Table Of ContentSAE Paper ?
Modeling of Diesel Combustion and NO Emissions Based on a
Modified Eddy Dissipation Concept
Sangjin Hong, Dennis N. Assanis, Margaret S. Wooldridge, Hong G. Im
The University of Michigan
Eric Kurtz
Ford Motor Company
Heinz Pitsch
Stanford University
Copyright © 2004 Society of Automotive Engineers, Inc.
ABSTRACT INTRODUCTION
This paper reports the development of an improved During the past century, the internal combustion
model of diesel combustion and NO emissions, (IC) engines have evolved dramatically in terms of
based on a modified eddy dissipation concept their fuel efficiency and exhaust emissions
(EDC), and its implementation into the KIVA-3V characteristics, primarily through extensive
multi-dimensional simulation. Compared to the experimental research and development. With
commonly used eddy break-up (EBU) model, the today’s rapid production cycles, however,
EDC model allows more realistic representation of development of new engines through experimental
the thin sub-grid scale reaction zone as well as the testing alone is costly and time consuming.
small-scale molecular mixing processes, thereby Moreover, the growing environmental concerns
achieving higher fidelity of the simulation. about global warming and hazardous emissions
Realistic chemical kinetic mechanisms for n- have led to the enforcement of even more stringent
heptane combustion and NOx formation processes regulations, and hence the need for an improved
are fully incorporated. In addition, a transition understanding of diesel combustion and pollutant
model based on the normalized fuel mass fraction is formation processes. To this end, advanced
successfully implemented to reproduce ignition and computational fluid dynamics (CFD) simulations of
combustion processes accurately. Simulations are engine reacting flow processes have emerged as a
performed for various engine speeds, injection complementary and efficient design tool for the
timings, and EGR content, and the results for the development of the next-generation engines [1-7].
basic engine performance agree well with the
experimental data. The predictions for NO Many of the early multi-dimensional CFD attempts
concentration also show a consistent trend with to predict engine combustion rates were conducted
experiments, demonstrating the improved predictive using simplified chemistry [8-10]. Typically, global
capability of the present model for diesel engine reaction models with rate constants obtained from
design and development. experimental results were used to predict reaction
rates during the ignition phase [8]. During the
turbulent combustion phase, the reaction rates were
determined based on a fast chemistry assumption
[11]. Such simplified models, however, are only the flamelet model [14] has been applied to engine
applicable to the conditions at which the rate simulations, by decoupling the chemical reaction
constants were determined [13]. In addition, it has into a one-dimensional mixture fraction space,
been found that combustion models based on the which is subsequently input into the 3-D turbulent
fast chemistry assumption can significantly over- mixing field solutions. While more physically
predict the reaction rates during the turbulent based, this flamelet approach tends to be quite
combustion phase [4]. Furthermore, since pollutant expensive when multiple flamelets need to be
formation depends strongly on heat release rates considered.
and the major and minor species concentrations,
simplified models without detailed chemistry are In this paper, we adopt a modified eddy dissipation
limited in terms of potential for accurately concept (EDC) as a reasonable compromise
predicting emissions. Therefore, consideration of between the EBU and the flamelet models. Unlike
detailed chemistry is crucial in developing a reliable the EBU model, the EDC model captures the
combustion model for engine emissions studies. characteristics of the thin reaction zone by
decomposing each computational cell into a narrow
Another deficiency in earlier CFD modeling is that “reaction zone” and the non-reacting “bulk zone”
the effects of mixing on ignition were neglected and where turbulent mixing and transport occur.
the transition between ignition and combustion was Therefore, the chemistry and mixing are effectively
abrupt. For example, Agarwal and Assanis [5] decoupled to allow the use of finite-rate detailed
employed detailed chemistry in predicting ignition chemistry in the reaction zone, yet the reaction zone
delay of natural gas combustion, where mixing does not need to be solved in a separate mixture
effects were neglected during the ignition phase. In fraction space.
