; from
an initial 800 K ambient to around 1000 K locally. This
activity is particularly present close to the place the flame
lift-off will settle. Further in time the outer contour of the
igniting spray is becoming clearer due to high values of
P V and T . Finally, the full outer edge will be reacting
and the combustion region expands to the inner volume
and the maximum temperature continues to rise.
Also a much simpler combustion model is used that
is available in Fluent, called eddy-dissipation model [2].
This model is, like the flamelet approach, a mixinglimited
combustion model, with the differences that only
the global reaction from fuel and O2 to CO2 and H2O is
considered and immediate reaction is assumed. So, it is
not expected that this simple model can be as accurate as
the much more detailed FGM method, but it gives nice
material to compare regarding for example temperature
profiles. Such a comparative picture is given in Figure 7,
taken at 1 ms. In contrast to the eddy-dissipation model,
apart from the inherent auto-ignition, also a flame lift-off
settles automatically using tabulated chemistry.
The diffusion flame at the spray edge stays the hottest
region, as can be expected on the basis of the used nonpremixed
flamelet database. But according to the conceptual
diesel combustion model of Dec [5] it is stated that
in DI diesel injection, regions with premixed and nonpremixed
combustion can be distinguished. The next step
Tmax = 807 K Tmax = 853 K
Figure 6: Case: IFP heptane. Temporal sequence of progress
variable and temperature contours showing the auto-ignition
process resulting in total combustion
5
Figure 7: Case: IFP heptane. Contours of temperature gained
with the eddy-dissipation model and the implemented FGM
model. Note the minimum/maximum values between the brackets
at the right hand side, the colorbar is scaled for each separately
may be the creation of a partially-premixed database in
order to capture the presence of both regimes at the same
time.
Unfortunately, there are no experimental ignition delay
and lift-off length data published for this case in the
paper of Verhoeven et al. [20]. However, the numerically
found delay time and lift-off length are in the order
of magnitude of comparable fuel sprays. Also two important
observations that are reported by Verhoeven et al.
are the auto-ignition position and the subsequent burning
behavior. They state that the first visible emission corresponds
roughly to the flame lift-off distance during quasisteady
state combustion phase observed later. And that
this auto-ignited kernel progresses along the spray until
it reaches the tip, after which no other development occurs,
except for further penetration. The above presented
numerical results of the Euler-Euler spray model together
with the FGM combustion model is completely coherent
with these experimental observations.
Conclusions
A 1D Euler-Euler spray model is implemented into 3D
CFD (Fluent). This 3D spray model is validated with inert
fuel spray penetration measurements and is able to predict
spray lengths and shapes quantitatively well. It also
offers the advantage of a proper mesh resolution behavior
(higher resolution gives better solutions), and is suitable
for parallel computing.
Combustion of the fuel spray is modeled with a tabulated
chemistry approach (FGM). The manifold is created
with igniting diffusion flame solutions. Important characteristics
like auto-ignition and flame lift-off are captured
without explicitly modeling them, showing the generic nature
and therefore the potential of the applied method.
A first study with heptane as a surrogate for diesel

fuel shows promising results concerning spray formation,
and subsequently auto-ignition and the settling of a lift-off
length.
Outlook - Future Research
In the future, direct validation with ignition delay
times and flame lift-off lengths will be done. And at the
same time the influence of the preprocessing phase on the
combustion behavior will be investigated. One can think
about the choice of a progress variable and the applied
FGM generation method.
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