Numerical analysis of confined laminar diffusion effects of chemical kinetic mech

International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976IN
INTERNATIONAL JOURNAL OF ADVANCED RESEARCH –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEME
ENGINEERING AND TECHNOLOGY (IJARET)
ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online)
Volume 4, Issue 1, January- February (2013), pp. 59-78 IJARET
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NUMERICAL ANALYSIS OF CONFINED LAMINAR
DIFFUSION FLAME - EFFECTS OF CHEMICAL KINETIC
MECHANISMS

Ahmed GUESSAB*, Abdelkader ARIS**, Abdelhamid BOUNIF**, Iscander GÖKALP***
*
Industrial Products and Systems Innovations Laboratory (IPSILab),Enset, Oran, Algérie -
E-mail : (med_guessab@yahoo.fr), Tel. : 00213560706424
**
Laboratoire des Carburants Gazeux et de l’Environnement, Institut de Génie
Mécanique,Université des Sciences et de la Technologie, Oran, Algérie.
E-mails : (arisaek@yahoo.fr) and (abdelbounif@yahoo.com)
*** Laboratoire de Combustions et Système Réactifs, Centre National de la Recherche
Scientifique, 1C, Avenue de la Recherche Scientifique, 45071 Orléans, cedex 2, France
e-mail : ( gokalp @cnrs-orleans.fr )

ABSTRACT

Two chemical kinetic mechanisms of methane combustion were tested and compared
using a confined axisymmetric laminar flame: 1-step global reaction mechanism [24], and 4-
step mechanism [25], to predict the velocity, temperature and species distributions that
describe the finite rate chemistry of methane combustion. The transport equations are solved
by FLUENT using a finite-volume method with a SIMPLE procedure. The numerical results
are presented and compared with the experimental data [5]. A 4-step methane mechanism
was successfully implanted into CFD solver Fluent. The precompiled mechanism was linked
to the solver by the means of a User Defined Function (UDF). The numerical solution is in
very good agreement with previous numerical of 4-step mechanism and the experimental
data.
Keywords: Laminar Flame, Axisymmetric Jet, confined, Chemical kinetic, Finite Rate
Chemistry.

1. INTRODUCTION
Combustion is a complex phenomenon that is controlled by many physical processes
including thermodynamics, buoyancy, chemical kinetics, radiation, mass and heat transfers
and fluid mechanics. This makes conducting experiments for multi-species reacting flames
extremely challenging and financially expensive. For these reasons, computer modeling of

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International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –

these processes is also playing a progressively important role in producing multi-scale
information that is not available by using other research techniques. In many cases, numerical
predictions are typically less expensive and can take less time than similar experimental
programs and therefore can effectively complement experimental programs.

Computational models can help in predicting flame composition, regions of high and low
temperature inside the burner, and detailed composition of byproducts being produced.
Detailed computational results can also help us better predict the chemical structure of flames
and understand flame stabilization processes. These capabilities make Computational Fluid
Dynamics (CFD) an excellent tool to complement experimental methods for understanding
combustion and thus help in designing and choosing better fuel composition according to the
specific needs of a burner. With the advent of more and more powerful computing resources,
better algorithms, and the numerous other computational tools in the last couple of decades,
CFD has evolved as a powerful tool to study and analyze combustion. However, numerous
challenges are involved in making CFD a reliable and robust tool for design and engineering
purposes. The numerical simulation is a useful tool because it can easily employ various
conditions by simply changing the parameters.

Laminar co-flow diffusion flames are very sensitive to initial conditions and
perturbations [1-2]. The gas jet diffusion flame is the basic element of many combustion
systems, such as gas turbines, ram jets, the power-plant and industrial furnaces. In these
systems, fuel is injected into a duct with a co-flowing or cross-flowing air stream.
Furthermore, the fundamental understanding of laminar diffusion flames plays a central role
in the modeling of turbulent diffusion flames through the concept of laminar flamelets and in
understanding the processes by which pollutants are formed.

Consequently, many experimental and numerical studies on confined laminar diffusion
flames have been performed: Numerical Simulation of Laminar Co-flow Methane-Oxygen
Diffusion Flames: Effect of Chemical Kinetic Mechanism [3]. Smooke et al. [4] obtained the
numerical solution of the two-dimensional axisymmetric laminar co-flowing jet diffusion
flame of methane and air both in the confined and the unconfined environment. Primitive
Variable Modeling of Multidimensional Laminar Flames by Xu et al. [5] to study the
temperature, velocity and concentration profiles of stable species. An Efficient Reduced
Mechanism for Methane Oxidation with NO Chemistry [6]. Experimental and Numerical
Study of a Co-flow Laminar CH4/Air Diffusion Flames [7, 31].

