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7/27/2019 The Ignition, Combustion and Flame Structure of Carbon Monoxide-hydrogen Mixtures. Note 2 Fluid Dynamics an
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International Journal of Hydrogen Energy 32 (2007) 3486 3500www.elsevier.com/locate/ijhydene
The ignition, combustion and flame structure of carbon monoxide/hydrogenmixtures. Note 2: Fluid dynamics and kinetic aspects of syngas combustion
A. Cuoci, A. Frassoldati, G. Buzzi Ferraris, T. Faravelli, E. Ranzi
CMIC Dipartimento di Chimica, Materiali e Ingegneria Chimica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
Received 28 November 2006; received in revised form 20 February 2007; accepted 21 February 2007
Available online 5 April 2007
Abstract
The kinetic characterization of the H2/CO system in presence of nitrogen components was systematically revised in the first note of this
work [Frassoldati A, Faravelli T, Ranzi E. The ignition, combustion and flame structure of carbon monoxide/hydrogen mixtures. Note 1:
detailed kinetic modeling of syngas combustion also in presence of nitrogen compounds. Int J Hydrogen Energy; 2007, in press]. This second
note analyses three different turbulent non-premixed syngas flames by using different approaches such as the Eddy dissipation (ED) the Eddy
dissipation concept (EDC) and steady laminar flamelets (SLF) model.
Detailed kinetic schemes are too large and computationally expensive to be directly applied to CFD codes. Pollutants marginally affect
the main combustion process and consequently it is feasible to post-process the CFD results with large detailed kinetic schemes, capable of
accurately predicting the formation of pollutants, such as NOx , CO, PAH and soot. Thus, in order to predict NO x formation in these flames,
a detailed kinetic scheme is applied by means of a newly conceived numerical tool: the kinetic post-processor (KPP).
The successful prediction of flame structures and NOx formation supports the proposed approach and makes the KPP code a useful tool for
optimizing the design of new burners.
2007 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.
Keywords: Syngas kinetics; Syngas flames; Turbulent combustion modeling; NOx formation
1. Introduction
Syngas is a mixture of hydrogen and carbon monoxide and
can be obtained from natural gas, coal, petroleum, biomass
and organic waste [1]. Methanol synthesis and FischerTropsch
synthesis remain the largest use of syngas. However, syngas
has also become a significant source of environmentally clean
fuels of late and this is why an accurate study of the structureof syngas flames with a special attention on pollutant formation
is of such interest.
The syngas-fuelled combustion system designs can utilize
CFD to optimize efficiency. At the same time, however, com-
bustion systems have to respect increasingly stringent pollutant
emission limits. Therefore, pollutant formation must be one
of the main focuses of new burner designs: this explains the
Corresponding author. Tel.: +39 02 33993286; fax: +39 02 70638173.
E-mail address: alessio.frassoldati@polimi.it (A. Frassoldati).
0360-3199/$- see front matter 2007 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijhydene.2007.02.026
increasing demand for computational tools capable of charac-
terizing the combustion systems in terms of pollutant species
also. The direct coupling of detailed kinetics and complex
CFD is a very difficult task, especially when considering the
typical dimensions of the computational grids used for com-
plex geometries and industrial applications. The computational
cost significantly increases with the number of computational
grids (NC) and also with the second or third power of thenumber of reacting species (NS). Moreover, the turbulent
flow of the practical combustion devices leads to and in-
volves strong interactions between fluid mixing and chemical
reactions.
The general concept of reactor network analysis has al-
ready been employed by various authors to post-process CFD
results and evaluate the formation of pollutants, using detailed
kinetic mechanisms for various applications by utilizing a dif-
ferent level of description and various numerical methodologies
[25].
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A. Cuoci et al. / International Journal of Hydrogen Energy 32 (2007) 3486 3500 3487
Nomenclature
Roman symbols
A pre-exponential factor, kmol, m3, s
CC correction coefficient due to temperature fluctua-
tionsCP specific heat, J/kg/K
C1 C2 turbulence model constants
E activation energy, kJ/kmol
H sensible enthalpy, kJ/kg
J diffusion flux, kg/m2/s
k reaction rate, kmol, m3, s
M molecular weight, kg/kmol
NC total number of computational cells
NP total number of reactors
NR total number of chemical reactions
NS total number of chemical species
NV total number unknown variables
Pr Prandtl number
r rate of formation, kg/m3/s
R universal gas constant, kJ/kmol/K
S surface, m2
Sc Schmidt number
SH heat source, J/m3/s
T temperature, K
Tk kinetic equivalent mean temperature, K
U velocity, m/s
V reactor volume, m3
V effective volume, m3
W total convective flux, kg/s
x axial distance from fuel inlet, m
Greek symbols
temperature exponent
kinetic energy dissipation rate, m2/s3
reactor volume fraction
stoichiometric coefficient
turbulent kinetic energy, m2/s2
thermal conductivity, J/m/s/K
dynamic viscosity, kg/m/s
kinematic viscosity, m2/s
mixture fraction
mixture fraction variance
density, kg/m3
T
temperature standard deviation, K
reactor residence time, s
mass fraction
x gradient of x
Subscripts
i species
j reaction
n reactor surface
p reactor
t turbulent value
In this paper we analyze and discuss different approaches to
tackling this problem. Pollutant species only marginally affect
the main combustion process and consequently do not signifi-
cantly influence the overall temperature and flow fields. Conse-
quently it is feasible to evaluate the structure of the flame with
simplified kinetic schemes first and then post-process the CFD
results with this newly conceived numerical tool, the kinetic
post-processor (KPP) [6,7]. This KPP model, which has already
been applied to evaluating industrial burner performance, is
able to accurately predict the formation of different pollutants,
such as NOx
, CO and unburned hydrocarbons as well as poly-
cyclic aromatic hydrocarbons and soot. In order to demonstrate
the validity of this approach, three different syngas turbulent
jet flames are used as typical test cases.
2. Experimental data
Three different turbulent non-premixed syngas flames were
studied in this paper, all flames consist of a central fuel jet
surrounded by a co-flowing air stream. The geometry of the
nozzle and the composition of the fuels are shown in Table 1.