addition, transition from ignition to combustion was
estimated using a global parameter, such as fuel Our earlier study [15] of the EDC model applied to
burned mass, leading to an abrupt transition. Kong a natural gas engine demonstrated excellent
and Reitz [3] incorporated turbulent mixing effects predictive capability of the model in combustion
in KIVA simulations by determining reaction rates and for qualitative trends in soot formation. One
through characteristic times. Although this limitation of the previous study was the lack of
approach resulted in an improved prediction, such quantitative experimental data for comparison
an empirical model may lead to unphysical purposes, particularly for soot formation. In the
solutions, such as negative species concentrations, present study, the EDC model is extended to
because a chemical time scale based on a reference consider n-heptane as a surrogate fuel for diesel
species is applied uniformly to all species. engines, and the modeling results are compared
with engine testing data. In the following sections,
Under most practical operating conditions in direct the basic concept of the EDC model and some new
injection (DI) engines, chemical reaction is most modifications are described. Results of the model
likely to occur within confined narrow zones predictions for selected cases of engine operating
represented by flamelets, which are distorted and conditions and comparison with experimental
stretched by the turbulent eddies. In this flamelet measurements are then presented.
regime, the thin reaction zone structure requires an
enormous demand on the grid resolution; hence it is COMPUTATIONAL SUB-MODELS
extremely difficult to capture all the details in a full-
scale engine simulation. To make the problem For the diesel combustion simulation, KIVA-3V
amenable to CFD simulations, the eddy break-up [16] has been adopted and modified to incorporate
(EBU) model has been widely used in the past. In CHEMKIN-II [17] for reaction source term
the EBU model, chemical reaction is assumed to be evaluations and CEA [18] for equilibrium
infinitely fast and only controlled by the mixing of calculations. A stiff ODE solver, LSODE, is linked
the fuel and oxidizer, which in turn is dictated by to KIVA3V to integrate the species and energy
the turbulent mixing process. Because of the equations involving detailed chemical reactions and
underlying simplifications, however, the EBU transport. As a chemical mechanism for a surrogate
model predicts combustion and emission diesel fuel, a skeletal mechanism of n-heptane
performance with limited success. More recently,
developed by Pitsch [19] with 44 species and 113 rate. The fine structure is not resolved in detail.
steps is used. Only the size of the fine structure is calculated
using a prescribed equation proposed by Magnussen.
To reproduce the ignition and subsequent Therefore, the EDC model effectively captures the
combustion processes, various physical submodels two essential characteristics of the combustion
are introduced, as described below. process: chemical reaction and mixing, without
having to resolve the sub-grid scale fine structures.
IGNITION
The time integration of the conservation equations
The key assumption used in the ignition model is proceeds as follows. At the beginning of each time
that in each computational cell, turbulent mixing is step, all the scalar variables in the fine structure are
sufficiently rapid (i.e. the Damköhler number is set to be at equilibrium conditions, which are
small) during the ignition stage, such that ignition is determined using the cell-averaged conditions.
controlled by chemical reaction with minimal Similarly, all the scalar variables in the bulk gas
effects due to mixing. Therefore, the reaction rate zone are determined based on the cell-averaged
for each species m in each cell is computed based conditions. Subsequently, the interaction between
on the cell-averaged temperature and species the fine structure and the bulk gas zone is integrated
concentration using: using the governing equations of the EDC model.
L ⎛ ⎛ N N ⎞⎞ At the end of each time step, the states of the fine
ω&m,Ignition= ∑ ⎜⎜(ν"mn−ν'mn)⎜⎜kfn ∏[Xm]νm′n −krn ∏[Xm]νm′′n⎟⎟⎟⎟ structure and the bulk gas zone are updated.
n=1⎝ ⎝ m=1 m=1 ⎠⎠
(1)
where ν" and ν' are the stoichiometric
mn mn
coefficients of the reactions, k and k are the
f r
forward and reverse rate constants, respectively, and
X is the molar concentration of species m. The
m
reaction rates during the ignition period are directly
calculated using CHEMKIN-II with the skeletal n-
heptane mechanism.