A numerical simulation of an axisymmetric confined diffusion flame formed between a
H2-N2 jet and co-flowing air, each at a velocity of 30 cm/s, were presented by Ellzey et al. [8]
and Li et al. [9] investigated a highly over-ventilated laminar co-flow diffusion flame in
axisymmetric geometry considering unity Lewis number and the effects of buoyancy.
Thomas et al. [10] Comparison of experimental and computed species concentration and
temperature profiles in laminar two-dimensional methane/air diffusion flame. Shmidt et al.
[11], Simulation of laminar methane-air flames using automatically simplified chemical
kinetics. Northrup et al. [12] solution of laminar diffusion flames using a parallel adaptive
mesh refinement algorithm. Mandal B.K. et al. [13] Numerical simulation of confined
laminar diffusion flame with variable property formulation, a numerical model is used for
simulation flame under normal gravity and pressure conditions to predict the velocity,
temperature and species distributions.
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Since methane is the simplest hydrocarbon fuel available; several studies have focused
on methane-air flames. The oxidation of methane is quite well understood and various
detailed reaction mechanisms are reported in literature [14]. They can be divided into full
mechanisms, skeletal mechanisms, and reduced mechanisms. The various mechanisms differ
with respect to the considered species and reactions. However, considering the uncertainties
and simplifications included in a turbulent flame calculation, the various mechanisms agree
reasonably well [15]. In literature, several mechanisms of methane combustion exist. We can
cite: for detailed mechanisms: Westbrook [16], Glarborg et al. [17], Miller and Bowman [18],
and recently, Konnov [19], Huges et al. [20], and the standard Gri-mech [21], for reduced
mechanisms: Westbrook and Dryer [22], and Jones and Lindstedt [23] (more than 2 global
reaction).
In summary, the major works of present paper include comparison between 1-step and 4-
step chemical reaction mechanism. A working model was developed that fully coupled a
comprehensive chemical kinetic mechanism with computational fluid dynamics in the
commercial software program Fluent modified such as to deal with Westbrook’s and Drayer,
[24], Jones et al. [25].
2. PROBLEM DESCRIPTION
The vertical cylindrical diffusion flame burner is shown in Fig. 1. The burner consists
of two concentric tubes of 12.7 mm and 50.8 mm. Fuel issues through the inner tube and air
issues through the outer. The fuel-jet velocity is 0.0455 m/s, with a temperature of 298K. A
uniform velocity 0.0988 m/s is specified for the air coflow with a temperature of 298 K. The
methane-jet is supplied at 3.71×10-6 Kg/s, or the Air is supplied at 2.214×10-4 Kg/s. The exit
pressure is specified 105 Pa, whereas a zero-gradient pressure conditions is imposed at the
inlet. The wall-function treatment is utilized at the walls. The fuel-jet and air coflow
compositions are specified in terms of the species mass fraction and based on the information
provided about the experiment [5].

Figure 1. Geometry of confined axisymmetric laminar diffusion flame [5].

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In the present computation, the reaction rate is computed by finite-rate for laminar flow. The
1-step and 4-step reactions are used in methane combustion (Tabs. 1-2).

For the one-step global reaction.

No. Reaction Ak βk Ek [j/molK] Reaction orders
WD1 CH4+2O2 → CO2+2H2O 1.0e+12 0 1.0e+08 [CH4]0.5 [O2]1.25

Tab. 1. Westbrook and Dryer Global Multi-Step Chemical Kinetics Mechanism for
CH4/air combustion and reaction rate coefficients [24].
For the four-step reaction.

No. reaction Ak βk Ek [Kj/mol] Reaction orders
JL1 CH4+0.5O2 → CO+2H2 7.82e+13 0 30.0e+03 [CH4]0.5 [O2]1.25
JL2 CH4+H2O → CO+3H2 0.30e+12 0 30.0e+03 [CH4][H2O]
JL3 H2+0.5O2 → H2O 1.21e+18 -1 40.0e+03 [H2]0.25[O2]1.5
JL4 CO+H2O → CO2+H2 2.75e+12 0 20.0e+03 [CO][H2O]

Tab. 2. Jones Lindstedt Global Multi-Step Chemical Kinetics Mechanism for
CH4/air combustion and reaction rate coefficients [25].