The first two flames (Flame A and B) are described by Bar-
low et al. [8,9] and were experimentally investigated in the
framework of the International Workshop on Measurements and
Computation of Turbulent Non-premixed Flames. The com-
position measurements were made at Sandia National Labo-
ratories, Livermore, California; velocity measurements were
obtained at ETH Zurich, Switzerland [10]. The flames are
unconfined and the fuel composition is 40% CO, 30% H 2, 30%
N2 (%Vol).
The burner has a central duct constructed from straight tubing
with squared-off ends with an internal diameter of 4.58 mm
for Flame A and 7.72 mm for Flame B. The thick wall of the
tubing (0.88mm) creates a small recirculation zone that aids
the flame stabilization. The computational grid was refined inthis zone to better resolve the details of the near-nozzle flow.
The central fuel jet mixes with the co-flow air stream, re-
sulting in a turbulent unconfined diffusion flame. The jet fuel
velocity is 76 m/s for Flame A and 45 m/s for Flame B, theco-flow air is 0.70 m/s velocity and both the streams areat a temperature of 292 K; the resulting Reynolds number is
16 700. Experimental results include axial and radial profilesof mean and root mean square (rms) values of temperatures
and major species concentrations as well as velocity statistics
and Reynolds stresses. Radial profiles of nitric oxide and OH
radical concentration are also available at different locations.
The third flame (Flame C) was experimentally investi-
gated by Drake et al. [11]. The fuel is fed in a central tube
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Table 1
Experimental syngas flames studied in this paper
Flame Nozzle ID (mm) Ujet (m/s) Rejet Ref. Fuel composition (% vol)
CO H2 N2 CH4 NH3
A 4.58 76.0 16700 [8,9] 40 30 30
B 7.72 45.0 16700 [8,9] 40 30 30 C 3.20 54.6 8500 [11] 39.7 29.9 29.7 0.7 01.64
(3.2 mm internal diameter and 1.6 mm wall thickness), cen-
tered in a 15 cm 15 cm square test section 1 m long, with flatpyrex windows on the four sides. The fuel molar composition,
very similar to the previous one, is 39.7% CO, 29.9 H2, 29.7
N2 and 0.70 CH4. Ammonia was added in different amounts
up to 1.64%; in the absence of ammonia, methane was not
included in the fuel mixture. The average fuel flow velocity
was 54.6 m/s with a resulting Reynolds number of8500; theinlet flow air velocity was 2.4 m/s. The inlet temperature of
both the streams is 300 K. Several radial profiles of velocity,temperature and species concentrations are available at differ-
ent distances from the fuel inlet. The NO concentration was
experimentally analyzed only at a distance of 100 diametersdownstream of the nozzle.
3. Flame modeling
The flames were simulated with the commercial CFD code
FLUENT 6.2. A 2D steady-state simulation of the physical do-
main was considered due to the axial symmetry of the system.
The adopted 2D grid for the Flame C was structured and non-uniform, with high resolution in the flame region close to the
inlets. The domain was resolved by 320 130 control volumesin a cylindrical coordinate system. The grid used for the Flames
A and B, on the other hand, was unstructured and consisted of
30 000 triangular computational cells. For the spatial resolu-tion the second-order upwind scheme was adopted. The segre-
gated implicit solver was used with the SIMPLE procedure for
pressurevelocity coupling. PRESTO! (PREssure Staggering
Options) algorithm was used for pressure interpolation [12].
Turbulence was modeled via the RANS approach, using the
standard model. However, it is well recognized that the
model poorly predicts the velocity field in round jets: in partic-ular it tends to overestimate the spreading rate and the decay
rate [13]. Also in these cases the model over-predicts the
diffusion of the central jet and predicts the axial velocity on
the centerline lower than the one actually measured. The mod-
ification suggested by McGuirk and Rodi was adopted to solve
this problem: the parameter C1 in the k model was corrected
from 1.44 to 1.60 [14,15]. The modified k model gives sat-
isfactory results using this correction and can be used to avoid
the additional computational expense of the Reynolds stress
model (RSM) [16]. The radiative heat transfer was calculated
with the DO model [12].
The description of the turbulencechemistry interactions rep-
resents one of the most difficult tasks in turbulent combustion.
Three different models were adopted: the Eddy dissipation (ED)
model [17], the Eddy dissipation concept (EDC) model [18,19]
and the Steady laminar flamelets (SLF) model [2022]. A brief
discussion of these approaches is reported in Appendix A.
4. The kinetic post-processor
As previously mentioned the KPP operates by assuming the
temperature and flow fields to be those predicted by the CFDcodes and solves the overall system of mass balance equations
in a complex reaction network with detailed kinetic schemes.
Even with new generation computers, the direct coupling of
detailed kinetics and complex CFD remains a very difficult and
expensive task, especially when considering the usual number
of grid points used in industrial applications. When referring
to 105106 grid cells and 100200 reacting species, the dimen-
sions of the overall system of mass balance equations become
higher than 107108.
Two major simplifications are applied and they make this
numerical approach feasible and advantageous over the direct
coupling of a detailed kinetic scheme inside the CFD code.The first feature is the transformation of the original compu-
tational grid into a reactor network. Knowledge of the thermo
fluid dynamic field, as evaluated by the CFD code, allows sev-
eral adjacent and very similar cells to be lumped or grouped
into single equivalent reactors. A second way of making the
numerical computations more stable and viable is to define an
average and fixed temperature inside the different reactors.
The solution of the CFD code provides the detailed flow,
composition and temperature fields, and this information al-
lows critical and non-critical zones in the overall reacting sys-
tem to be identified. The description detail can be reduced in
several regions without affecting significantly the results. The
grouping or clustering of several kinetically similar cells intoa single lumped reactor reduces the dimensions of the overall
system. The fixed temperature inside these reactors reduces the
extreme non-linearity of the system which is mainly related to
the reaction rates and to the coupling between mass and energy
balances.
