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Investigation of Cycle-to-Cycle Variability
of NO in Homogeneous Combustion
A. Karvountzis-Kontakiotis and L. Ntziachristos*
Aristotle University of Thessaloniki, Laboratory of Applied Thermodynamics (LAT), GR54125, POB 458, Thessaloniki, Greece
e-mail: akarvout@auth.gr - leon@auth.gr
* Corresponding author
Abstract — Cyclic variability of spark ignition engines is recognized as a scatter in the combustion
parameter recordings during actual operation in steady state conditions. Combustion variability may
occur due to fluctuations in both early flame kernel development and in turbulent flame propagation
with an impact on fuel consumption and emissions. In this study, a detailed chemistry model for the
prediction of NO formation in homogeneous engine conditions is presented. The Wiebe parameter-
ization is used for the prediction of heat release; then the calculated thermodynamic data are fed into
the chemistry model to predict NO evolution at each degree of crank angle. Experimental data
obtained from literature studies were used to validate the mean NO levels calculated. Then the model
was applied to predict the impact of cyclic variability on mean NO and the amplitude of its variation.
The cyclic variability was simulated by introducing random perturbations, which followed a normal
distribution, to the Wiebe function parameters. The results of this approach show that the model
proposed better predicts mean NO formation than earlier methods. Also, it shows that to the non
linear formation rate of NO with temperature, cycle-to-cycle variation leads to higher mean NO
emission levels than what one would predict without taking cyclic variation into account.
Re
´sume
´—Enque
ˆte de la variabilite
´cycle-a
`-cycle du NO dans la combustion homoge
`ne —
La variabilite
´cyclique des moteurs a
`allumage commande
´est reconnue comme une dispersion
dans les enregistrements des parame
`tres de combustion lors du fonctionnement re
´el dans des
conditions stables. Des variabilite
´s de combustion peuvent se produire en raison des
fluctuations dans le de
´veloppement pre
´coce du noyau de la flamme et dans la propagation
turbulente de la flamme avec un impact sur la consommation de carburant et les e
´missions.
Cette e
´tude pre
´sente un mode
`le chimique de
´taille
´pour pre
´voir la formation de NO dans des
conditions de combustion homoge
`ne. Le parame
´trage de Wiebe est utilise
´pour pre
´voir le
de
´gagement de chaleur ; les donne
´es thermodynamiques calcule
´es sont ensuite inte
´gre
´es au
mode
`le chimique pour pre
´voir l’e
´volution de NO a
`chaque degre
´d’angle de rotation du
vilebrequin. Les donne
´es expe
´rimentales obtenues a
`partir de l’analyse des publications
ante
´rieures ont e
´te
´utilise
´es pour valider les niveaux moyens de NO calcule
´s. Le mode
`le a
ensuite e
´te
´applique
´pour pre
´voir l’impact de la variabilite
´cyclique sur le taux moyen de NO
forme
´et l’amplitude de sa variation. La variabilite
´cyclique a e
´te
´simule
´e en introduisant des
perturbations ale
´atoires qui suivent une distribution normale, aux parame
`tres de la fonction de
Wiebe. Les re
´sultats de cette approche montrent que le mode
`le propose
´pre
´dit mieux le taux
moyen de formation de NO que les me
´thodes pre
´ce
´dentes. Les re
´sultats montrent e
´galement
Oil & Gas Science and Technology – Rev. IFP Energies nouvelles, Vol. 70 (2015), No. 1, pp. 111-123
ÓA. Karvountzis-Kontakiotis and L. Ntziachristos, published by IFP Energies nouvelles, 2014
DOI: 10.2516/ogst/2013199
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0),
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
qu’une vitesse de formation non line
´aire de NO avec la tempe
´rature et la variation cycle-
a
`-cycle, entraıˆne une moyenne plus e
´leve
´e des niveaux d’e
´mission de NO que celle pre
´dite sans
prendre en compte la variation cyclique.
NOMENCLATURE
ABDC After Bottom Dead Centre
ATDC After Top Dead Centre
BBDC Before Bottom Dead Centre
BTDC Before Top Dead Centre
CCV Cycle to Cycle Variation
CD Combustion Duration
CFD Computational Fluid Dynamics
COV Coefficient Of Variation
EVC Exhaust Valve Close
EVO Exhaust Valve Open
imep indicated mean effective pressure
IVC Intake Valve Close
IVO Intake Valve Open
mWiebe shape coefficient
MC Mean Cycle
PL Partial Load
SD Standard Deviation
SI Spark Ignition
SOI Start Of Ignition
WOT Wide Open Throttle
INTRODUCTION
Combustion in engines evolves differently in each oper-
ation cycle even at steady state operating conditions.