3. GOVERNING EQUATIONS

The description of a problem in combustion can be given by the the conservation
equation of mass, momentum, species concentrations and energy. In primitive variabl where
x and r denote axial and radial coordinates, respectevely, incompressible conservation
equations for an axisymmetric, laminar diffusion flame in cylindrical coordinates can be
written as follows:

For the mass: ∂ ρ(U ) 1 ∂( ρV ) (1)
+ =0
∂x r ∂r

x-momentum:
( )
∂ ρU 2 1 ∂ (rρ UV ) ∂ P 1 ∂   ∂ U ∂ V  ∂  ∂U 
+ =− + rµ +  + 2 µ 
∂x r ∂r ∂ x r ∂ r   ∂ r ∂ x  ∂x ∂x (2)
2 ∂   ∂ V ∂ U V 
−  µ + +  + ρg x
3 ∂ x   ∂ r ∂ x r 

r-momentum
(
∂ ( ρUV ) 1 ∂ rρ V 2) ∂ P 2 ∂  ∂V
 rµ
 2 V
− µ 2 +
∂   ∂ U ∂ V 
+ =− +  µ + 
∂x r ∂r ∂r r ∂r  ∂r  r r ∂ x   ∂ r ∂ x  (3)
2 ∂   ∂V V ∂U 
−  µ + + 
3 ∂r  ∂r r ∂x




The density is computed from the ideal gas law.

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4. SPECIES TRANSPORT EQUATIONS

The conservation of species (i) transport equation takes the following general form [26]:

 →  →
ˆ
∇ . ρ u Y i  = −∇ . J i + R i + S i (4)
 

Where Ri is the net rate of production of species i by chemical reaction and Yi is the
mass fraction of species i. An equation of this form will be solved for N-1 species where N is
the total number of fluid phase chemical species present in the system. Si is the rate of
→
creation by addition from the dispersed phase plus any user-defined sources. J i is the
diffusion flux of species i, which arises due to concentration gradients. The diffusion flux in
laminar flows can be written as:

→
J i = − ρD,m ∇.Yi
i (5)

Here Di,m is the diffusion coefficient for species i in the mixture. The reactions rates that
appear in Equation (4) as source terms Ri can be computed from Arrhenius rate expressions.
Models of this type are suitable for a wide range of applications including laminar or
turbulent reaction systems, and combustion systems including premixed or diffusion flames.

4.1. Treatment of species transport in the energy equation
For many multi-component mixing flows, the transport of enthalpy due to species
diffusion

n → 
∇. ∑ hi J i  (6)
 i =1 

Can have a significant effect on the enthalpy field and should not be neglected. In
particular, when the Lewis number:

λ
Lei = (7)
ρC p Di ,m

λ is the thermal conductivity.

For any species is far from unity, neglected this term can lead to significant errors. Fluent
will include this term by default.

In cylindrical coordinates equation (6) can be written as follows:

63


∂ ( ρUh ) 1 ∂ (rρ Vh ) 1 ∂  λ ∂ h  ∂  λ ∂ h 
r +  
+ =
∂x r ∂r r ∂r  Cp ∂r  ∂ x Cp ∂ x 
   
1 ∂  λ n ∂Cj  ∂  λ n ∂Cj 
+
 C ∑ j
r
r ∂r 
( )
h Le − 1 − 1
j  ∂xC ∑ j
+
∂r 
 ( )
h Le − 1 − 1
j
∂x 

p j =1  p j =1 
(8)

4.2. The laminar finite rate model
The laminar finite-rate model computes the chemical source terms using Arrhenius
expressions, and ignores the effects of turbulent fluctuations. The model is exact for laminar
flames, but is generally inaccurate for turbulent flames due to highly non-linear Arrhenius
chemical kinetics. The net source of chemical species i due to reaction am computed s the
sum of the Arrhenius reaction sources over the NR reactions that the species may participate
in:
NR
Ri = Mw,i ∑Ri,k
ˆ ˆ (9)
k=1