4.1. Grouping of cells and grid sensitivity
The temperature, composition and fluid dynamic fields ob-
tained through the CFD code allow the identification of the
critical zones in the combustion chamber, i.e. the specific re-
gions where large temperature and/or composition gradients are
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A. Cuoci et al. / International Journal of Hydrogen Energy 32 (2007) 3486 3500 3489
CO
NOx (x300)
number of reactors
massfra
ction
1.0E-02
9.0E-03
8.0E-03
7.0E-03
6.0E-03
5.0E-03
4.0E-03
3.0E-03
2.0E-03
1.0E-03
0.0E+000 2000 4000 6000 8000 10000120001400016000
Fig. 1. Predicted CO and NOx emissions in the exit flue gases as a function
of the number of reactors used in the simulation (Flame A).
present. It is convenient to retain the original detail of the CFD
grid in these zones. However, large volumes of the system are
less critical from a kinetic point of view, e.g. cold and/or non-
reactive zones. This fact suggests that the detail of the grid can
be locally reduced by clustering and combining several cells
into a single equivalent reactor. Of course, the lumped cell vol-
ume is simply the sum of the volumes of the grouped cells. The
original grid size is thus transformed into a network of several
reactors where the links between the different reactors simply
combine and reflect the original flow field as evaluated by the
CFD code. This allows the total number of equivalent reactorsto be reduced and makes it feasible to handle the mass balance
equations by using detailed kinetic schemes with a large num-
ber of species. The original 105106 cells can be conveniently
grouped into 103104 equivalent reactors thus maintaining a
more than reasonable description of the flame structure and the
reacting system.
The mesh-coarsening algorithm was designed in order to
prevent possible dangerous situations such as the creation of ge-
ometrical irregularities and/or non-smooth transition between
zones with very different volumes. The interlinking flows are
evaluated on the basis of the convective rates exchanged be-
tween the cells belonging to the different reactors. The massdiffusion coefficients for the coarse mesh are calculated in
agreement with the original diffusive flow rates. Temperature
and initial compositions in the equivalent reactors are the
volume averaged values of the combined cells. Different clus-
tering levels are sequentially adopted and calculations are iter-
atively performed by increasing the number of cells up to the
final convergence, i.e. up to the point where a further increase
in the reactor network dimensions makes no significant differ-
ence to the final solution. The accuracy and convergence of the
solution together with the effect of the coarsening of the mesh
need to be monitored and these points are analyzed later in this
paper when numerical procedure is discussed. Fig. 1 shows
the typical effect of clustering on NOx and CO predictions.
4.2. Average temperature, temperature fluctuations and rate
constant evaluations
As already mentioned, the KPP uses the temperature field
as obtained by the CFD computations. A fixed average tem-
perature is assumed in each equivalent reactor and the rates of
all the reactions involved in the kinetic scheme are evaluated.In turbulent combustion conditions, these reaction rates cannot
simply be calculated as a function of the mean temperature and
composition, mainly due to the highly non-linear dependence
of reaction rates on temperature. Temperature dependence of
rate constants is usually described via the modified Arrhenius
equation:
k(T ) = A T exp
E
RT
. (1)
Consequently, during turbulent combustions, temperature fluc-
tuations in particular have a significant effect on the average
rates of reactions with high activation energy. This effect is
very important for the reactions involved in NOx formation and
needs to be taken into account [18]. The average fluid dynamic
temperature T is different from the equivalent average temper-
ature from a kinetic point of view Tk. In other words, the av-
erage rate value (which accounts for temperature fluctuations
over the time) is very different from the reaction rate calculated
at the mean temperature T
k =
0 k(T(t)) dt
= k(T). (2)
This difference obviously increases for high temperature fluctu-ations and for reactions with high activation energies. To tackle
this problem with reasonable computational efforts, the Taylor
expansion of the reaction rate around T is used in the post-
processing procedure:
k(T ) = k(T ) +
n=1
1
n!
jnk
jTn
T
Tn
(3)
a few mathematical arrangements allow the following to be
deduced:
k = k(T)
1 +
2R2 R2 + 2ERT1( 1) + E2T2
4R2
T
T
2+
= k(T) CC = k(Tk), (4)
where CC is a correction coefficient due to the temperature
fluctuations. Because of the high fluctuations and slow con-
vergence, the series expansion needs to account for up to the
eighth order terms.
Of course, CC value changes for the various reactions due to
the different activation energies.
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T=2000 KCorrection
Coefficient(Cc)
T=2000 K
T=1500 KT=1500 K
0 0.2 0.4 0.60
5
10
15
E/R=15000
0 0.2 0.4 0.60
500
1000
1500
E/R=35000
'T0 /T'T0 /T
Fig. 2. Correction coefficient of the rate constants versus the intensity of temperature fluctuations at average temperatures of 1500 and 2000K. Continuous
lines refer to series truncated at the eighth order whilst pointed lines are limited to the sixth order: (a) activation energy = 30000 cal/mol; (b) activationenergy = 70000cal/mol.
Fig. 2a and b show the values of the correction coefficient
as a function of temperature fluctuations, respectively, for twodifferent activation energies (30 000 and 70 000cal/mol) at
average temperatures of 1500 and 2000 K, and assuming a
sinusoidal fluctuation T(t ) = T0 sin(t ). As expected, this co-efficient is higher at 1500 K and increases with the activation
energy. These figures also show the results obtained with dif-
ferent truncation orders; CC coefficient estimation converge
when accounting the first 34 terms of the series (up to the
eighth order). These results have been proved to be fully
consistent with those obtained through rigorous computation
k(T ) CC =
0 k(T + T
0 sin(t)) dt
. (5)
The correction coefficients calculated using this approach also
agree with those predicted by the more accurate but computa-
tionally more expensive -pdf model [22]. To further clarify the
physical meaning of these corrections, we should point out that
the equivalent average kinetic temperature Tk becomes 2630K
instead of the average temperature T = 2000 K, when assum-ing the higher activation energy and T0/T = 0.5. Similarly, Tkwould become 2030K when the average temperature is 1500 K.
Correction coefficients for the reverse reactions are calculated
with the same procedure but only using the parameters of the
reverse reactions.