TURBULENT COMBUSTION
A modified eddy dissipation concept model is
developed and implemented as a physical subgrid
level model for turbulent combustion. The
Figure 1: Schematic of a computational cell
modified EDC model accounts for the effects of
structure based on the EDC model.
turbulent mixing on combustion. Recognizing that
the chemical reaction occurs within a thin confined
In the current work, the original EDC model
reaction zone which is typically smaller than the
proposed by Magnussen is modified to accurately
size of the numerical grid, the original EDC model
predict the unsteady characteristics of diesel engine
[20] divides the computational cell into two sub-
combustion processes. As mentioned earlier, we
zones: the fine structure and the bulk gas zone.
have previously developed and implemented a
Figure 1 shows a schematic of a computational cell
modified EDC model for computational studies of
based on the EDC model. Chemical reactions occur
natural gas engine operating conditions [15]. A
only in the fine structure where reactants are mixed
detailed description of the formulation and relevant
at the molecular level at sufficiently high
parameters can be found in that work, so only some
temperatures. In the bulk gas zone, only turbulent
key steps will be summarized here.
mixing takes place (without chemical reaction),
thereby transporting the surrounding reactant and
As the original EDC model was developed for
product gases to and from the fine structure. The
steady state conditions, unsteady terms were
coupling between the fine structure and the bulk gas
incorporated into the governing equations for the
zone interactively affects the overall combustion
fine structure and the bulk gas zone [15]. The
modified EDC governing equations for the fine rates in the current work. It is anticipated that the
structures are: reaction rate is dominated by the ignition process
during the early ignition phase. After the initial
dYm* = − 1 (Y* −Y )+ω&*mWm , (2) icgonmitbiounst iotnr amnsoideenlt shiosu ldc odmomplientaet,e . tTheh e ttruarnbsuitlieonnt
dt τ m m ρ*
r from ignition to combustion is expected to occur
when sufficient radical growth and thermal runaway
dT* = 1 ⎢⎡ 1 ∑M Y (h −h* )−∑M hm*ω&*mWm⎥⎤, (3) are achieved [21]. Using the reaction rate for
dt C*p ⎣τr m=1 m m m m=1 ρ* ⎦ species m determined by the ignition and the EDC
turbulent combustion models (Eqs. (1) and (5)), we
introduce the transition parameter, α, such that the
where * represents the fine structures and bar
overall reaction rate is determined as a linear
represents the cell-averaged values. Y , h , ω& ,
m m m combination of the two reaction rates,
and W are the mass fraction, the enthalpy, the
m
reaction rate, and the molecular weight of species ω& = (1−α)⋅ω& +α⋅ω& (6)
m m,Ignition m,EDC
m, respectively. C is the heat capacity, and ρ is
p
the density of the gas mixture. The residence time, The transition parameter α represents the progress
τr, during which the species remain in the fine of the ignition-controlled reaction (α = 0) toward
structure is expressed as:
the combustion-controlled reaction (α = 1). In our
previous work, we used an abrupt transition
(1−χγ*) between the ignition and turbulent combustion
τ = , (4)
r m&* models [15]. In this study, we assume that the
transition is dictated by the amount of the reactants
remaining in each cell. Based on this approach, a
where m&∗ is the mass exchange rate between the
normalized fuel mass fraction, β, is introduced as
fine structure and the bulk gas zone, γ∗ is the mass
fraction occupied by the fine structure, and χ
Y −Y
represents the fraction of the fine structure that β= f f,eq (7)
reacts. Y −Y
f,mix f,eq
The solution to the equations of the fine structure
where Y is the cell-averaged fuel mass fraction
f,mix
determines its state conditions. Assuming that
assuming only mixing occurs with no fuel
chemical reactions take place only in the fine
oxidation. Y is the cell-averaged fuel mass
structures, the net mean species reaction rate for the
f,eq
transport equation is given by: fraction when the same mixture is allowed to reach
an equilibrium state at the cell-averaged state
ω&m,EDC =ρχγ* (Ym* −Ym). (5) conditions. Yf,eq is calculated using the CEA
τ equilibrium code. Y is a function of the
r
f,mix
equivalence ratio only, while Y depends
The reaction rates in the fine structure are f,eq
additionally on temperature and pressure. Figure 2
determined using the CHEMKIN II subroutines that
shows the possible range of actual Y values
are interfaced with the KIVA-3V code. In this
f
study, we assume that the entirety of the fine (shown in the shaded area) that may be present
structure reacts, hence χ is set to unity in Eqs. (4) when the complete range of mixture equivalence
and (5). ratios are considered.
