A quasi-dimensional combustion model for performance and emissions of SI engines running on hydrogen–methane blends Federico Perini*, Fabrizio Paltrinieri, Enrico Mattarelli Dipartimento di Ingegneria Meccanica e Civile, Universita ` di Modena e Reggio Emilia, strada Vignolese, 905/B – I-41125 Modena, Italy article info Article history: Received 22 December 2009 Received in revised form 16 February 2010 Accepted 16 February 2010 Available online 24 March 2010 Keywords: Hydrogen–methane blends Quasi-dimensional model Spark ignition engine Pollutant emissions Laminar burning velocity Fractal model abstract The development of a predictive two-zone, quasi-dimensional model for the simulation of the combustion process in spark ignited engines fueled with hydrogen, methane, or hydrogen–methane blends is presented. The code is based on a general-purpose thermo- dynamic framework for the simulation of the power cycle of internal combustion engines. Quasi-dimensional modelling describes the flame front development assuming a simpli- fied spherical geometry, as well as infinitesimal thickness. The flame front subdivides the in-cylinder volume into a zone of unburned mixture, and a second zone of burned gases. As far as the combustion process is concerned, attention is paid to the description of the physical and chemical phenomena controlling the flame development and the formation of combustion products. First of all, an empirical correlation has been defined for esti- mating the laminar burning velocity. The equation, tailored for arbitrary fuel blendings and equivalence ratios, has been validated against detailed experimental data. Furthermore, the influence of turbulence on flame evolution has been implemented according to a fractal-based model. Then, a physical and chemical computing environment for evalu- ating both gaseous mixtures’ thermodynamic properties, and equilibrium species concentrations of combustion products has been developed and coupled to the code. The validation has been performed by comparing numerical pressure traces against literature experimental data, on a standard CFR single-cylinder engine. A unique set-up of the model parameters has been obtained, suitable for both pure hydrogen and pure methane fuelings; finally, the predictive capabilities of the model have been applied to analyze different fuel blends and equivalence ratios: the comparison against experimental pollutant emissions (NO and CO) shows a reasonable accuracy. ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved. 1. Introduction The enrichment of natural gas with hydrogen is a promising technique for decreasing engine pollutant emissions in terms of unburned hydrocarbons, CO and CO 2 , with only minor drawbacks on power output. Furthermore, NO x emissions at partial load can be slightly reduced, as hydrogen extends the lean flammability limit of the mixture [1]. Since the end of the last century, many researchers have explored the performance and emissions of SI engines running on hydrogen–methane blends. In 1999, Bade Shrestha and Karim [2] adopted an analytical engine model for * Corresponding author. Tel.: þ39 059 2056101; fax: þ39 059 2056126. E-mail address: [email protected](F. Perini). Available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/he international journal of hydrogen energy 35 (2010) 4687–4701 0360-3199/$ – see front matter ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2010.02.083
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A Quasi-dimensional Combustion Model for Performance
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 4 6 8 7 – 4 7 0 1
Avai lab le a t www.sc iencedi rec t .com
j ourna l homepage : www.e lsev ier . com/ loca te /he
A quasi-dimensional combustion model for performanceand emissions of SI engines running onhydrogen–methane blends
The Arrhenius-type forward reaction coefficients are sum-
marised in Table 1.
As far as carbon monoxide emissions are concerned, it is
acknowledged that CO formation is kinetically controlled, and
predictions based on equilibrium assumptions only would
0 0.5 1 1.5 2 2.5 3 3.5 4
0
2
4
6
8
10
x 1011
CO + OH <=> CO2 + H
1000/T [K−1
]
kf [c
m3 m
ol−
1 s
−1]
1992BAU/COB411−429
1984WAR197C
1972WIL535−573
1972DIX219
1965WES/FRI473
1961WES/FRI591
Adopted correlation
Fig. 8 – Comparison among the overall forward reaction
rate for reaction no. 1 according to the CO formation model
adopted, and some alternative correlations available in
literature [46].
Table 1 – Arrhenius-type coefficients for forward reactionrates adopted in the extended Zel’dovich mechanism[24], in the form k [ ATb exp(LE/T ). Units are cm, mol, s, K[26].