Experimentally, Cycle-to-Cycle Variability (CCV) is best
observed by the scatter of the measured cylinder pressure
around the mean pressure curve. Such fluctuations of the
cylinder pressure have an impact on engine performance
[1], fuel consumption [2] and pollutant emissions [3, 4],
while in some extreme cases such as highly diluted lean
mixtures could result in misfiring or knocking [2]. The
Coefficient Of Variation of the indicated mean effective
pressure (COV
imep
) is used for the classification of CCV
[5]. In general, COV
imep
should be limited to up to about
10% in order to avoid vehicle drivability problems
[5, 6].
There are several reasons that may cause CCV. These
may include variations in the early flame kernel develop-
ment due to corresponding spark variance in each cycle
or the turbulence conditions in the spark neigh-
bourhood. The kernel development affects flame
propagation, which by turn results to different macro-
scopic combustion parameters. The spark discharge
characteristics [2], the local equivalence ratio of the mix-
ture and its inhomogeneity close to the spark plug [2, 7,
8], turbulence in the vicinity of spark plug at the ignition
time [8], and mixture temperature and pressure at the
time of ignition [8] are all related with the variations of
the early flame kernel development. On the other hand,
the overall equivalence ratio [9], the extent of mixture
homogeneity [10, 11], the percentage of the residual gas
fraction of the mixture [10] and the averaged turbulence
intensity [12-16] are factors that affect the main flame
propagation.
Combustion CCV also leads to variability in the com-
bustion products. NO
x
formation in particular shows a
strong dependence on combustion duration. NO
x
emis-
sions decrease as combustion time decreases and this
dependence becomes stronger as air-fuel ratio becomes
leaner [17]. In other studies, it was found that the vari-
ance of NO
x
is higher compared with the variance of
imep and the maximum combustion pressure [3, 18].
There have been several model approaches aiming at
simulating combustion development and pollutants for-
mation in SI engines. The Wiebe function [19] has been
applied in most studies for the approximation of heat
release due to fuel consumption. However this empirical
function does not have a physical meaning and its pre-
dictability is not always satisfactory. Zero-dimensional
phenomenological models may better approach the
actual physics, taking into account different temperature
zones and compositions. However the turbulence condi-
tions in the combustion chamber cannot be modeled
with this kind of models [20], hence they cannot be used
to simulate CCV. As a result, CFD models (1D/3D) are
mainly used for the simulation of CCV, because they are
able to precisely simulate both the rate of the early flame
development and the flame propagation [12, 13, 21, 22].
Their disadvantage is their high computational cost and
the difficulty in setting up a satisfactory combustion
CFD model [20].
In SI modeling, NO emissions are usually simulated
by applying the extended Zeldovich mechanism, also
known as the thermal mechanism [23, 24]. However, in
stoichiometric and slightly rich mixtures, the prompt
(also known as Fenimore) mechanism could be responsi-
ble for up to fifteen percent of the total nitric oxide emis-
sions [25].
The objective of this study is the investigation of the
combustion CCV in nitric oxide emissions, using a
detailed chemical mechanism. The simple two-zone
112 Oil & Gas Science and Technology – Rev. IFP Energies nouvelles, Vol. 70 (2015), No. 1
Wiebe model is used for the description of the mixture
temperature and pressure during combustion. The ther-
modynamic parameters for each cycle are used as input
in the detailed chemical mechanism for the prediction
of NO formation as a function of degree of crank angle.
The model is then used to predict the impact of CCV on
NO emission levels.
1 MODEL APPROACH
The model presented in this paper consists of a detailed
chemical mechanism, coupled to a two zone Wiebe
model [19, 23]. For the aim of this study, the three
parameters of the Wiebe function were individually per-
turbated around central values to simulate CCV, thus
having an impact on the burning rate and the NO
formation.
1.1 Thermodynamic Model
The commercial engine simulation package AVL
BOOST was used for the simulation of the heat release
rate and the in-cylinder thermodynamic properties.
The combustion submodel used for the prediction of
heat release was a two-zone Wiebe model. The Wiebe
function describes the burned gas mass fraction at a
given crank angle:
Qf/ðÞ
Qf;total
¼1ea//SOI
/CD
mþ1
ð1Þ
In Equation (1), /
SOI
is the degree of crank angle
where ignition starts, D/
CD
is the duration of combus-
tion in crank angle degrees, mis a shape parameter for
the Wiebe function, and ais a combustion efficiency
parameter.