If not directly available from the CFD simulation, the tem-
perature variance calculation is based on an approximate form
of the variance transport equation obtained assuming equal pro-
duction and dissipation of variance [12,23]
2T =C1 t (T )
2
C2 (/k), C1 = 2.86, C2 = 2.0. (6)
4.3. Mass balance equations
CFD results are used to define the overall system by describ-
ing the mass balance equations of all the chemical species in-
volved in the detailed kinetic scheme as well as providing the
initial composition guess.
For all the equivalent reactors, the steady mass balance of
each species (i ) accounts for convection, diffusion and chem-ical reaction terms:
Wp inp,i Wp
outp,i +
NFn=1
[ Jp,n,i Sp,n]
+ Vp Mi
NRj=1
ij rp,j = 0, i = 1, . . . , N C,
p = 1, . . . , N P, (7)
where Wp is the total convective flow pertaining to the reactor.
The mass diffusion term is the sum of all the contributions
pertaining to the adjacent reactors and is computed in the fol-
lowing form:
Ji = t
Sc t i , (8)
where Sct is the turbulent Schmidt number and t the turbulent
viscosity. Laminar diffusion is neglected because it is usually
overwhelmed by turbulent transport, at least for high Reynolds
numbers. Sn is the surface between the adjacent reactors. The
reaction term contains the molecular weight Mi and the alge-
braic sum of all the reaction rates evaluated at the equivalent
kinetic temperature:
rj = kj(Tkj) f (c ). (9)
The mean reaction term in each computational cell is calcu-
lated according to the EDC model [18] and by referring to the
effective volume V.
4.4. Numerical method and control of convergence
As already mentioned, the dimension of the overall system,
which is conveniently reduced using the grouping procedure,
becomes NP NS (NP is the total number of lumped reactors)to ensure that the KPP can handle this overall system.
As an example, Fig. 3 shows a typical Boolean structure of
the whole matrix system for a simple structured 2D grid as well
as the structure of the single block.
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0500
520
540
560
580
600
500 520 540 560 580 600 620
500
1000
1500
2000
0 500 1000 1500 2000
reactorindex
reactorindex
reactorindex
reactor index reactor index reactor index
0
5
10
15
20
25
3035
40
45
50
0 5 10 15 20 25 30 35 4540 50
Fig. 3. Panel a: example of a Boolean structure of the whole matrix system for a simple structured 2D computational mesh. Panel b: zoom of the diagonal
region (square in panel a). Panel c: zoom of the single block structure (square in panel b).
The global Newton or modified Newton methods are notrobust enough to solve the system using CFD results as a first-
guess. It is therefore convenient to approach a better estimate
of the solution by iteratively solving the sequence of individual
reactors with successive substitutions. Each reactor is solved by
using a local Newton method with the possible use of a false
transient method (time stepping) to improve the initial guess
or to approach the solution.
Only when the residuals of all the equations reach sufficiently
low values, can a modified global Newton method be applied to
the whole system. Otherwise the previous procedure is iterated
to further improve the residuals.
The Newton method involves the solution of a linear system
of the Jacobian coefficient matrix. In order to increase the com-putational efficiency, special attention is devoted to the evalu-
ation of the sparse Jacobian coefficients. The derivates of rate
equations are evaluated analytically rather than numerically.
The bottleneck of this very large system comes both in mem-
ory allocation and in CPU time when a Gauss factorization
method is applied to the whole system. Thus, Gauss factoriza-
tion is applied only to the main diagonal blocks, while an iter-
ative method is applied to the other terms. This approach saves
the memory allocation and makes the solution of this overall
system viable.
In this case too, if the global Newton method does not con-
verge, a false transient method is applied to ensure a betterapproach to the solution of the whole system.
The global Newton method not only increases efficiency but,
more importantly still, ensures the complete convergence to the
solution. In fact, it is necessary to speed up the convergence
procedure, very slow in the case of direct substitutions. More-
over, it has to be clearly underlined that high attention is re-
quired in the convergence check. In fact, in the case of direct
substitution, convergence is generally controlled by the typical
normalized error sum of squares:
err =Nv
i=1
(n)i
(n1)
i
(n)i
2
, (10)
CFD Results
First guess solution
Local solution in each reactor
Newtons method
OK
No
Time integration
(ODE)
Time integration
(ODE)
Yes
OK
No
Yes
Low residuals in all equations? Yes
Global solution for all reactors
Newtons method
SolutionLow pollutant concentrations(ppm)
Needof very low residuals
No
Fig. 4. Numerical procedure to solve the global system.
where NV = NS NP is the total number of variables (massfractions) and the suffix (n) refers to the iteration. The request
that err has to be less than a fixed minimum () is a neces-
sary but not sufficient condition. A small err value may just
be the result of convergence difficulties rather than the numeri-
cal solution. The KPP complete numerical procedure is shown
schematically in Fig. 4. Additional details regarding the KPP
are reported in [7,24].
5. Kinetic schemes
The reactions adopted for the ED simulation are very
simple and correspond to the complete oxidation of syngas
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x/d=40x/d=20
x/d=20x/d=40
x/d=20 x/d=40
x/d=20x/d=40
Fig. 7. Temperature and composition profiles (Flame A) [9] along the axis and at different distances from the burner surface in radial direction ( d is the
internal diameter of the nozzle, x is the axial distance from the nozzle outlet). EDC model: black line, SLF model: gray line, ED model: dashed line.
major species for the three different turbulent combustion mod-
els. The ED model coupled with a simplified kinetic mechanism
gives unsatisfactory predictions, both for the temperature and
compositional fields. A better and satisfactory agreement with
experimental measurements is obtained with the EDC model.
SLF model overestimates the axial temperature profile, espe-
cially in the post-flame zone (x/d > 40).
Hewson and Kerstein [26] studied flame A using a RANS
approach and overpredicted the temperature in the flame tail by
50150 K. According to their work there are two possible rea-
sons responsible for temperature overprediction in this flame:
neglect of radiative heat losses and underprediction of the dis-
sipation rate. They estimated that radiation is not expected to
play a major role in this flame, because the time scales for ra-
diative heat losses are long relative to the flame evolution time.