Reaction A b E
1 N2 þO/NOþN 3.30 eþ12 0.20 0.0
2 Nþ O2/NOþ O 6.40 eþ09 1.00 3160.0
3 Nþ OH/NOþH 3.80 eþ13 0.00 0.0
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 4 6 8 7 – 4 7 0 14694
yield poor results [25,45]. For this reason, a specific model has
been developed, considering the three reactions governing CO
formation in the post-flame area:
COþOH#CO2 þHCO2 þO#COþO2
COþOþM#CO2 þM:(26)
Due to its strong nonlinearity, according to Warnatz [26], the
first reaction in (26) has been split into three concurrent
reactions, with slightly different Arrhenius coefficients (cf.
Table 2). Furthermore, molecularity [M] has been defined as:
[M]¼ [H2]þ 6.5[H2O]þ 0.4[O2]þ 0.4[N2]
þ 0.75[CO]þ 1.5[CO2]. (27)
Tabrateform
1a.
1b.
1c.
2.
3.
The main advantage of considering the first reaction as
three split concurring reactions – involving the same reactants
and products – relies in the accuracy it allows to get at both
low and high temperatures. As a matter of fact, the three
concurrent reactions are characterized by slightly different
activation energy values, which make each one of them rule
over a specific temperature range. In Fig. 8, the overall forward
reaction rate of the first reaction, given by the sum of the three
concurring reactions (namely, 1a, 1b and 1c), is plotted against
some alternative correlations available in literature [46]. From
the plot, it’s clear that the adopted correlation suits both the
lowest temperature values, as achieved by most of the
explored correlations, and the range of temperatures higher
than 1000 K – which is of crucial importance when dealing
with in-cylinder combustion of gaseous fuels – where similar
results can otherwise be achieved adopting correlations
tailored for the high temperature range only.
Finally, the CO concentration is evaluated according to the
following ODE:
d½CO�dt
¼ ðcCOR1þ R2þ R3Þ
1� ½CO�½CO�eq
�;
R1 ¼�kf;1a þ kf;1b þ kf;1c
½CO�eq½OH�eq;
R2 ¼ kb;2½CO�eq½O2�eq
R3 ¼ kf ;3½CO�eq½O�eq½M�eq;
(28)
le 2 – Arrhenius-type coefficients for forward reactions adopted in the CO formation mechanism [26], in the
k [ ATb exp(LE/T ). Units are cm, mol, s, K [26].
Reaction A b E
COþOH/CO2 þH 1.00 eþ13 0.00 8.05 eþ3
COþOH/CO2 þH 1.01 eþ11 0.00 30.0698
COþOH/CO2 þH 9.03 eþ11 0.00 2.30 eþ3
CO2 þO/COþO2 2.50 eþ12 0.00 2.41 eþ4
COþOþM/CO2 þM 1.54 eþ15 0.00 1.50 eþ3
where the species’ concentrations defining the reactions
progress are evaluated at the reference equilibrium condi-
tions, and cCO is a tuning constant affecting the rate of the first
reaction in the mechanism.
4. Results and discussion
The calibration process has been focused on a set of five
interaction and heat transfer submodels. Despite the differ-
ences between methane and hydrogen combustion, a unique
set of values has been identified; two different in-cylinder
pressure traces, referred to the same engine while running
either on pure methane, or on pure hydrogen, have been
considered. These two fuel mixture compositions represent
the extreme bounds of the desired validity range over which
the model is expected to behave consistently. Due to the lack
of experimental apparatus, model testing has been carried on
over detailed experimental data available in literature and, in
particular, the standard CFR, single cylinder, 0.6l-displace-
ment engine has been chosen for the simulations. As far as
hydrogen fueling is concerned, the extensive measurements
by Verhelst [7] have been chosen as a reference, while the in-
cylinder pressure traces by Bade Shrestha [2] have been
considered when dealing with methane.
