Int. J. Energy Technology and Policy, Vol. 6, Nos. 1/2, 2008
5
NOx re-burn simulation in a double-jet counter-flow
flame
Dragos Isvoranu
Department of Thermodynamics,
University Politehnica of Bucharest,
313 Spl. Independentei, Sect. 6,
Bucharest 060042,
Romania
E-mail: dragos@aero.pub.ro
Abstract: The paper investigates the main features of NOx emission in a
laminar double-jet counter-flow diffusion flame for later use as a possible
physical model for NOx reduction through turbine in situ reheat. The oxidizer
stream consists of exhaust gas resulted from a conventional combustor and the
fuel stream is represented by an air–methane mixture. The main interest rests
on the distribution of NOx species and especially on NO production rate that
controls the pollutant emission index. The most interesting outcome of the
research is that NO emission index has a minimum value depending on the
equivalence ratio of the air–methane mixture.
Keywords: combustion; NOx; numerical modelling; pollutant emission.
Reference to this paper should be made as follows: Isvoranu, D. (2008) ‘NOx
re-burn simulation in a double-jet counter-flow flame’, Int. J. Energy
Technology and Policy, Vol. 6, Nos. 1/2, pp.5–16.
Biographical note: Dragos Isvoranu is a Lecturer at the Department of
Thermodynamics, University Politehnica of Bucharest, since 1996. He received
his PhD in Engineering Thermodynamics from the same university in 1999.
Between 2000 and 2001, he was engaged in a post-doc research activity at
Texas A&M University. His main areas of expertise are thermodynamics, gasdynamics, combustion, numerical modelling.
1
Introduction
Currently, the reduction of NOx emissions from all combustion sources is of vital
importance and a key issue of most combustion research. In the case of gas turbine
engines, the current NOx regulations are met mainly by injection of water or steam or by
re-designing the conventional combustor. In recent years, there has been much more
attention paid on the development of low-NOx industrial combustors (Sotheran, Pearce
and Overton, 1984; Kuroda et al., 1987; Andrews et al., 1990). The current design of
these devices focuses on air or fuel staging with premixed combustion at high power
regimes. Although the general design principles for ultra low-NOx combustors are
known, i.e. very lean primary zones and good fuel–air mixing, methods for successfully
achieving these aims have yet to be established for liquid fuels to ensure the stability
Copyright © 2008 Inderscience Enterprises Ltd.
6
D. Isvoranu
requirements of gas turbines in the hole range of operating conditions. In the following
endeavour, the author was inspired by a possible turbine engine development based on
in situ reheat (Isvoranu and Cizmas, 2003). Under these circumstances, the reheat process
through methane injection at the trailing edge of the vane blades in the turbine stage may
be considered as an exhaust gas re-burn process which leads not only to a gain in specific
thrust but also to a pollutants reduction. The main objective of this paper is to assess the
NOx production behaviour at atmospheric pressure in the stagnation plane of a diffusion
flame generated by two jets counter-flow, one comprising of air–methane mixture and the
other products of a previously combustion process.
2
Physical model
To simplify the complexity of the combustion process in a turbine-combustor such that
the salient features of the NOx re-burn become obvious, a laminar double-jet counter-flow
model has been taken into account. This choice has the advantage of simulating the
purely or premixed diffusion flame that has to be modelled for the turbine-combustor
operating conditions. The fuel jet consists of either pure methane or air–methane mixture
at different equivalence ratios. The oxidizer jet is represented by the main combustor
exhaust gas mixture. The various equivalence ratio of air–methane mixture flows
upwards through a lower nozzle and after meeting the oxidizer jet flowing downward
through an upper nozzle (Figure 1). Porous plates are attached to both the nozzles at exit
such that uniform flow is maintained at inlets. The steady conservation equations for
mass, momentum, energy and species written in cylindrical coordinates are used to model
the counter-flow diffusion flame. In all these equations: x, axial coordinate; r, radial
coordinate; T, temperature; yk, mass fraction of the kth species (there are K species); Xk,
molar fraction of the kth species; p, pressure; u, axial velocity of the mixture; v, radial
velocity of the mixture; U, mass density; Wk, molecular weight of the kth species; W,
mean molecular weight of the mixture; RM, universal gas constant; O, thermal
conductivity of the mixture; cp, constant pressure specific heat of the mixture; cpk,
k , molar production rate by chemical
constant pressure specific heat of the kth species; Z
reactions of the kth species; hk, specific enthalpy of the kth species; P, dynamic viscosity
of the mixture. Recognising that v / r and other quantities should be a function of x only,
new similarity variables are defined to produce a 1D system of equations to be solved
(Lutz et al., 1997).