The two-zone approach consists of a burned zone
with a temperature for the combustion products and
an unburned zone with a different temperature for the
unburned mixture and any residuals from the previous
combustion cycle. A uniform pressure for both zones is
assumed. Although the Wiebe model is an empirical
model and it is not recommended for the investigation
of the CCV origins, variation of its parameters provides
a good approximation in simulating combustion exo-
thermy variability.
1.2 Emission Model
The chemistry model used to predict NO formation was
based on SENKIN, a FORTRAN based code developed
in Sandia Laboratories [26] that has been later evolved
into the CHEMKIN software package. SENKIN calcu-
lates combustion evolution in homogeneous gas phase
mixtures. The code solves the chemical kinetics differen-
tial equations and predicts the formation rate of prod-
ucts. This solution can refer either to constant
pressure, constant volume, or constant temperature con-
ditions. The default reaction scheme of SENKIN v1.8
that was used in this study, consisted of 53 species and
325 chemical reactions [26, 27]. The reaction scheme
involved of a number of carbon-nitrogen species and
radicals which are relevant in the NO formation chemis-
try, including HCN, H
2
CN, CN, HCNO and HOCN.
Figure 1 illustrates the coupling between the thermo-
dynamic and the chemical kinetic modeling developed
in the current study. The thermodynamic data for the
hot zone are imported in the converter at each crank
angle. The burned mass fraction from the Wiebe func-
tion defines the newly burned moles which enter from
the flame front to the burned zone. The newly burned
moles are calculated from the oxidation rate of the fuel,
according to the stoichiometry of the combustion shown
in Table 1.
The newly burned moles and the composition from the
previous step are imported as the initial input composi-
tion of the burned zone in SENKIN. SENKIN calculates
as an output the new composition of the burned zone
which will be again imported in the next crank angle.
Cylinder
Burned
zone
Burned zone
themodynamic
data
Burned
moles
Senkin
Emissions
New burned
moles
Pollutant formation
Fresh zone
Figure 1
Schematic of the emission modeling approach.
A. Karvountzis-Kontakiotis and L. Ntziachristos / Investigation of Cycle-to-Cycle
Variability of NO in Homogeneous Combustion
113
When the thermodynamic model calculates the end of
combustion, no new moles are assumed in the SENKIN
input scenario. The loop therefore ends and kinetics are
thereafter considered frozen. In earlier typical two zone
models [18, 22, 23, 28] only the thermal mechanism
was considered, while the other necessary species for
the thermal mechanism (H
2
,H,O
2
, O, OH, H
2
O) were
calculated assuming equilibrium. The proposed emission
model uses a detailed chemical mechanism which
includes the thermal and the prompt mechanism, while
the other necessary species are calculated from detailed
kinetics. This improves the precision in NO
x
prediction,
with a cost in computational time. A reduced detailed
chemical mechanism but with explicit kinetics for inter-
mediate species could serve as a compromise between
accuracy and computational time.
1.3 Modeling of NO CCV
The modeling of NO CCV was performed by introduc-
ing perturbations into the Wiebe function parameters,
regarding the ignition timing (SOI), the Combustion
Duration (CD) and the parameter m. Each of these three
parameters was described by a normal distribution,
characterized by a mean value and a standard deviation.
The mean value of each distribution was the Wiebe value
of the mean-cycle model, while the range of perturba-
tions was taken from experimental data, as it will be later
discussed. Finally the CCV thermodynamic data were
imported in the detailed chemical mechanism. This pro-
cedure was modeled in MATLAB.
1.4 Modeling Assumptions
The following assumptions were considered for the sim-
plification of the emission modeling and the CCV analy-
sis:
– uniform pressure in the cylinder (burned and
unburned zone at the same pressure);
– a complete combustion of hydrocarbon fuel with air;
– uniform composition in the burned zone;
–NO
x
emissions solely consisting of NO.
The validity and impact of these assumptions in the final
results is investigated in the results section.