IGNITION-COMBUSTION TRANSITION For a given cell, during the course of ignition and
combustion, the fuel mass fraction can change from
Both the ignition and combustion models described the limiting value defined by frozen chemistry (i.e.
above are used in the determination of the reaction Y ) to the limiting value defined by complete
f,mix
reaction (i.e. Y ). The limits correspond to the mechanisms, numerical simulations were performed
f,eq
to reproduce the shock tube experiments by Ciezki
normalized fuel mass fraction of β = 1 and β = 0,
and Adomeit [26], in which ignition delays for
respectively, according to Eq. (7) .
premixed n-heptane/air mixtures were measured.
The ignition delays were predicted using constant
volume, homogeneous ignition simulations using
SENKIN [27]. We found that, for all the reaction
mechanisms considered, our predictions agree with
the experimental measurements within a similar
range of error (almost 80% error occurs at
temperature lower than 800K and pressure of 41 bar
condition). Therefore, the choice of mechanism
was based upon two criteria: the size of the
mechanism and the numerical stiffness of the
mechanism. The size of the mechanism affects the
simulation time by increasing the number of species
transport equations. The stiffness affects the
Figure 2: Schematic indicating the range of possible simulation time by increasing the number of time
steps required to integrate the equations by a unit
Y values as a function of equivalence ratio. Figure
f
physical time. After extensive test calculations, we
reproduced from [15] for methane fuel.
found that the skeletal mechanism developed by
Pitsch was reasonable in terms of these criteria,
Based on the definition of β, the transition
while showing good predictive capabilities for
parameter α is defined as:
ignition delay over wide temperature and pressure
ranges.
⎧ 0 if β > β
⎪ i
⎪ β −β Figure 4 is a comparison of the predicted and
α= ⎨ i if β > β>β (8)
i f measured values for the ignition delays. The
β −β
⎪ i f
numerical results were obtained using the skeletal
⎪ 1 if β < β
⎩ f
mechanism for various pressure and temperature
conditions with a fixed equivalence ratio (φ = 1).
where β and β represent the starting and ending
i f The predictions agree with the experimental data
points of transition, respectively. The values for β
i both qualitatively and quantitatively, reproducing
and β are numerical constants, and appropriate
f the negative temperature coefficient (NTC) regime
values for βi and βf are explored as part of this study. with very good agreement.
Figure 3 shows how the transition parameter, α,
varies as the normalized fuel mass fraction, β,
varies for arbitrary values of β and β . Note that
i f
the formulation for the reaction rate (Eq. (6)) based
on the transition parameter allows a numerically
smooth and physically realistic transition process
from ignition to turbulent combustion.
VALIDATION OF REACTION MECHANISM
In this study, n-heptane is used as a surrogate for
diesel fuel, due to its similar cetane number. Prior
to adopting the skeletal mechanism used in this
study, several reaction mechanisms for n-heptane
Figure 3: Variation of the transition parameter, α, as
were investigated [22, 23, 24, 25], including the
a function of the normalized fuel mass fraction, β .
mechanism of Pitsch [19]. To validate the reaction
3
10
Exp ( P = 13.5 bar )
Pitsch ( P = 13.5 bar )
2 Exp ( P = 30 bar )
10
s) Pitsch ( P = 30 bar )
m
Exp ( P = 41 bar )
y ( Pitsch ( P = 41 bar )
a 1
el 10
d
n
o
niti 100
g
al i
ot
T 10-1 Figure 5: The computational mesh structure of the
combustion chamber at TDC.