The first constant to be calibrated is the tuning coefficient
CQ, modelling heat transfer: the total heat flux through the
cylinder walls is amplified/reduced according to the value of
this constant. In order to broaden the applicability of this
approach, this value applies, unchanged, to the whole engine
cycle, as no differences have been imposed among compres-
sion, combustion and expansion. A second constant CD3 has
been used for tuning the fractal dimension of the developed
flame front surface, which depends on wrinkling due to
turbulent convective transport, as suggested by Matthews and
Table 3 – CFR engine simulations initialisationparameters, operating conditions and calibrationconstants for pure hydrogen and pure methane fuels,respectively.
where mi is the molecular mass, kB Boltzmann’s universal
constant, T the absolute gas temperature, s the Lennard–Jones
collision diameter. The collision integral value U(2,2)* is
computed as a function of the reduced temperature Ti*¼ kBT/3i
and of the reduced molecule dipole moment di¼ mi2/(23isi
3) [48]:
Uð2;2Þ� ¼ 45
�1þ 1
T�iþ d2
i
4T�i
�: (A.6)
The Lennard–Jones collision diameters s, potential well
depths 3i, dipole moments mi, polarizabilities and rotational
relaxation collision numbers have been gathered from [49].
The final mixture viscosity is then obtained from [48]:
h ¼Xi˛Ns
xiffiffiffiffihip
xi=ffiffiffihp þ
Pj˛Ns ;jsi
�xjsijAijffiffiffi
hjp
�; (A.7)
where Aij is a function of molecular weights, and sij represents
a corrective factor for collisions between unlike molecules
[48]. The results have been compared to both experimental
and numerical data in [48].
A.2. Stoichiometric combustion and mixture composition
Chemical composition of the unburned mixture is simplified
as containing only air (21% oxygen, 79% nitrogen) and the fuel
blend, which is characterized by a molar hydrogen fraction
fH2 . Under this hypothesis, the composition of the mixture
involved in the one-step combustion reaction has been esti-
mated as [15]:
�1� fH2
�CH4 þ fH2
H2 þ�2f
1� fH2
�þ fH2
2f
�ðO2 þ 3:762N2Þ; (A.8)
and thus the combustion products have been evaluated as
summarised in Table 4, where f¼ as/a represents the mixture
equivalence ratio, and the stoichiometric air–fuel mass ratio
has been accordingly computed as [3]:
Fig. 13 – Computed burned gas composition under the chemical equilibrium assumption. (a) First row: f [ 0.5, lean mixture;
(b) second row: f [ 1.0, stoichiometric mixture; (c) f [ 2.3, rich mixture. Reference pressure: 30 bar.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 4 6 8 7 – 4 7 0 14698
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 4 6 8 7 – 4 7 0 1 4699
a ¼4:76
2:0� 1:5fH2
�Wair � : (A.9)
s
1� fH2WCH4 þ fH2
WH2
The composition of the burned mixture after the stoichio-
metric combustion of the hydrogen–methane blend is needed
to initialise the computation of the dissociation chemical
equilibrium. In the following, the computation environment,
developed on the basis of [50], is presented.
A one-step dissociation equation, from six to 11 species is
considered for the equilibrium:
CH4 þO2 þN2 þ CO2 þH2OþH2/O2 þN2 þ CO2 þH2OþH
þH2 þNþNOþOþOHþ CO: ðA:10Þ
This reaction yields four equations which describe the
atomic balances of C, O, H, N atoms in the system:
xoCH4þxo
CO2¼J
xCO2
þxCO
�4xo
CH4þ2xo
H2Oþ2xoH2¼J
2xH2OþxHþ2xH2
þxOH
�2xo
O2¼J
2xN2
þxNþxNO
�2xo
O2þ2xo
CO2þxo
H2O ¼J 2xO2
þ2xCO2þ2xH2OþxNOþxOþxOHþxCO
�(A.11)
where the superscript o denotes initial conditions prior to the
dissociation, and J the ratio between the total number of
moles of the products for each mole of reactants. Seven more
equation descend from the seven following chemical disso-
ciation equilibria:
H2#2H; O2#2O; H2O#OHþ 12O2;
2H2O#2H2 þO2; N2#2N; H2 þ CO2#H2Oþ CO;H2Oþ 1
2N2#H2 þNO;(A.12)
where the equilibrium constants Kp, j are known as a function
of the absolute temperature, and computed from the Gibbs
free-energy change [26]:
ln Kp ¼1
RuT
24X
j˛Ns
n00j � n0j
�Dgo
35: (A.13)
According to the definition, they are then expressed as
a function of the molar fractions of products and reactants, as
follows [26]:
Kp ¼Yj˛Ns
hxMj ;eqp
in00j�n0
j
�; (A.14)
where Mj denotes the jth species in the chemical set. The
nonlinear system of eleven equations from Eqs. (39) and (42) is
finally solved adopting the iterative Newton–Raphson
method. In Fig. 13, the results of the computation of equilib-
rium concentrations of the species in the burned gas mixture
are plotted for pure hydrogen, 50% hydrogen–50% methane,
and pure methane fueling, at different equivalence ratios,
versus temperatures ranging from 1000 K to 4000 K.