Thermal radiation, which is taken into account in this work us-
ing the discrete ordinates model [12], affects the peak temper-
ature only by about 3040 K.
We performed a sensitivity analysis on the SLF simula-
tions, which confirmed that the predicted temperature profile
is nearly insensitive to the grid and the numerical schemes
or to the kinetic mechanism used to generate the flamelet li-
brary, but is mostly affected by the turbulence model used.
In fact, different turbulence models affect the jet penetration
but also the scalar dissipation rate and thus turbulent mixing.
Higher mixing rates noticeably shorten the flame, as already
discussed elsewhere [26]. In fact, better temperature profiles
in the flame tail can be obtained adopting SLF with RSM or
the standard k turbulence models, but the consequence is
the overestimation of the temperature close to the nozzle. A
further discussion on SLF modeling goes beyond the scope of
this work which will focus on the NOx chemistry in syngas
flames.
It is evident that any model overestimations of the flame
temperature affect the prediction of pollutant species with
the KPP.
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2.59e-05
2.46e-05
2.33e-05
2.20e-05
2.07e-05
1.94e-051.81e-05
1.68e-05
1.55e-05
1.42e-05
1.29e-05
1.16e-05
1.04e-05
9.08e-06
7.76e-06
6.47e-06
5.18e-06
3.88e-06
2.59e-06
1.29e-06
0.00e+00
1.00e-05
9.50e-06
9.00e-06
8.50e-06
8.00e-06
7.50e-06
7.00e-06
6.50e-06
6.00e-06
5.50e-06
5.00e-06
4.50e-06
4.00e-06
3.50e-06
3.00e-06
2.50e-06
2.00e-06
1.50e-06
1.00e-06
5.00e-070.00e+00
5.29e-06
5.03e-06
4.76e-06
4.50e-06
4.23e-06
3.97e-063.70e-06
3.44e-06
3.17e-06
2.91e-06
2.64e-06
2.38e-06
2.12e-06
1.85e-06
1.59e-06
1.32e-06
1.06e-06
7.93e-07
5.29e-07
2.64e-07
0.00e+00
Fig. 8. Predicted maps of NOx mass fractions for Flame A. Panel (a) NO, Panel (b) N 2O, Panel (c) NO2. (a) NO Mass fraction; (b) N2O mass fraction;
(c) NO2 mass fraction.
Moving from these fields obtained with the EDC model for
Flames A and B, the KPP is applied with the detailed kinetic
scheme to predict NOx formation in the flame also. The pre-
dicted NOx species maps are reported in Fig. 8 for flame A.
The significant role played by N2O in the flame front and for-
mation of NO2 in the post-flame zone can be observed.
Two main NOx -forming reaction paths are relevant in these
syngas flames: thermal NO and the nitrous oxide mechanism
(N2O). The NO formation through N2O is initiated by the third
order reaction N2 + O + M = N2O + M which is followed byseveral N2O reactions with O, OH and H radicals, ultimately
leading to the formation of NO and N2. The selectivity of thisprocess is ruled by the local temperature and composition of
the flame. The NOx is formed mostly via the N2O mecha-
nism and, to a limited extent, through the thermal mechanism
(about 25% for Flame A). The significant role played by the
N2O mechanism in syngas combustion is a consequence of the
significantly enhanced production of O radicals [27].
The thermal mechanism is initiated and controlled by the so-
called Zeldovich mechanism through O + N2 = NO + N, whichis followed by N + O2 = NO + O and N + OH = NO + H.
Fig. 9 shows a comparison of NO measurements and predic-
tions along the axis of the flame and the effect of temperature
fluctuations on NO formation. The effect of temperature fluc-
tuations is relevant especially for flame B where the thermal
mechanism accounts for about half of the NO formed.
The agreement on these absolute values is satisfactory, even
though there are some discrepancies. The shape of the radial NO
profile in flame is correctly reproduced at the various distances
from the burner surface and is in very good agreement with
measurement results at x/d > 30. NO concentration is, how-
ever, overestimated close to the nozzle (x/d < 30) as shown in
Fig. 10 which compares NOx instantaneous measurements and
predictions at different axial locations. The measurements of
Fig. 10 are single-shot NO and OH measurements [9] and are
shown in scatter plot as a function of the mixture fraction at dif-ferent axial locations of Flame A. The mixture fraction is calcu-
lated here from the local composition using the Bilger formula
[28]. NO predictions, obtained using the KPP, are compared
with the scatter plot measurements of NO using a continuous
line. It is quite evident that the predicted NO mass fraction is in
good agreement with the average NO at high x/d while close
to the nozzle NO tends to be overestimated. It is interesting to
note that the predicted NO profile obtained when suppressing
the effect of temperature fluctuations (CC = 1, dashed line) liesat the lower boundary of the scatter plot.
Panel b shows the comparison between single-shot OH mea-
surements [9] and predictions obtained directly in the CFD
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0 100
Flame B 2.46e-052.33e-05
2.20e-05
2.07e-05
1.94e-051.81e-05
1.68e-05
1.55e-05
1.42e-05
1.29e-05
1.16e-05
1.04e-05
9.06e-06
7.76e-06
6.47e-06
5.18e-06
3.88e-06
2.59e-06
1.29e-06
0.00e+00
2.59e-05
NO [m.f.]5.00E-05
4.00E-05
3.00E-05
2.00E-05
1.00E-05
0.00E+00
NOMassFractio
n
Flame A
Axial Position [mm]
200 300 400 500 600 700
Fig. 9. Panel a: NO mass fraction profiles along the centerline for Flame A (continuous line and symbols) and Flame B (dashed line and open symbols).Gray lines indicate the prediction of NO obtained without the proper correction for temperature fluctuations. Panel b: map of predicted NO (mass fraction)
for Flame A. The map on the right side is obtained neglecting the effect of temperature fluctuations.