10-2
0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
RESULTS AND DISCUSSIONS
1000/T (1/K)
Figure 4: Comparison of ignition delays predicted
Sensitivity Analysis
using the skeletal mechanism developed by Pitsch
[19] with experimental measurements of Ciezki and
There are several parameters appearing in the
Adomeit [26] for various temperature and pressures
ignition, combustion, and transition models which
conditions (φ = 1).
need to be determined before starting a parametric
study of the engine operating conditions. In this
ENGINE SIMULATION DETAILS
work, a specific simulation case was selected from
the ranges shown in Table 1 and used to assess the
Using the validated skeletal kinetic mechanism for
sensitivity of the modeling parameters such that
n-heptane and the ignition model combined with the
optimal values for the parameters can be determined.
modified EDC model, KIVA simulations are
The results of the sensitivity analysis as well as the
performed for a light-duty diesel engine operating at
method for selecting the parameters are presented
steady state conditions. The engine parameters and
below. Once a reasonable set of such parameters
operating conditions are provided in Table 1.
were decided, no further adjustments were made
throughout the remainder of the computational
Operating Conditions
analysis. The operating conditions for the
Speed (RPM) 1250 / 1500 / 1750 sensitivity analysis (Case 1) are EGR = 0 %,
EGR (%) 0 ~ 25 injection timing = 3° ATDC and fuel mass = 0.03 g.
Injection timing
-7 ~ 4
(°ATDC) In determining the various model parameters, the
first issue encountered is to determine the initial
Fuel mass (g) 0.01 ~ 0.05
conditions for the fine structure in each cell at the
Modeling Choices
beginning of each time step. The original EDC
model was developed for steady-state combustion
Injection Model TAB
systems, therefore initial thermodynamic conditions
Turbulence Model RNG Based k-ε
of the fine structure do not affect the results. In the
Cylinder Wall Heat Flux Fixed wall temperature
transient engine simulations, however, the initial
Table 1: Engine parameters and simulation
conditions for the fine structure are important as
conditions
they determine the subsequent reaction rates.
The engine mesh geometry is shown in Figure 5.
To estimate the initial conditions for the fine
Because a six-hole injector is implemented in the
structure, the most accurate method would be to
cylinder, a 60° sector mesh is used for the
solve additional transport equations for the
calculations. Periodic boundary conditions are
quantities inside the fine structure. Since this is a
assumed in the azimuthal direction. A single three-
computationally demanding process, in the present
dimensional sector consists of approximately 5100
study the initial conditions are estimated based on
cells at TDC.
the cell-averaged quantities provided by KIVA-3V.
In doing so, we may estimate the initial conditions the combustion process, the cylinder pressure
for the fine structure by the cell-averaged quantities, variations predicted for different values of β and β
i f
or alternatively by the equilibrium condition based were explored. To isolate the effects of each
on the cell-averaged quantities. The former parameter, one parameter was set at a constant
effectively implies a rapid mixing model, i.e. the value while the other was varied for this exercise.
fine structure conditions are completely Note that β represents the point at which the
i
homogenized with the bulk gas zone at every time turbulent mixing starts to affect the reaction rates,
step. On the other hand, the latter implies that the and β represents the end of the ignition model, such
f
fine structure experiences vigorous combustion (i.e. that combustion is entirely controlled by the
a rapid chemistry model), which appears to be a interaction between the fine structure and the bulk
more reasonable assumption. gas zone.
90 100
Experiment Experiment
with Mean quantities β = 0.101 - 0.1
with Equilibrium quantities i
80 β = 0.5 - 0.1
i
β = 0.7 - 0.1
Pressure ( bar ) 3600 Pressure ( bar ) 4600 i
20
0 0
-180.0 -120.0 -60.0 0.0 60.0 120.0 180.0 -60.0 -40.0 -20.0 0.0 20.0 40.0 60.0
CA CA
Figure 6: Effects of different initial conditions for
Figure 7: Effects of β on the cylinder pressure
i
the fine structure on the predicted cylinder pressure
variation through a cycle.
for engine simulation conditions of Case 1
It was found that the results for cylinder pressure
The two initial condition strategies are compared in
were little affected by different values of β. On the
f
Fig. 6, where the cylinder pressure variation is
other hand, the onset of the turbulent combustion
plotted through a cycle. The results show that the
model, β, showed a significant impact on the
i
initial conditions based on the cell-equilibrium
overall prediction. To explore this effect further,
conditions yield better agreement with the
three values for β were tested while β was fixed at
experimental data, confirming the expectation that i f
0.1. The results are presented in Figure 7. Note
the fine structure maintains a near equilibrium
that the ignition delay (characterized by the rapid
condition. Note that, since the fine-structure
pressure rise) is advanced as β increases, because
conditions will eventually approach those of the i
the intense turbulent mixing and combustion are
final equilibrium product, the two initial conditions
initiated at an earlier time. Since the initial
will not affect the long-time behavior of the solution.