ˆ
Where Mw,i is the molecular mass of species i and Ri ,k is the molar rate of
creation/destruction of species i in reaction k. Reaction may occur in the continuous phase
between continuous phase species only, or at resulting in the surface deposition or evolution
ˆ
of a continuous-phase species. The reaction rate, Ri , k , is controlled either by an Arrhenius
kinetic rate expression or by mixing of the turbulent eddies containing fluctuating species
concentrations.
4.3. The Arrhenius Rate
Chemical kinetic governs the behavior of reacting chemical species. As explained earlier,
a combustion reaction proceeds over many reaction steps, characterized by the production
and consumption of intermediate reactants. Several conditions determining the rate of
reaction are the concentration of reactants and the temperature. The concentration of the
reactants affects the probability of reactant collision, while the temperature determines the
probability of the reaction occurring given a collision. In general, a chemical reaction can be
written in the form as follows:

N N

∑υ'i,k Ai ⇔∑υ"i,k Ai
i=1 i'=1
(10)

Where
N = number of chemical species in the system
υ'i',k = Stoichiometric coefficient for reactant i in reaction k
υ"i',k = Stoichiometric coefficient for product i in reaction k
Ai = chemical symbol denoting species i
kf,k = forward rate constant for reaction k
kb,k = backward rate constant for reaction k

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Equation (10) is valid for both reversible and non-reversible reactions. For non-reversible
reactions, the backward rate constant kb,k is simply omitted. The summations in Equation (10)
are for all chemical species in the system, but only species involved as reactants or products
will have non-zero stoichiometric coefficients, species that are not involved will drop of the
equation except for third-body reaction species. The molar rate of creation/destruction of
ˆ ˆ
species i’ in reaction k, Ri' ,k , in Equation (4) Ri' ,k is given by:

 N N
η" 
 [ ]
Ri' ,k = Γ(υ"i,k − υ'' ,k ) k f,k ∏ C j j,k − kb,k ∏ C j j,k 
ˆ η'
 [ ] (11)
 j =1 j =1 
Where:
Cj = Molar concentration of each reactant or product species j [Kmol m-3]
η' j ,k = Rate exponent for reactant j’ in reaction k
η"jk = Rate exponent for product j’ in reaction k
Γ = represents the net effect of third bodies on the reaction rate.
This term is given by:

N
Γ = ∑γ j,k Cj (12)
j'

Where γ j'k is the third-body efficiency of the j'th species in the kth reaction. The forward
rate constant for reaction k, kf,k, is computed using the Arrhenius expression

k f, k
= Ak T βk
exp (− E k /RT ) (13)

Where:
Ak = pre-exponential factor (consistent units)
βk = temperature exponent (dimensionless
Ek = activation energy for the reaction [J Kgmol-1]
R = universal gas constant (8313 [J Kmol-1K-1])

The values of υ' i , k ,υ" ' , k ,η' ' , k ,η" i , k , β k , A k , E k and γ j 'k can be provided the problem
definition. If the reaction is reversible, the backward rate constant for reaction k, kb,k, is
computed from the forward rate constant using the following relation:
k f,k
k b,k = (14)
Kk
Where k k is the equilibrium constant for the k-th reaction. Computed from:
NR

 ∆S k0 ∆H k  Patm ∑ (υ i' ',k −υ i' ,k )
 k =1
0
K k = exp 
 R − 
 RT  (15)
 RT  
Where Patm denotes atmospheric pressure (101325Pa). The term within the exponential
represents the change in Gibbs free energy, and its components are computed as follows:

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N 0
∆S k ° S
R
= ∑ (υ" i,k − υ' i,k ) i
i' = 1 R
(16)

∆H k0 N 0

RT
= ∑ (υ "
i ,k − υ i' ,k ) hR
i
(17)
i' = 1

Where S i0' and hi0' are, respectively, the standard-state entropy and standard-state enthalpy
including heat of formation.

5. SIMULATION DETAILS

The governing equations are solved using the CFD package Fluent [26] modified with
User Defined Functions in order to integrate the reaction rate formula proposed by
Westbrook et al. [24] and Jones et al. [25]. We have used finite-rate approach. Fluent was
utilized due to its ability to couple chemical kinetics and fluid dynamics. In computational
fluid dynamics, the differential equations govern the problem are discretized into finite
volume and then solved using algebraic approximations of differential equations. These
numerical approximations of the solution are then iterated until adequate flow convergence is
reached. Fluent is also capable of importing kinetic mechanisms and solving the equations
governing chemical kinetics. The chemical kinetics information is then coupled into fluid
dynamics equations to allow both phenomena to be incorporate into a single problem. There
are many options to specify when setting up a computational fluid dynamics model. The
options used in this work are presented in Tabs. 3 and 4.