G( x) { Uv
r
; F ( x) {
Uu
2
(1)
Under these circumstances, the mass conservation equation reduces to
G ( x) dF ( x )
dx
0
(2)
NOx re-burn simulation in a double-jet counter-flow flame
7
Geometry of the counter-flow diffusion flame
Figure 1
Because F and G are the functions of x only, so are U, u, T and yk. The radial momentum
equation is satisfied by the eigenvalue
1 wp
r wr
H
constant
(3)
The radial momentum equation becomes
H 2
d § FG · 3G 2 d § d § G · ·
¨ P ¨ ¸¸
¨
¸
U
dx © U ¹
dx © dx © U ¹ ¹
0
(4)
while the energy and species equations are:
Uu
dT 1 d § dT
¨O
dx c p dx © dx
· U
¸
¹ cp
¦
dy k d
kWk
( U yk Vk ) Z
dx dx
pW
U
RMT
Uu
K
c pk yk Vk
k 1
0, k
dT 1
dx c p
K
¦ h Z
k
k
0,
k 1
1, }, K
(5)
The diffusion velocities Vk are given by the mixture-averaged formulation
Vk
Dkm
dX k
1
Dkm
Xk
dx
1 yk
¦
K
jzk
X j / D jk
where Dkm and Djk represent the mixture-averaged and binary diffusion coefficients.
(6)
(7)
8
D. Isvoranu
3
Combustion model
The adopted reaction scheme to describe combustion reactions in the flame was the
Leeds mechanism (www.chem.leeds.ac.uk), which is based on the so-called C2 chemistry
compiled by Miller and Bowman (1989). To describe the NOx formation, the prompt and
thermal mechanisms were used. The reactions leading to the NO2 formation and the NOx
re-burn were also included. The resulting mechanism involves 56 species and 334
reactions. Thermal NOx is formed by the oxidation of the nitrogen present in the
combustion air. Prompt NOx is produced by the Fenimore mechanism high-speed
reactions in the flame front, while re-burning scheme reduces the total level of NOx
formation by NOx reactions with other hydrocarbon species like CH, CH2 and CH3.
3.1 Thermal NO
The formation of thermal NO is determined by a set of highly temperature dependent
chemical reactions known as Zeldovich mechanism:
O N 2 œ N NO
N O 2 œ O NO
(8)
N OH œ H NO
3.2 Prompt NO
The presence of a second mechanism leading to the NO formation was first identified by
Fenimore (1971) and was termed as ‘prompt NO’. There is good evidence that the
prompt NO can appear in several combustion environment conditions such as lowtemperature, fuel-rich and short residence times. The characteristic reactions are:
CH N 2 œ HCN N,
N O 2 œ NO O,
CN O 2 œ NO CO,
(9)
CH 2 N 2 œ HCN NH,
HCN OH œ CN H 2 O.
3.3 N2O formation
The main branch for N2O formation-destruction comes from the following reactions
(Nishioka et al., 1994):
N 2 O CO œ NCO NO,
N 2 O H œ NH NO,
N 2 O O œ 2NO.