2 EXPERIMENTAL DATA
Experimental data are necessary for the validation of the
model developed in this study. In most CCV analysis,
only the thermodynamic data are measured, without
considering the emission data. Ball et al. (1998) [4] used
experimental data from a Rover K4 optical engine to
investigate cycle-to-cycle variation in combustion and
NO emissions. The fuel used in those experiments was
methane. That engine from the Ball et al. (1998) [4] work
was simulated in the present study, as many engine spec-
ifications necessary for the modeling are contained in
that publication and are summarized in Table 2. The
model was applied to this engine and the results of the
TABLE 2
The Rover K4 optical engine characteristics (Ball et al., 1998) [4]
Main specification
Bore 80 (mm)
Stroke 89 (mm)
ConRod length 160 (mm)
Compression ratio 10 (-)
Cam timing
IVO 12 BTDC
IVC 52 ABDC
Peak lift inlet 8.8 (mm) at 70 BBDC
EVO 52 BBDC
EVC 12 ATDC
Peak lift exhaust 8.8 (mm) at 70 ABDC
Cylinder head
Type Rover K16 1.4 MPI
Pent angle 45
Inlet valve seat
diameter
24 (mm)
Inlet valve seat
diameter
19.6 (mm)
Number of valves 4 (-)
TABLE 1
The new species imported in the emission model at each iteration,
assuming C
a
H
b
as the chemical formula of the hydrocarbon fuel
Species k1 0.9 < k<1
CO
2
aa(2k1) + b/2(k1)
H
2
Ob/2 b/2
CO 0 (2a+b/2)(1 k)
O
2
(2a+b/2)(k1) 0
N
2
3.76k(a+b/4) 3.76kas
114 Oil & Gas Science and Technology – Rev. IFP Energies nouvelles, Vol. 70 (2015), No. 1
simulations were compared with the experimental data
for validation.
This optical engine was measured under partial load
and Wide Open Throttle conditions (WOT), for different
crank angle ignition durations and lambda values. Infor-
mation about the engine performance and the engine
emissions (NO
x
, HC) was also available for each mea-
sured engine point.
3 EFFECT OF ENGINE OPERATION PARAMETERS
ON EMISSIONS
Based on the experimental data presented in the previous
section, Figure 2 presents a graph of imep and NO
x
con-
centration for stoichiometric combustion, during Partial
Load (PL) and WOT operation. It is observed that while
the Start Of Ignition (SOI) changed from 15°BTDC to
45°BTDC partial load imep only differed by 18%, the
WOT imep differed by 9.5%, while NO
x
concentrations
changed by 183% and 46%, respectively. This shows
how much more sensitive NO formation is than the ther-
modynamic properties of the engine when combustion
parameters change.
The corresponding graph for lean operation (k= 1.5)
is shown in Figure 3. The impact of the variation in com-
bustion parameters on NO
x
formation is even more
magnified in this case compared to the stoichiometric
combustion.
By comparing the two cases, it is observed that in lean
operating conditions, the impact of the ignition timing
on the indicated mean effective pressure is higher com-
pared to the stoichiometric mixture, an observation
which is in agreement with other studies [2-9]. From
these data it seems that cycle-to-cycle combustion
variability is more pronounced in lean and highly diluted
mixtures, even with slight modification of the combus-
tion parameters. In addition such conditions lead to high
NO
x
formation, hence the CCV effect is magnified in this
case as well.
This non-linearity of NO
x
formation is not easy to
simulate in detail with a simplified mechanism. Hence,
a detailed and more precise chemical mechanism is
applied in this study, in order to simulate this non-
linearity and high sensitivity in NO
x
formation. The
model presented in this study can be used to predict
the amplitude of variation of NO
x
emissions due to
CCV and, in this way, to more accurately predict the com-
pliance of an engine with a given emission limit target.
4 RESULTS
For validation, the proposed emission model is first used
to predict the Rover K4 NO
x
measured emissions at both
stoichiometric and lean conditions. First, the measured
data of Rover K4 are used regarding NO
x
emissions
and engine performance characteristics to relate the ten-
dency between performance and emissions. Second, the
comparison between simulated and experimental cycle-
averaged NO data is presented for the validation of the
simulation. Measurement and simulation are discussed
and the importance of the prompt NO formation mech-
anism is justified. Last but not least, the NO CCV is
investigated.
4.1 Mean Cycle NO Modeling
The Rover K4 was simulated with the AVL BOOST
model for mean cycle Wiebe parameters and the results
8
6
4
2
0
-50 -20 -10
0
500
1
000
1
500
2
000
2
500
3
000
-30-40
46%
183%
-18%
-9.5%
WOT imep
WOT No
x
PL imep
PL NO
x
λ =1
I
g
nition crankan
g
le
NO
x
(ppm)
Imep (bar)
Figure 2
Effect of the ignition timing on imep and NO
x
for stoichi-
ometric conditions.
-50 -20 -10
-30
-40
WOT imep
WOT NO
x
PL imep
PL NO
x
λ = 1.5
Ignition crankangle
NO
x
(ppm)
Imep (bar)
54%
971%
14% 1000%
120
90
60
30
0
8
6
4
2
0
Figure 3
Effect of ignition timing on imep and NO
x
for lean
conditions.