Pressure 0.3
Density 0.5
Body forces 1
Momentum 0.7
Yi 0.9
Energy 0.4
Table 3. Under-relaxation factors.

Solver Type Pressure Based
Viscous Model Laminar
Gravitational Effect On
2D-Space Axisymmetric
Pressure-Velocity Coupling SIMPLE
Momentum Equations Discretization First Order Upwind
Species Equations Discretization First Order Upwind
Energy Equations Discretization First Order Upwind
Table 4. Computational model step.

The SMPLE algorithm [27] of velocity-coupling was used in which the mass
conservation solution is used to obtain the pressure field at each flow iteration. The numerical

66


approximations for momentum, energy, and species transport equations were all set to first
order Upwind. This means that the solution approximation in each finite volume was
assumed to be linear. This saved on computational expense. In order to properly justify using
a first order scheme, it was necessary to show that the grid used in this work had adequate
resolution to accurately capture the physics occurring within the domain. In other words, the
results needed to be independent of the grid resolution. This was verified by running
simulations with higher resolution grids. In a reacting flow such as that studied in this work,
there are significant time scale differences between the general flow characteristics and the
chemical reactions. In order to handle the numerical difficulties that arise from this, the
STIFF Chemistry Solver was enabled in Fluent.
The STIFF Chemistry Solver integrates the individual species reaction rates over a time
scale that is on the same order of magnitude as the general fluid flow, alleviating some of the
numerical difficulties but adding computational expense. For more information about this
technique refer to Fluent [26]. Overall, the computational model solved the following flow
equations: mass continuity, r momentum, x momentum, energy, and n-1 species conservation
equations where n is the number of species in the reaction. The n-th species was determined
by the simple fact that the summation of mass fractions in the system must equal one.
The combustion system, the vertical, cylindrical diffusion flame burner [5] as can be seen
in Figure 2, consists of two concentric tubes through which the fuel and air issue,
respectively. The burner nozzle was set as inlet with a uniform velocity normal to the
boundary. The exhaust of the burner was set as an atmospheric pressure outlet. The walls
were set as adiabatic with zero flux of both mass and chemical species. Due to the geometry
of the model, only half of the domain needed to be modeled since a symmetry condition
could be assumed along the centerline of the burner.

Figure 2. Schematic diagram of the laminar co-flow diffusion flame.

67


The Computational domain and boundary conditions used are also shown. The
computational space seen in Fig. 2 given a finite volume mesh is divided by a staggered non-
uniform quadrilateral cell (Fig. 3). The computational domain extends for 0.3 m after the
burner nozzle, and 0.00508 m from the centerline. These dimensions correspond to 48djet and
0.8djet, respectively. A total number of 1500 (50 × 30 ) quadrilateral cells were generated
using non- uniform grid spacing to provide an adequate resolution near the jet axis and close
to the burner where gradients were large. The grid spacing increased in the radial and axial
directions since gradients were small in the far-field.

Figure 3. Mesh of combustion chamber.

6. RESULTS

In this study, we investigate the effect of two mechanisms models 1-step global
mechanism [24] and 4-step mechanism [25] on the laminar diffusion flame.

The 5 species ( 4-step) reduced mechanism has been implemented and tested in Fluent.

Fluent has UDF capabilities to allow for such implementation. The precompiled
mechanism was linked to the solver by the means of a User Defined Function (UDF). The
UDF communicates the chemical source terms the solver through the subroutine ‘Define Net
Reaction Rates’. The subroutine then returns the molar production rates of the species given
the pressure, temperature, and mass fractions. The predictions from the present simulation are
compared with the experimental results [5] for the same operating conditions. Radial
distributions of temperature, axial velocity and major product species (CO2, H2O, CO, N2 and
H2) concentrations at a height of 1.2 cm, 2.4 cm and 5 cm above the burner rim are shown.
Clearly the figures show a good agreement between the predict values with 4-step mechanism
and experimental values.

We begin by comparing the computational cost of the two kinetic models in terms of the
average CPU (execution) time per time step. The relative elapsed CPU times are compared in
Table 5.