3.00 E-05 6.00 E-03
5.00 E-03
4.00 E-03
3.00 E-03
2.00 E-03
1.00 E-03
0.00 E+00
6.00 E-05
5.00 E-05
4.00 E-05
3.00 E-05
2.00 E-05
1.00 E-05
0.00 E+00
2.50 E-05
2.00 E-05
1.50 E-05
1.00 E-05
5.00 E-06
0.00 E-000
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
x/d=20 x/d=20
x/d=50x/d=50
0.9 1
NOMassFraction
NO
MassFra
ction
NO
MassFra
ction
OHMa
ssFraction
Mixture fraction
Mixture fraction
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Mixture fraction
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Mixture fraction
5.00 E-03
4.00 E-03
3.00 E-03
2.00 E-03
1.00 E-03
0.00 E+00
Fig. 10. NO and OH mass fraction at different distances from the nozzle for Flame A. Comparison between single shot measurements (symbols) [9] and
average model results (lines). Panel a: continuous lines are the result of the KPP, dashed lines show the effect of neglecting temperature fluctuations on NO
predictions. Panel b: OH radicals calculated using the EDC model in FLUENT (dotted line) and the KPP (continuous line).
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x/d=50
0 1 2 3 4 6 7 8
ED
SLF
x/d=50x/d=10
x/d=50x/d=10
0 5 10 15 20 25 30 35
0 5 10 15 20 25 30 35
0 5 10 15 20 25 30 35
0 5 10 15 20 25 30 35
x/d=50x/d=10
Temp
erature[K]
1.80E+03
1.60E+03
1.40E+03
1.20E+03
1.00E+03
8.00E+02
6.00E+02
4.00E+02
2.00E+025
Radial position [mm]
0 1 2 3 4 6 7 85
Radial position [mm]
Radial position [mm]
Radial position [mm]
0 1 2 3 4 6 7 85
Radial position [mm] Radial position [mm]
0 1 2 3 4 6 7 85
Radial position [mm]
2.00E+03
1.80E+03
1.60E+03
1.40E+03
Temp
erature[K]
1.20E+03
1.00E+03
8.00E+02
6.00E+02
4.00E+02
2.00E+02
Radial position[mm]
CO
2ma
ssfraction
1.40E-01
1.20E-01
1.00E-01
8.00E-02
6.00E-02
4.00E-02
2.00E-02
0.00E+00
CO
2ma
ssfraction
1.40E-01
1.20E-01
1.00E-01
8.00E-02
6.00E-02
4.00E-02
2.00E-02
0.00E+00
H2
Omassfraction
1.60E-01
1.40E-01
1.20E-01
1.00E-01
8.00E-026.00E-02
4.00E-02
2.00E-02
0.00E+00
1.20E-01
1.00E-01
8.00E-02
6.00E-02
4.00E-02
2.00E-02
0.00E+00
H2
O
massfraction
4.00E-01
3.50E-01
CO
massfraction3.00E-01
2.50E-01
2.00E-01
1.50E-01
1.00E-01
5.00E-02
0.00E+00
7.00E-02
6.00E-02
5.00E-02
CO
massfraction
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
x/d=10exp
EDC
Fig. 13. Temperature and composition profiles (in terms of mass fractions) along the axis and at different distances from the burner surface in radial direction
(d is the internal diameter of the nozzle, x is the axial distance from the nozzle outlet) doped with 0.80% (volume) of NH 3. EDC model: black line, SLF
model: gray line, ED model: dashed line.
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3.18e-03
3.05e-03
2.96e-03
2.86e-032.76e-03
2.67e-03
2.57e-03
2.48e-03
2.38e-03
2.29e-03
2.19e-03
2.10e-03
2.00e-03
1.91e-03
1.81e-03
1.72e-03
1.62e-03
1.53e-03
1.43e-03
1.33e-03
1.24e-03
1.14e-031.05e-03
9.53e-04
8.58e-04
7.63e-04
6.67e-04
5.72e-04
4.77e-04
3.81e-04
2.86e-04
1.91e-04
9.53e-05
0.00e-00
4.95e-05
4.75e-05
4.60e-05
4.45e-054.30e-05
4.16e-05
4.01e-05
3.86e-05
3.71e-05
3.56e-05
3.41e-05
3.27e-05
3.12e-05
2.97e-05
2.82e-05
2.67e-05
2.52e-05
2.38e-05
2.23e-05
2.08e-05
1.93e-05
1.78e-051.63e-05
1.48e-05
1.34e-05
1.19e-05
1.04e-05
8.91e-06
7.42e-06
5.94e-06
4.45e-06
2.97e-06
1.48e-06
0.00e+00
1.96e+03
1.89e+03
1.83e+031.76e+03
1.69e+03
1.63e+03
1.56e+03
1.49e+03
1.43e+03
1.36e+03
1.29e+03
1.23e+03
1.16e+03
1.10e+03
1.03e+03
9.63e+02
8.97e+028.30e+02
7.64e+02
6.98e+02
6.32e+02
5.65e+02
4.99e+02
4.33e+02
3.66e+02
3.00e+02
Fig. 14. Temperature and NOx mass fraction fields with 0.80% of total amount of added NH3. (a) NO mass fraction; (b) NO2 mass fraction; (c) Temperature (K).
N
Experimenal
Simulation
NO - Experimenal
NO - Simulation
NOx - Experimental
NOx - SimulationN
O
[ppmb
yvolumedry]
150
140
130
120
110
100
90
80
700 0.5 1 1.5 2 2
Yie
ld
[molesNO/molesNH3]
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0 0.5 1 1.5Total amount of added NH3 [%] Total amount of added NH3 [%]
Fig. 15. Panel a: comparison of measured [11] and predicted peak axial values of NO at x/d = 100. Panel b: total yield of NO and NOx formation atx/d = 100 as a function of added NH3.
various amounts of added NH3 [11]. The agreement is very sat-
isfactory, even though the predicted results tend to slightly un-
derestimate NO formation with larger amounts of added NH 3.