A. Karvountzis-Kontakiotis and L. Ntziachristos / Investigation of Cycle-to-Cycle
Variability of NO in Homogeneous Combustion
115
were compared with the experimental cycle-averaged
engine data found in Ball et al. (1998) [4]. The compar-
ison between experimental and simulated data refers to
the imep, the maximum pressure during the combus-
tion phase, the crank-angle degree where maximum
pressure occurs, and the crank angle degree where 10%
of the fuel mass is burned (MFR). All these data
are presented in Table 3. The designation of each
point in Table 3 is done with the P and W initials
corresponding to partial load or wide open throttle
operation, respectively, followed by two digits corre-
sponding to the lambda value (10 corresponding to
k= 1 and 15 corresponding to k= 1.5), followed
by two digits of crank angle degree where ignition
starts before top dead centre.
The predicted thermodynamic data of the ten simu-
lated operating points were used as an input for the
NO prediction. The simulated NO emissions are com-
pared with the experimental NO emissions in Figure 4
for stoichiometric combustion and in Figure 5 for the
lean combustion. In the stoichiometric combustion,
NO emissions are presented with and without the effect
of the prompt mechanism. The prompt mechanism has
been switched off by zeroing the HCN radicals in the
chemical mechanism.
The model appears to have a rather good accuracy
over a wide NO
x
range, that is from NO
x
concentrations
of less than 10 ppm (P1515) to more than 2 000 ppm
(W1030). For these cases where large differences can
be seen (e.g. W1015), one should also observe related
TABLE 3
Validation of the thermodynamic model
Case khign (BTDC) Imep (bar) Pmax (bar) CaPmax (ATDC) 10% MFB (ATDC)
Part load
P1015 exp 1 15 3.84 18.05 20 5
P1015 sim 1 15 3.84 16.45 20.11 4.94
P1030 exp 1 30 3.27 25.92 7 10
P1030 sim 1 30 3.27 20.47 10.92 11.42
P1045 exp 1 45 3.15 29.34 2 18
P1045 sim 1 45 3.14 32.37 3.07 18.32
P1515 exp 1.5 15 1.46 10.23 0 19
P1515 sim 1.5 15 1.44 12.2 1.34 19.37
P1530 exp 1.5 30 2.33 15.13 12 2
P1530 sim 1.5 30 2.33 14.96 11.84 2.24
P1545 exp 1.5 45 2.25 21.44 6 16
P1545 sim 1.5 45 2.23 25.48 6.26 15.91
WOT
W1015 exp 1 15 6.14 33.02 18 3
W1015 sim 1 15 6.15 35.76 19.99 2.27
W1030 exp 1 30 5.55 45.68 5 11
W1030 sim 1 30 5.55 55.34 7.45 11.18
W1515 exp 1.5 15 3.83 17.33 10 11
W1515 sim 1.5 15 3.82 21.07 3.51 10
W1530 exp 1.5 30 4.38 29.2 12 3
W1530 sim 1.5 30 4.38 29.67 13.83 3.23
116 Oil & Gas Science and Technology – Rev. IFP Energies nouvelles, Vol. 70 (2015), No. 1
differences in the thermodynamic data and not only in
the reaction modeling. Cases with lower thermodynamic
error show better prediction in NO
x
results (example
P1015). By using a more sophisticated combustion
model [21, 22], the burning rate prediction could be
improved with significant improvement in NO
x
predic-
tion as well.
As one might expect, the availability of oxygen is the
key variable affecting NO
x
prediction. This may be an
additional reason of difference between measured and
experimental data. Within a typical stoichiometric win-
dow of [0.95< k<1.05] that appears in actual engines
during stoichiometric operation, slight differences in
lambda could affect the total amount of NO
x
formed
during combustion. The stoichiometric cases of the
experimental data were also simulated with a slightly
rich (k= 0.95) and slightly lean (k= 1.05) mixture.
The results are presented in Figure 6. It is observed that
the measured NO
x
concentration is almost always
between these slightly lean and rich simulated values.
Hence, slight departures from the set lambda in the
experimental data may be a significant reason for the dif-
ference between experiment and simulation.
Figure 4 also shows that the “prompt” mechanism
increases the total amount of NO
x
concentrations by
10%-15% in case of stoichiometric combustion.
Including the prompt formation one can increase the
accuracy of the chemical mechanism. Bachmaier
et al. (1973) [25] used an experimental configuration
to define the equivalence ratio in which the prompt
mechanism becomes significant in terms of total NO
x
formation for various hydrocarbon mixtures. They
found that the prompt NO formation starts to become
significant as the mixture moves towards stoichiometry
from k= 1.33, in the case of methane. The prompt
mechanism was negligible for leaner (k1.5) condi-
tions. Our results confirm the significance of the
prompt mechanism in addition to the thermal one,
even for stoichiometric combustion.