3.4 NO2 formation
NO2 mechanism involves the five following reactions (Nishioka et al., 1994):
(10)
NOx re-burn simulation in a double-jet counter-flow flame
9
NO 2 CO œ NCO NO,
NO 2 H œ OH NO,
NO 2 M œ O M NO,
(11)
NO 2 OH œ HO 2 NO,
NO 2 O œ O 2 NO,
where M stands for any other third body species in the mixture.
3.5 NO re-burning
The re-burning NO mechanism is a pathway whereby NO reacts with hydrocarbons and
is subsequently reduced. Typical reactions are:
CH NO œ HCN O,
CH 2 NO œ HCN OH,
(12)
CH 3 NO œ HCN H 2 O.
The net chemical production rate Z k of each species results from a competition between
all chemical reactions involving that species.
R
k
Z
¦Q
i 1,}, R
ki qi
(13)
i 1
Q ki
Q ccki Q cki ,
where R stands for the total number of reactions involved in the chemical mechanism and
Q ccki , Q cki for the stoichiometric coefficients of the kth species in the ith reaction. Presuming
that each reaction proceeds according to the law of mass action, and the forward rate
coefficients is in the modified Arrhenius form
kf
§ E ·
AT E exp ¨ A ¸ ,
© RMT ¹
(14)
the rate-of-progress variable qi reads
K
qi
k fi
–[ X
k 1
K
Qcki
k]
kri
–[ X
Qccki
k]
(15)
k 1
where kri is the reverse rate of reaction. In the case of reversible reactions,
kri
k fi
K ci
,
(16)
where Kci is the equilibrium constant calculated from thermo dynamical data which is
given as
D. Isvoranu
10
K
K ci
§ 'S 0 'H i0 · § p
exp ¨ i ¸¸ ¨
¨R
© M RMT ¹ © RMT
·¦ k 1
¸
¹
Q ki
.
(17)
The symbol ' refers to the change that occurs in the standard state entropy ( Si0 ) or
enthalpy ( H i0 ) in passing from reactants to products in the ith reaction. All the necessary
thermo-chemical and transport properties were obtained from the CHEMKIN database
(Kee et al., 1986; Kee, Miller and Rupley, 1987).
4
Numerical model
The theoretical model for the double-jet counter-flow diffusion flame is very familiar and
extensively presented in literature (Kee et al., 1988). The adopted numerical procedure
was the one described by Kee et al. (1985), i.e. the finite difference approximations were
used to reduce the two-point boundary value problem to a system of algebraic equations.
Upward difference formula was used for convective terms and second-order central
difference formula was used for diffusive terms in the first two relations of Equation (5).
After obtaining a solution on a coarse mesh, new mesh points are added in the regions
where the solution or its gradients are rapidly changing. Taking into account that the
problem we are dealing with is a two-point boundary value problem, for which most of
the unknowns (species concentrations) are not given at either ends, minimising the
residual of transport equations, constrained by some of the variables known at both ends,
could be an attractive method of solution. Technically this means that, given the
unknown vector I
I
T1 , y1,1 , }, yK ,1 , }, T j , y1, j , }, yK , j ,}, TJ , y1, J ,}, yK , J
(18)
we would like to find the solution of R(I) = 0, where R is the residual vector of Equation
(5). Newton’s damped algorithm is able to provide this solution if it exists. Starting with
an initial estimate I(0), the method reads
1
I
(n)
I
( n 1)
O
( n 1)
§ wR ·
( n 1)
)
¨ ( n 1) ¸ R(I
© wI
¹
(19)
where, 0 < O(n–1) d 1 is the damping parameter. The selection of the Jacobian matrix
wR / wI and of the parameter O is governed by a look-ahead procedure consisting in
accepting the vector I, if the following condition
1
1
§ wR ·
§ wR ·
(n)
( n 1)
)
¨ ( n 1) ¸ R (I ) ¨ ( n 1) ¸ R (I
wI
wI
©
¹
©
¹
(20)
fulfils, hence, preventing the iteration to step away from the region where the solution
might reside. Newton’s iteration continues until the maximum norm of the correction
vector ¨I = I(n) – I(n–1) is reduced to within a user-specified tolerance.