conditions for the fine structure are determined by
However, in engine simulations the duration of the
the equilibrium calculations, an earlier action of the
chemistry and mixing events are finite, hence the
combustion model always tends to advance the
initial conditions affect the overall outcome of the
ignition delay and rapid pressure rise. It is
predictions as demonstrated in Fig. 6.
interesting to note that a slightly higher peak
pressure is achieved with a lower value of β. This
Additional important parameters are associated with i
results from the fact that a longer ignition delay
the transition model. As expected from Eqs. (6)-(8),
causes a higher heat release rate during the
changes in the starting and ending points of
premixed combustion phase.
transition, β and β, can affect the overall reactivity
i f
of the system. To evaluate the effects of the
To assess the effect of β on heat generation, the
transition parameters on the reaction rates during i
computed heat release rate is compared with
experimental determinations. Since the heat release chamber with the surrounding air. The degree of
rate is difficult to measure, a net apparent heat this premixing determines the strength of the
release rate is defined from the experimentally and premixed combustion phase after it is ignited.
computationally measured pressure time history and Therefore, the case with β of 0.5 produces a higher
i
the piston displacement profile: peak value for the heat release rate compared to the
case with β of 0.7.
i
dQ γ dV 1 dp
n = p + V (9)
Parametric Studies
dt γ−1 dt γ−1 dt
Based on the sensitivity studies, two key decisions
where Q is the net apparent heat release rate, p is
n
were made regarding the model parameters. The
the cylinder pressure, V is the cylinder volume, and
initial conditions of the fine structure were set as the
γ is the specific heat ratio. Equation (9) is taken
equilibrium values at each time step, and the
from [28] in which γ = 1.35 is recommended as an
transition parameters were set as β = 0.7 and as β
appropriate value at the end of the compression i f
= 0.1. These parameters were adopted for the
stroke, and γ = 1.26 – 1.3 is recommended for the
remainder of the simulations without any further
burned gas. In this study, γ = 1.325 is used.
modification.
15000
D ) Experiment 80
A Experiment
C β = 0.5, β = 0.1
J/ i f Prediction
ate ( 11000 βi = 0.7, βf = 0.1 60
ease r bar )
at rel 7000 ure ( 40
e s
net h Pres
nt 3000 20
e
r
a
p
p
A
-1000
-10.0 0.0 10.0 20.0 30.0 0
-60.0 -40.0 -20.0 0.0 20.0 40.0 60.0
CA
CA
Figure 8: Nominal heat release rate calculated using
Figure 9: Cylinder pressure time history for
Eq. (9).
injection timing of 2.0° ATDC and EGR of 10%
(Case 2).
The comparison of the nominal heat release rate
with the predicted heat release rate is shown in
As a first variation to the baseline test case (Case 1),
Figure 8. The results clearly show that the ignition
Case 2 is chosen for a different injection timing and
delay is advanced as the value for β is increased.
i different EGR ratio with the same speed and load as
When the ignition delay is defined as the time from
Case 1 (1500 RPM and 0.03 gm). Figure 9 is the
start of fuel injection to the point of maximum heat
predicted cylinder pressure trace for an injection
release, it is found that the ignition delay for β =
i timing of 2.0° ATDC and EGR of 10%. The results
0.7 is shorter than that for β = 0.5, which is
i show a slightly delayed ignition and a lower peak
consistent with the result of ignition delay defined
pressure compared to the experimental data, both of
using pressure rise.
which are consistent with the results of Case 1. The
agreement between the simulation and experiment
In contrast to the peak pressure behavior shown in
is good and comparable to that of Case 1.