The thermodynamic input scenario is also important
in lean conditions; however the oxygen availability does
not affect the final results as much as in the stoichiome-
tric case. In lean combustion, it seems that non-homoge-
neities in the burned zone can become important for
accurately predicting final NO emissions. Multi-zoning
is mostly used in 0D-engine models to take into account
mixture stratification. In multi-zone modeling, different
lambda and temperatures are assumed in each zone.
Including multi-zones is a development we are currently
working on in our model.
Another reason for differences between the simu-
lated and experimental results could be the uncertainty
in the high concentration of hydrocarbons (HC) that
3
000
2
000
1
500
1
000
500
2
500
0
P1015 P1030 P1045 W1015 W1030
Full mechanism w/o prompt
Full mechanism
Exp.
NO (ppm)
Figure 4
Comparison of measured and simulated NO molar frac-
tions for stoichiometric combustion. Results without
prompt mechanism are also included.
7
000
6
000
5
000
4
000
3
000
2
000
1
000
0P1015 P1030 P1045 W1015 W1030
NO (ppm)
λ = 0.95
λ = 1.00
λ = 1.05
Exp.
Figure 6
Impact of slight stoichiometry variation on NO
x
formation.
P1515 P1530 P1545 W1515 W1530
Full mechanism
Exp.
NO (ppm)
160
140
120
100
80
60
40
20
0
200
180
Figure 5
Comparison of measured and simulated NO molar frac-
tions for lean (k=1.5) operating engine conditions.
A. Karvountzis-Kontakiotis and L. Ntziachristos / Investigation of Cycle-to-Cycle
Variability of NO in Homogeneous Combustion
117
this engine emits (up to 9 000 ppm). By assuming the
measured concentration of HC in the model, the
prompt mechanism appears very significant, even in
the lean case. As this engine is an optical and not a
production one, these HC were assumed to be gener-
ated from crevices in the piston/cylinder interface and
oil oxidation, rather than from fuel combustion itself.
Although these HC do not participate in combustion,
they could have an effect in a cold outer zone of a
multi-zone model.
4.2 Cycle-to-Cycle NO Variability
The detailed chemical mechanism was then used for the
investigation of NO CCV. From the various engine
points in Figure 4, four engine points were chosen for
the CCV analysis; two in partial load (P1015, P1030)
and two at wide open throttle operation (W1015,
W1030). All engine points were selected in stoichiometric
conditions, to also include the effect of the prompt mech-
anism in NO formation.
NO variability was investigated using a statistical
analysis. Wiebe combustion parameters such as the igni-
tion timing (SOI), the CD and the Wiebe shape coeffi-
cient (m) were randomly varied within limits, assuming
that these parameters follow a normal distribution.
The mean values for these distributions were equal to
the values used in the case of mean cycle modeling.
The range of the variation considered was taken from
a relevant analysis in the framework of the FP6 LESS-
CCV research project [29] and differed for partial load
and WOT operation. Full load points correspond to
higher CCV than low load engine points [2]. One hun-
dred engine cycles were simulated in each engine point
and the results of imep and NO
x
concentrations are pre-
sented in distributions. Differences between mean cycle
indices and CCV values are discussed.
4.2.1 Results of Cycle-to-Cycle Variation
Cycle-to-cycle variation of pressure and temperature are
illustrated in Figures 7 and 8, respectively, for the engine
point of partial load and ignition timing of 15
o
BTDC
(P1015). The mean value of maximum pressure is
16.6 bar and the standard deviation is 0.98 bar, while
the peak temperature has a mean value of 2 172 K and
a standard deviation of 20 K.
Figures 9 and 10 illustrate the distributions of imep and
NO concentration, respectively, for the same engine point
(P1015), due to the variation of the combustion parame-
ters. Both figures include the statistical characteristics
of the distributions such as the mean value and the
Standard Deviation (SD). Mean Cycle imep (MC imep)
20
16
12
8
4
0
240 300 360 420 480
CAD
Cylinder pressure (bar)
Figure 7
CCV of in-cylinder pressure (P1015 point).
240
2
500
2
000
1
000
1
500
300 360 420 480
CAD
500
0
Gas temperature (°C)
Figure 8
CCV of temperature evolution (P1015 point).
20
25
15
10
5
0
3.7 3.8 3.9 4.0
Imep (bar)
Frequency (%)
Mean: 3.84 bar
SD: 0.07 bar
Figure 9
CCV of imep (P1015 point).