If damping cannot produce a suitable correction, then a new Jacobian is computed
and the procedure is carried out again.
NOx re-burn simulation in a double-jet counter-flow flame
5
11
Boundary conditions
The inflow boundary conditions comprise of the total specific mass flux of species,
including diffusion and convection, temperature and velocity for both streams.
x
x
0 F
L F
0.5(Uu )F
0.5(Uu )O
G
G
0 T
0 T
TF
TO
(Uuyk )F
(Uuyk )O
Uuyk UykVk
Uuyk UykVk
(21)
Following the simulation conditions of Isvoranu and Cizmas (2003), the fuel stream
temperature was selected at 313 K, while for the oxidizer stream 1850 K was considered
to be the temperature of the burnt mixture evacuated from the main combustor.
X CO2
X O2
0.049762; X H 2O
0.099888; X N 2
0.106793; X CO
0.732987; X NO
0.0015; X AR
0.00025
0.00882;
(22)
The composition of the exhaust gas is based on the main components resulted from
kerosene combustion in a conventional combustor and adjusted to fit a 277 ppm NO
concentration (Drennan et al., 1993). Atmospheric pressure condition is considered.
6
Results
In this paper, the main interest was the influence of fuel stream equivalence ratio to the
total NOx formation. The composition of the fuel stream was expressed in terms of
equivalence ratio, defined as the ratio between fuel to oxygen molar or mass fractions at
actual operating conditions and stoichiometric fuel to oxygen molar or mass fractions.
Under this circumstance, the fuel inlet composition was varied from lean I < 1,
stoichiometric I = 1, to infinity, while keeping its injection velocity constant at
u = 16 cm sec1. In addition, the composition of the oxidizer stream as well as its
injection velocity was kept constant. The pure diffusion flame is obtained when I is
infinite. The selection of u = 16 cm sec1 is rather arbitrary, but it was chosen for
comparison reasons with similar numerical simulations (Nishioka et al., 1994) of a
classical air–methane air opposed flame. The same stands for choosing L = 1.5 cm
distance between the nozzles.
Figure 2 shows the flame structure for four representative values of fuel stream
equivalence ratio. The abscissa is the axial distance from the upper to lower nozzle. The
vertical dash-dotted line in the figures indicates the position of the stagnation plane, while
the upper small arrows illustrate the positions, where the CH and OH molar fractions are
maximal. These species are considered to be the main emitters of the premixed,
respectively, of the diffusion flame (Nishioka, et al., 1993) and hence, will represent a
measure of the position of respective flame fronts. Important variations in the flame
structure are observed as fuel stream equivalence ratio which is increased. For the lean
and stoichiometric fuel stream mixture, I d 1, there is only a premixed flame front
positioned right beside the fuel exit nozzle, while for moderate rich mixtures, 1 < I < 4, a
premixed-diffusion flame structure can be observed based on the large gap between the
CH and OH peaks. As I is increased more, the two flames merge to give one pure
diffusion flame at I = f.
12
Figure 2
D. Isvoranu
Flame structure for four representative values of fuel stream equivalence ratio:
(a) I 1 ; (b) I 1.55 ; (c) I 22 ; (d) I 371
Figure 3 shows the corresponding NOx distributions. For I d 1, there is no peak in the NO
concentration, due to the massive amount of NO in the oxidizer stream which diffuses
towards the fuel nozzle. Both the N2O and NO2 concentrations peak near inlets follow
different mechanisms. The fuel exit peak corresponds with the CH peak in the premixed
flame, which in turn, is consistent with the low temperature Fenimore mechanism. The
oxidizer peak is due to the high-temperature formation mechanism involving large
amounts of NO and CO. In the case of rich fuel stream mixtures, I > 1, the structure of
NOx distribution remains the same. There is a peak in NO distribution near the diffusion
flame front (OH maximum) and a central peak of NO2 which is consistent with high
values in the CO concentration and depletion of NO, according to NO mole production
rate distribution shown in Figure 4.