This agreement is quite clearly confirmed by the comparisons
reported in Fig. 15b in which total NO (and NOx = NO+ NO2)formation is related to the NH3 feed. It is clear that the pre-
dicted results are very close to the experimental measurements
and therefore not only is the adopted kinetic scheme capable
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A. Cuoci et al. / International Journal of Hydrogen Energy 32 (2007) 3486 3500 3499
of correctly describing NOx formation and NH3 consumption,
but the CFD simulation of the flame was properly grasped. The
difference between NOx and NO is mainly due to the succes-
sive formation of NO2 when the temperature is decreasing.
7. Conclusions
The detailed kinetic scheme of oxidation and combustion of
syngas, already discussed and validated in the previous note of
this paper [25], is here successfully applied to model turbulent
diffusion flames and to predict NOx formation mechanisms.
Detailed kinetic schemes are usually too large and computa-
tionally expensive for their direct application in the CFD code,
especially in the case of large 3D grids. For this reason three
different flames have been here analyzed with a new and effec-
tive numerical tool: the kinetic post-processor (KPP). Pollutant
species only marginally affect the main structure of the flame
(i.e. temperature and flow field). Thus, the CFD results obtained
with simpler kinetics are post-processed by using large detailed
kinetic schemes, able to accurately predict also the formation of
different pollutants, such as NOx , CO, PAH and soot. A global
solution method is discussed and applied in order to overcome
the difficulties and uncertainties in the convergence attainment.
The successful prediction of flame structures and NOx for-
mation in these flames not only contributes to a further val-
idation of the kinetic scheme but also supports the proposed
approach for the KPP. The KPP code already is a very useful
tool for the optimal design of new burners with a particular at-
tention to pollutants formation. Prediction of soot formation in
turbulent diffusion flames will be the natural extension and ap-
plication of this tool. A good prediction of the flame structures
is obviously a necessary condition for the correct applicationof the KPP. In fact, the reliability of the KPP results in terms
of pollutant predictions is strongly dependent on the complete-
ness and consistency of the original CFD simulation.
Acknowledgments
The authors acknowledge the financial support of Technip
BV and of ENEA (FISR project).
Appendix A.
A.1. Eddy dissipation model
The idea behind this model is that chemistry does not play
any explicit role while turbulence controls the reaction rate. In
fact most fuels are fast burning, and the overall reaction rate is
controlled by turbulent mixing. In non-premixed flames, turbu-
lence slowly convects/mixes fuel and oxidizer into the reaction
zones where they burn quickly. In such cases, the combustion
is mixing-limited, and the complex and often unknown, chem-
ical kinetic rates can be safely ignored. For the simple reaction
F + qO (1 + q)P, the fuel burning rate is estimated frommean mass fractions of fuel F, oxidizer O and products P,
and from a turbulent mixing time tmix. If the turbulence
model is adopted for turbulence modeling, the mixing time is
inversely proportional to the specific turbulent dissipation rate
/ and the burning rate is
RF = A1
tmixmin
F,
O
q, B
P
1 + q
= A
minF, Oq
, BP
1 + q , (11)
where A and B are two model constants. In this equation the
reaction rate is limited by the deficient mean species. This is
acceptable if the reactions are very fast compared to the turbu-
lent time scales. Generally speaking, this model is too simple
to correctly predict the thermal and compositional fields for
turbulent non-premixed flames, but can be useful as the first-
guess solution for the application of different and more detailed
combustion models.
A.2. Eddy dissipation concept model
In a turbulent environment, combustion takes place wherethere is a molecular mixing, i.e. at small turbulence scales. Ac-
cording to the EDC model, the chemical reactions occur only
in small scale micro-mixed turbulent structures known as fine
structures. These fine structures are treated as a perfectly stirred
reactors (PSR) with a residence time and mass fraction .
Their volume fraction is a function of turbulent properties;
the reactions proceed in the fine structures, according to a de-
tailed kinetic scheme, for a time equal to a residence time
and an effective volume V
= 0.41
1/2
, = 2.13
2 1/4
, V = V. (12)
Based on the mass transfer between the fine structures and their
surroundings, the mean reaction term becomes
Ri =2
(1 3
)(i
0i ), (13)
where is the density and the laminar kinematic viscosity.
The basic assumption is that chemical reactions are quenched if
the characteristic chemical times for limiting species are longer
than .
The EDC model can incorporate detailed chemical mecha-
nisms into turbulent reacting flows and can be used when the
assumption of fast chemistry is invalid. However, typical mech-
anisms are invariably stiff and their numerical integration is
computationally costly.
A.3. Steady laminar flamelets model
The basic assumption is that instantaneous thermo-chemical
state of the fluid is related to a conserved scalar quantity known
as the mixture fraction. In this way the species transport equa-
tions can be reduced to a transport equation for the mixture
fraction and one for its variance 2:
j
jt() +
j
jxi(Ui) =
j
jxi t
Sct
j
jxi , (14)
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j
jt
2
+j
jxi(Ui
2)
=j
jxi
t
Sct
j2
jxi
+ 2
tSc t
j
2
jxi
2 C
2. (15)
The constant C appearing in the dissipation term can be de-rived by turbulent spectral analysis and is usually set at 2. If
the system is not adiabatic, the enthalpy balance equation must
be solved
j
jt(H) +
j
jxi(Ui H) =
j
jxi
kt
Cp
jH
jxi
+ SH, (16)
where kt and Cp are thermal conductivity and specific heat of
the mixture, and SH is a generic source term which accounts
for the non-adiabatic behavior of the system.
The temperature and thermo-chemical variables are extracted
from a flamelets library, in which the temperature and compo-
sition corresponding to each value of mean mixture fraction ,
mixture fraction variance 2 and enthalpy H are stored. The
average value of the generic scalar stored in the library is
evaluated by the following integral:
=
10
f() (, H ) d, (17)
where f() is the mixture fraction probability distribution
function (PDF) and (, H ) is the relationship that links mix-
ture fraction and enthalpy to the scalar . In general a -PDF
is employed. The function (, H ), which takes into account
the treatment of complex chemistry, can be modeled following
different approach. In the case of the SLF model the turbulent
flame is considered as an ensemble of discrete, steady laminar
flames, called flamelets. The individual flamelets are assumed
to have the same structure as laminar flames in simple config-
urations.