118 Oil & Gas Science and Technology – Rev. IFP Energies nouvelles, Vol. 70 (2015), No. 1
and the mean imep value of the CCV analysis coincide
perfectly, while MC NO
x
value and CCV mean NO
x
value seems to have a slight deviation.
The same approach was also followed for the oper-
ation point at partial load (P1030) with ignition tim-
ing 30
o
BTDC. The peak pressure distribution has a
mean value of 20.6 bar and the standard deviation
is 1.05 bar. The peak temperature has a mean of
2 173 K and 30 K respectively. Distributions of this
engine point for imep present no difference for the
MC imep and the CCV imep value. In the case of
NO, a small difference between MC NO
x
and CCV
NO
x
values is again shown.
In the case of WOT, the same approach with a higher
range of Wiebe parameters was used for the CCV anal-
ysis. Pressure and temperature plots of the engine point
of 30
o
BTDC (W1030) are presented in Figures 11 and
12, respectively. Pressure and temperature peak values
have a higher range as a result of higher range in the
combustion parameters. In the case of W1015, the mean
value of the maximum pressure is 35.7 bar and SD is
equal with 3.1 bar, while the peak temperature varies
from 2 121 K to 2 310 K with a mean value and standard
deviation equal with 2 200 K and 39 K, respectively.
Same order of magnitude differences are noticed for
the case of W1030, where peak pressure varies from
45.5 bar to 61.7 bar (mean 55.5 bar, standard deviation
2.9 bar) and peak temperature varies from 2 281 K to
2 503 K (mean 2 410 K, standard deviation 42 K).
The distributions of imep and NO are illustrated in
Figures 13 and 14. Due to higher CCV, MC imep and
CCV imep are slightly different in both cases. Thus,
MC NO
x
value and CCV NO
x
values present a higher
deviation compared with the partial load. This also indi-
cates that deviation between MC and CCV NO values is
affected by the range of change of the combustion
parameters.
4.2.2 Contribution of Prompt Mechanism
on the Cycle-to-Cycle NO Variation
The impact of the prompt mechanism on NO
x
CCV has
been also investigated. In the case of mean cycle model-
ing, it was observed that the prompt mechanism
accounts for an additional 10% to 15% in the final
NO
x
concentration. Therefore, it is expected that the
20
15
10
5
0
Mean: 728 ppm
SD: 104 ppm
500 600 700 800 900 1
000
NOx (ppm)
Frequence (%)
Figure 10
CCV NO
x
(P1015 point).
240 300 360 420 480
CAD
Cylinder pressure (bar)
70
60
50
40
30
20
10
0
Figure 11
CCV of in-cylinder pressure (W1030 point).
2
500
2
000
3
000
1
000
1
500
240 300 360 420 480
CAD
500
0
Gas temperature (°C)
Figure 12
CCV of temperature evolution (W1030 point).
A. Karvountzis-Kontakiotis and L. Ntziachristos / Investigation of Cycle-to-Cycle
Variability of NO in Homogeneous Combustion
119
prompt mechanism should have a corresponding effect
on NO CCV.
Figures 15 and 16 demonstrate the distributions of
NO for a partial load and a full load engine point of
CCV analysis, considering only the thermal mechanism.
Mean values of NO distribution show a decrease
compared to the mean CCV NO values using the full
mechanism. In addition, for the case of using the detailed
chemical mechanism without the prompt one, a slight
difference between MC NO values and CCV NO values
25
20
15
10
5
5.0 5.5 6.0
0
Imep (bar)
Frequency (%)
Mean: 5.5 bar
SD: 0.21 bar
Figure 13
CCV of imep (W1030 point).
NOx (ppm)
25
20
15
10
5
0
Frequency (%)
2
000 2
5001
5001
000
Mean: 1
842 ppm
SD: 215.7 ppm
Figure 14
CCV NO
x
(W1030 point).
25
20
15
10
5
0
Frequency (%)
Mean: 612.5 ppm
SD: 88 ppm
400 500 600 700 800
NOx (ppm)
Figure 15
CCV NO
x
without the prompt mechanism (P1015 point).
Frequency (%)
Mean: 1
703 ppm
SD: 288.5 ppm
NOx (ppm)
30
25
20
15
10
5
01
000 1
500 2
000 2
500
Figure 16
CCV NO
x
without the prompt mechanism (W1030 point).
120 Oil & Gas Science and Technology – Rev. IFP Energies nouvelles, Vol. 70 (2015), No. 1
is also observed. However, the prompt mechanism has
an additional impact in the statistic characteristics of
the NO distribution, which is described in the next
section.