However, there is only a slight contribution of NO2 and N2O in the total NOx
formation. Analysing the mole production rate distributions, one can easily see that the
more the flame approaches the pure diffusion flame, the greater the consumption rate
becomes, reaching values almost two orders of magnitude higher. On the other hand, the
position of the maximum depletion rate moves towards the stagnation plane, i.e. the exit
NOx re-burn simulation in a double-jet counter-flow flame
13
plane of the chemical reactor. On this basis, we infer that the abrupt descending profile of
the NO concentration for the rich fuel stream cases towards the stagnation plane is mainly
due the to re-burning mechanism, which is consistent with the peak CH concentration
values. In order to assess the efficiency of the fuel re-burn procedure regarding NOx
emission reduction, we have considered determining both the NO molar fraction along
the stagnation plane and the so-called emission index, an intensive flame parameter,
whose definition, following Equation (9), reads
L
³ Z
EI
NOWNO dx
0
L
.
(23)
³ Z
CH 4 WCH 4 dx
0
Figure 3
NOx concentration distribution for four representative values of fuel stream equivalence
ratio: (a) I = 1; (b) I = 1.55; (c) I = 22; (d) I = 371
D. Isvoranu
14
Figure 4
NO production rate distribution for four representative values of fuel stream
equivalence ratio: (a) I = 1; (b); I = 1.55; (c) I = 22; (d) I = 371
Figure 5a reflects the influence of the NO formation-depletion mechanism on the
stagnation NO concentration by comparison with the free-nitrogen reaction mechanism
solution. It is obvious that the NO re-burn mechanism represents the major cause for the
noticeable decreasing trend of the NO stagnation molar fraction for equivalence ratios
greater than 4.
Figure 5b presents a log-plot of the emission index against fuel stream equivalence
ratio. The increased NO production for the premix-diffusion flame structure (1 < I < 4) is
well illustrated by the strong peak of the emission index plot. Surprisingly, the presence
of a minimum value of the emission index is observed, likewise in the NO stagnation
molar fraction. The minimum value of 1.61 is attained for equivalence ratios around
I = 22, i.e. 70% methane in the fuel stream. The emission index of the pure diffusion
flame is 2.26.
The stage combustion alternative, i.e. splitting the combustion process either between
two injectors in the same combustion chamber or, e.g. between main combustor and a
turbine-combustor, leads to an overall emission index
EI ov
1
ª ( m F ) main EI main ( m F ) re-burn EI re-burn º
¼
(m F ) main (m F ) re-burn ¬
(24)
NOx re-burn simulation in a double-jet counter-flow flame
15
where subscript F refers to fuel. Based on the above relation, one can easily see that, an
inspired choice of fuel types in the main and re-burn combustors or of their flow rates or
both, can provide reasonable values of the pollutants emissions.
Figure 5
7
(a) NO stagnation molar fraction with and without NO mechanism; (b) Emission index
of counter-flow flame at different fuel stream equivalence ratio
Conclusions
In the particular case, it is investigated that one has to be aware of the emission index
which is not only an intensive parameter for this double jet flame environment, but also a
combined feature of the whole combustion process through the inherited NO influx.
Different NO boundary conditions on the oxidizer side will lead to different emission
index values. Taking into account that, according to Drennan et al. (1993), the 277 ppm
NO boundary condition (21) corresponds to an emission index of 13.5 g NO per kg fuel
in the main combustor, it seems that the re-burn process may represent a valuable
alternative in the NOx emission reduction, but further work has to be done. The numerical
simulations based on the temperature and pressure conditions mentioned before are just a
first step in a palette of more elaborate simulations in order to assess the pollutant
emission index, in this particular configuration, and in the range of conditions usually
found in turbo-machinery. Further investigation is needed to evaluate the influence of the
inlet velocities (or strain rate) on emission index.
Acknowledgements
This work has been supported by the National Academic Research Council under grant
36/2006.
16
D. Isvoranu
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