Figure 7, Figure 8 indicates that the maximum heat
release rate decreases as βi increases. It appears To validate the combustion model further, a case
that this behavior is strongly related to the ignition
with very high EGR ratio (25%) and advanced
delay. A longer ignition delay implies a longer time
injection timing (−7° BTDC) was considered. The
for mixing of the fuel injected into the cylinder
results for Case 3, plotted in Figure 10, exhibit a
similar degree of agreement between prediction and temperature. Therefore, it can be said that NO
experiment as for the previous cases. The prediction is similar to post processing at each time
difference between the two pressure profiles is less step.
than 5% at the injection timing, and good overall
agreement is achieved throughout the cycle. As Figure 11 shows the predicted NO concentrations
seen in Cases 1 and 2, the ignition delay is slightly normalized by measured NO concentrations for the
longer than experimentally observed. On the other three cases studied. Clearly, the predicted NO
hand, the peak pressure is slightly higher than the concentrations are consistently lower than the
experimental data. This is attributed to the higher experimental measurements approximately by 70%.
pressure during the compression phase. Nevertheless, the combustion model does reproduce
the correct trends observed in the experiments.
90
Experiment
1.00
Prediction
0.80
r ) 60 m )
re ( ba O ( pp 0.60
u N
Press 30 alized 0.40
m
r
o
N
0.20
0
-60.0 -40.0 -20.0 0.0 20.0 40.0 60.0
0.00
CA 0 1 2 3 4
Figure 10: Cylinder pressure time history for Cases
injection timing of −7.0° BTDC and EGR of 25% Figure 11: Comparison of predicted and
(Case 3). experimental measurements of NO concentrations
for all cases. (Normalized by experimental NO
For all three cases studied, the ignition delay and concentration.)
peak pressure are within 0.5 °CA and 3 bar,
respectively, of the experimental data. Therefore, SUMMARY AND CONCLUSIONS
we conclude that the ignition and turbulent
combustion models used in this study predict the In the current work, we have attempted to improve
engine conditions very well for the fixed speeds and the fidelity of the combustion model used in the
loads considered. Evaluation of the model fidelity KIVA-3V simulation by incorporating a sub-grid
at different speed and load conditions is currently level EDC-based combustion model. This
underway. combustion model represents an improvement over
our previous work by incorporating a more
NOx Emissions physically realistic transition between ignition and
combustion. Additionally, we have incorporated
NOx emissions depend strongly on the history of detailed kinetics in the form of a skeletal
the heat release rates and the major and minor mechanism for n-heptane as a surrogate for diesel
species concentrations. In this work, NOx fuel. The sub-models and the engine modeling
predictions are attempted by employing the were validated by comparison with experimental
extended Zeldovich mechanism. Since the latter measurements. The following conclusions are
mechanism is not included in the n-heptane outcomes of the study:
mechanism, prediction of NO is performed in a
different way compared to prediction of other • With properly defined initial conditions for the
species. By assuming that NO formation is slower fine structure and the transition parameters, the
than other species, its concentrations are predicted modified-EDC turbulent combustion model
using cell-averaged species concentrations and successfully predicts experimental pressure-time
histories for a diesel engine operating at fixed 6. Pitsch, H., Wan, Y. P., and Peters, N.,
speeds and loads. “Numerical Investigation of Soot Formation
and Oxidation Under Diesel Engine
• Ignition delays and peak pressures indicate Conditions,” SAE 952357, 1995.
excellent agreement with experimental values 7. Ishii, H., Goto, Y., Odaka, M, Kazakov, A.,
for a large range of EGR conditions (including and Foster, D. E., “Comparison of Numerical
EGR levels as high as 25%) and a large range of Results and Experimental Data on Emission
injection timings (including both early and late Production Processes in a Diesel Engine,”
injection timings). SAE 2001-01-0656, 2001.
8. Halstead, M. P., Kirsch, L. J., and Quinn, C. P,
• Trends for NO emissions are in good qualitative “The Autoignition of Hydrocarbon Fuels at
agreement with the experimental data. High Temperatures and Pressures – Fitting of
a Mathematical Model,” Combust. Flame Vol.
ACKNOWLEDGMENTS 30, 45 – 60, 1977.
9. Surovikin, V. F., “Analytical Description of
This work has been supported and funded through the Processes of Nucleus-Formation and
an Agreement (Simulation Based Design and Growth of Particles of Carbon Black in the
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