5 DEVIATION BETWEEN MEAN CYCLE VALUES AND
MEAN CCV VALUES
CCV does not only result in a range of values for NO
x
emissions but, due to the non-linearity of NO
x
formation
with combustion parameters and primarily with temper-
ature, it may also have an impact on the average NO
x
emitted. Hence, comparison between cycle-averaged val-
ues and the mean CCV value is important.
Partial load and full load are two cases that exhibit
different variability for the combustion parameters. In
partial load, the mean value of imep CCV distribution
is almost the same to the mean cycle imep value. On
the other hand, the CCV imep values are always lower
than the mean cycle imep values in full load operation
(Tab. 4). This means that the impact of CCV on average
is a degradation of the engine performance.
NO formation is also affected by the variability in the
combustion parameters. Both in full and partial load
CCV NO
x
values are always less than MC NO
x
values,
which reflects the CCV impact in NO formation
(Tab. 4). In WOT operation, this impact is higher than
in partial load. This result is related with the non-
linearity of NO formation and for this reason it can
not quantitatively correlated with imep variation. As
shown in Table 4, the higher the difference between
CCV imep and MC imep is, the higher is this difference
between CCV NO
x
and MC NO
x
, too.
The coefficient of variation is used as a metric of the
intention of the NO CCV in Table 5. The impact of
the prompt mechanism is also separated in this table.
NO in general presents higher variability due to CCV
than imep does. Also, the results show that it is not pos-
sible to establish a direct link between imep CCV and
NO CCV. The latter is dependant on both the operation
point and the CCV of imep. Finally, the impact of the
prompt mechanism on CCV is also specific to the engine
point considered. In one of the WOT conditions exam-
ined, the prompt mechanism led to a significant increase
in NO CCV, that is not obvious in the other cases. This
means that the combination of heat release rate with
reaction kinetics is unique for each engine point that
results to a behaviour which cannot be generalized at this
stage. Simulations with other engines and further refine-
ments in the model may lead to a more consistent behav-
iour of CCV NO with CCV in other combustion
parameters.
TABLE 4
Comparison of mean cycle values (MC) and CCV values for imep and NO
Engine point Case Imep (bar) Diff (%) NO full model
(ppm)
Diff (%) NO w/o
prompt (ppm)
Diff (%)
P1015
MC 3.84
0.00
735
0.99
623
1.71
CCV 3.84 728 613
P1030
MC 3.27
0.00
1 320
0.65
1 230
4.14
CCV 3.27 1 311 1 181
W1015
MC 6.15
0.49
646
2.02
516
1.78
CCV 6.12 633 507
W1030
MC 5.55
0.90
1 990
8.05
1 720
0.97
CCV 5.5 1 842 1 703
TABLE 5
Comparison of COV values for imep and NO with and without the
prompt mechanism
Case Imep COV
(%)
NO full
model COV
(%)
NO w/o
prompt COV
(%)
P1015 1.81 14.30 14.35
P1030 0.84 14.50 13.77
W1015 0.81 26.03 26.89
W1030 3.81 11.71 16.94
A. Karvountzis-Kontakiotis and L. Ntziachristos / Investigation of Cycle-to-Cycle
Variability of NO in Homogeneous Combustion
121
CONCLUSIONS
In this study, a detailed chemical mechanism was used
for the prediction of homogeneous engine-out NO emis-
sions. Literature experimental data were used for the val-
idation of the simulated values. The model satisfactorily
predicts NO emissions, ranging from a few ppm to a cou-
ple of thousand of ppm of NO molar fraction, in both
stoichiometric and lean conditions. Then, the model
was used for the simulation of NO variation due to com-
bustion CCV. It was found that CCV NO distributions
exhibit a higher COV compared to the imep distribu-
tions. In addition, mean CCV NO values are always
lower than the average cycle NO values. The impact of
prompt mechanism in NO result was also investigated.
In the case of average cycle emissions, it was found that
the prompt mechanism increases the accuracy of the pre-
diction, especially in stoichiometric conditions by up to
15%. In CCV, the prompt mechanism has an impact
in the COV and mean value of NO distributions,
although the impact was dependant on the engine oper-
ation point considered.
ACKNOWLEDGMENTS
This study was performed within the framework of the
FP7 LESSCCV research project (Grant agreement
233615).
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Manuscript accepted in October 2013
Published online in March 2014
Cite this article as: A. Karvountzis-Kontakiotis and L. Ntziachristos (2015). Investigation of Cycle-to-Cycle Variability
of NO in Homogeneous Combustion, Oil Gas Sci. Technol 70, 1, 111-123.
A. Karvountzis-Kontakiotis and L. Ntziachristos / Investigation of Cycle-to-Cycle
Variability of NO in Homogeneous Combustion
123