References
[1] Wender I. Reactions of synthesis gas. Fuel processing technology, vol.
48; 1996. p. 189207.
[2] Falcitelli M, Pasini S, Tognotti L. An algorithm for extracting chemical
reactor network models from CFD simulation of industrial combustion
systems. Combust Sci Technol 2002;174:22.
[3] Falcitelli M, Pasini S, Rossi N, Tognotti L. CFD+reactor network
analysis: an integrated methodology for the modelling and optimisation
of industrial systems for energy saving and pollution reduction. Appl
Therm Eng 2002;22:971.
[4] SkjZth-Rasmussen MS, Holm-Christensen O, ]stberg M, Christensen
TS, Johannessen T, Jensen A. et al. Post-processing of detailed
chemical kinetic mechanism onto CFD simulations. Comput Chem Eng
2004;28:235161.
[5] Novosselov IV, Malte PC, Yuan S, Srinivasan R, Lee JCY. Chemical
reactor network application to emissions prediction for industrial DLE
gas turbine. Presented at Proceedings of GT2006 ASME Turbo Expo
2006: Power for Land, Sea and Air, Barcelona, Spain; 2006.
[6] Faravelli T, Bua L, Frassoldati A, Antifora A, Tognotti L, Ranzi E. A
new procedure for predicting NOx emissions from furnaces. Comput
Chem Eng 2001;25:6138.
[7] Frassoldati A, Buzzi-Ferraris G, Faravelli T, Ranzi E. Post-processing
of CFD simulations with detailed kinetics. Presented at 28th meeting of
Italian Section of The Combustion Institute, Naples, Italy; 2005.
[8] Barlow RS, Fiechtner GJ, Carter CD, Chen JY. Experiments on the
scalar structure of turbulent CO/H2/N2 jet flames. Combust Flame
2000;120:54969.
[9] Barlow RS, Fiechtner GJ, Carter CD, Chen JY. Sandia/ETH-Zurich
CO/H2/N2 Flame Data - Release 1.1. www.ca.sandia.gov/TNF , SandiaNational Laboratories, 2002.
[10] Flury M. Experimentelle Analyze der Mischungsstruktur in turbulenten
nicht vorgemischten Flammen. PhD thesis, ETH Zurich, Switzerland,
1999.
[11] Drake MC, Correa SM, Pitz RW, Lapp M. Nitric oxide formation from
thermal and fuel-bound nitrogen sources in a turbulent nonpremixed
syngas flame. Proceedings of the Combustion Institute, vol. 20; 1984.
p. 198390.
[12] FLUENT 6.2Users Guide.
[13] Wilcox DC. Turbulence modeling for CFD2nd ed. DCW Industries,
Inc.; 2004.
[14] Hossain M, Jones JC, Malalasekera W. Modelling of a bluff-body
nonpremixed flame using a coupled radiation/flamelet combustion model.
Turb Combust 2001;67:217.
[15] Dally BB, Fletcher DF, Masri AR. Modelling of turbulent flamesstabilised on a bluff-body. Combust Theory and Modell 1998;2:193.
[16] Zucca A. Modelling of turbulence-chemistry interaction and soot
formation in turbulent flames. PhD thesis, Department of Chemical
Engineering, Politecnico di Torino, Italy; 2004.
[17] Magnussen BF, Hiertager BH. On mathematical modeling of turbulent
combustion. 16th symposium (Int.) on combustion, The Combustion
Institute, Pittsburgh; 1976. p. 71927.
[18] Magnussen BF. On the structure of turbulence and a generalized Eddy
dissipation concept for chemical reactions in turbulent flows. 19th AIAA
aerospace science meeting, St. Louis, Missouri, 1981.
[19] Magnussen BF. Modeling of pollutant formation in gas turbine
combustor with special emphasis on soot formation and combustion.
18th international congress on combustion engines, international council
on combustion engines, Tianjin, China; 1989.
[20] Peters N. Turbulent combustion. Cambridge: Cambridge UniversityPress; 2000.
[21] Poinsot T, Veynante D. Theoretical and numerical combustion.
Philadelphia: Edwards; 2001.
[22] Fox RO. Computational models for turbulent reacting flows. Cambridge:
Cambridge University Press; 2003.
[23] Beretta A, Mancini N, Podenzani F, Vigevano L. The influence of the
temperature fluctuations variance on NO predictions for a gas flame.
Combust Sci Technol 1996;121:193216.
[24] Frassoldati A, Cuoci A, Faravelli T, Ranzi E. Optimal design of burners
and furnaces with CFD simulations and detailed kinetics. Presented at
6th international symposium on high temperature air combustion and
gasification, Essen, Germany; 2005.
[25] Frassoldati A, Faravelli T, Ranzi E. The ignition, combustion and
flame structure of carbon monoxide/hydrogen mixtures. Note 1:
detailed kinetic modeling of syngas combustion also in presence ofnitrogen compounds. Int J Hydrogen Energy; 2007, in press, doi:
10.1016/j.ijhydene.2007.01.011 .
[26] Hewson JC, Kerstein AR. Stochastic simulation of transport and chemical
kinetics in turbulent CO/H2/N2 flames. Combust Theory Modell
2001;5:669897.
[27] Steele RC, Malte PC, Nicol DG, Kramlich JC. NOx and N2 O in lean-
premixed jet-stirred flames. Combust Flame 1995;100:4409.
[28] Bilger RW, Starner SH, Kee RJ. On reduced mechanisms for methaneair
combustion in nonpremixed flames. Combust Flame 1990;80:13549.
[29] Barlow RS, Smith NSA, Chen JY, Bilger RW. Nitric oxide formation
in dilute hydrogen jet flames: isolation of the effects of radiation and
turbulence-chemistry submodels. Combust and Flame 1999;117:431.
http://www.ca.sandia.gov/TNFhttp://www.ca.sandia.gov/TNFhttp://10.0.3.248/j.ijhydene.2007.01.011http://10.0.3.248/j.ijhydene.2007.01.011http://10.0.3.248/j.ijhydene.2007.01.011http://www.ca.sandia.gov/TNFRecommended