Nomenclature
[] concentration [mol/cm3]
A;B;E; F;G laminar speed constants [16]
A Area [m2]
C constant [–]
D3 fractal dimension of a 3D rough surface
Dt turbulent diffusivity
Kp chemical equilibrium constant
Kst flame stretch factor
L length [m]
LI integral scale of turbulence [m]
LK Kolmogrov scale of turbulence [m]
LT Taylor’s micro-scale of turbulence [m]
Ns set of species
Q heat [J]
Ret turbulent Reynolds number
Rm specific gas constant of a mixture [J kg�1 K�1]
Ru universal gas constant [J K�1 mol�1]
SL laminar burning velocity [m/s]
T temperature [K]
U internal energy [J]
V volume [m3]
W species molecular weight [kg/kmol]
W work [J]
a polynomial interpolation coefficient
b cylinder bore [m]
cp specific heat capacity at constant pressure
[J kg�1 K�1]
cv specific heat capacity at constant volume [J kg�1 K�1]
f fraction (f˛[0; 1])
h specific enthalpy [J/kg]
kf; kb forward, backward rate coefficients
kB Boltzmann’s universal constant [J/K]
m mass [kg]
n engine rotating speed [rpm], number of moles [mol]
p pressure [Pa]
r radius [m]
s engine stroke [m]
t time [s]
u specific internal energy [J kg�1]
u velocity [m/s]
uL stretched laminar burning velocity [m/s]
x molar fraction
y mass fraction
zc instantaneous combustion chamber height [m]
Greek letters
a air-fuel mass ratio
b engine compression ratio [–]
Dgo Gibbs free-energy change
3 average turbulent dissipation [m2 s�3]
3a apparent grey-body emissivity [–]
h molecular viscosity [mP]
g laminar speed residuals correlation coefficient [17]
n stoichiometric reaction coefficient
U(2;2) collision integral
f mixture equivalence ratio
J molar ratio between products and reactants
r density [kg/m3]
s0 Stefan-Boltzmann’s constant [J m�2 K�4 s�1]
s Lennard-Jones collision diameter [A]
s time constant [s]
q engine crank angle [CA]
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 4 6 8 7 – 4 7 0 14700
w generic variable
Superscripts0 RMS turbulent uctuation
� time average
a laminar speed temperature correlation exponent
[17]
b laminar speed pressure correlation exponent [17]
m; n laminar speed fuel mass correlation exponents [16]
o initial conditions
Subscripts
0 reference condition
a apparent
ad adiabatic flame
air standard air
b burning, burned zone
CH4 methane
e entrainment
eq chemical equilibrium conditions
F fuel
f flame, flame front
g bulk in-cylinder gas
H2 hydrogen
K Kolmogrov
k flame kernel
max maximum
min minimum
p engine piston
r radiative heat transfer
res residual gases
s stoichiometric
t turbulent
te turbulent entrainment
tot total in-cylinder
t, t in development (transient) turbulent
u unburned zone
w wall
Wo Woschni convective term
Abbreviations
ATDC after top dead center
BTDC before top dead center
CA crank angle degrees
CFR Cooperative Fuel Research
EVO Exhaust Valve Opening
ICE Internal Combustion Engine
IVC Intake Valve Closure
NOx Nitrogen oxides (NO, NO2)
SI spark ignition
SOI start of ignition
TDC top dead center
r e f e r e n c e s
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