Kinetic model Species Reaction CPU Nb.
Time/iter. (s) iterations
1-step [WD] 05 01 0.00396 635
4-step [JL] 06 04 0.0454 2845
Table 5. Average execution time per time step.

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In the 4-step mechanism [25], more reaction equations are computed, them more CPU
time is spent and more difficult it is to convergence. That in general the computational cost
increases with the number of reaction-step and species and more difficult it is to convergence.

Figure 4 shows the contour plot of the temperature for temperature fields from the
simulation using the ‘WD’ and ‘JL’ mechanism (Fig. 4b and 4c) compared with experiment
[5] (Fig. 4a). Is noticed that the smallest flame is predicted by the 1-step model ‘WD’,
whereas the largest flame is predicted by the 4-step model ‘JL’ (Fig. 4c) and it is observed
that the predicted maximum temperature calculated for the laminar co-flow diffusion flame
using different chemical kinetic schemes for 1-step model is 2218 K, but in the 4-step
scheme, it is 1955 K. The maximum center-line temperature reported by Xu and al. is 2180
K. The 1-step mechanism assumes that the reaction products are CO2 and H2O, the total heat
of reaction is over predicted. In the actual situation, some CO and H2 exist in the combustion
products with CO2 and H2O. This lowers the total heat of reaction and decreases the flame
temperature. The 4-step mechanism includes CO and H2, so we can get more detailed
chemical species distribution.

Figure 4. Shape and size of the flame CH4/Air.

The maximum temperature predicted by the detailed-chemistry schemes (4-step) are
much closer to the experimental results in literature [6-7] than the results predicted by the 1-
step mechanism, indicating the importance of finite-rate chemistry for diffusion flames of this
type. An accurate balance between transport and chemical reaction rates is needed to predict
accurately the flame temperature and this cannot be provided by simple one-step mechanisms
for the diffusion flame. Radial composition profiles of CH4 O2, CO2, H2O, CO, H2 and N2 at
several axial locations (x=1.2, 2.4, 5.0 cm) are shown on fig. 5-9 and the test results for Xu et
al. [5] are also shown. For O2, both results are the same and the 1-step global mechanism and
the 4-step mechanism over predict the CO2 concentration. From fig. 5-6 and 7, the H2O
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profile first increases with radial distance, peaks at 7.5 mm in predicted result (Fig. 5-6) and
6.75mm in experimental result and 5.25mm (Fig. 7) in predict result and 4.5 mm in
experimental result, then decreases to zero. The higher H2O concentration in the experimental
data is caused by the moisture carried by the re-entrant flow from the exit due to recirculation
in the burner. The comparison of H2 and CO is shown in Fig. 8 and 9.

The 1-step model neglects the energy-absorbing pyrolysis reaction and over predicts the
temperature by about 200-250K. The 4-step model is lower than the experimental result by
50-100K (Fig. 10, 11 and 12). The chemical reaction model mainly affects the species and
the temperature distribution and has a little effect on velocity. This disagreement between the
numerical and experimental data has been observed by Bhadraiah et al. [3], Liu et al. [7]
and Mitchell et al. [28]. As well, even though they were employing a detailed chemistry as a
combustion model. In fact, this over prediction is physically consistent with the higher
temperature predictions and flame length that produces a large buoyancy force and
recirculation zone in the burner [13]. A comparison of species profiles obtained by the
present study and by Xu et al.[5] showed that the present predictions are in better agreement
with the experimental data at the fuel side; however, the predictions of Xu and Smooke [5] at
the oxidizer side agreed more favorably with the data than those of the present study. This
discrepancy may be due to the deployment solution of the governing equations in non
conservative and conservative forms and the numerical solution techniques utilized in these
two studies. The radial profiles of axial velocity for two axial locations are shown in fig. 13.
The agreement between the prediction and measurement is very good. The axial velocity
away from the centreline decreases at all heights and becomes very low beyond a radial
distance [3-7].

0,50

0,45 Exp. [5] CH4
Exp. [5] H2O
0,40 Exp. [5] O2
Exp. [5] CO2
0,35
4-step (JL)
1-step (WD)
Mass Fraction

0,30

0,25

0,20

0,15

0,10

0,05

0,00
0,000 0,003 0,006 0,009 0,012 0,015

Radial distance (m)

Figure 5. Radial profiles of the species mass fractions at x=1.2cm.

70


0,40
Exp. [5] CH4
0,35 Exp. [5] H2O
Exp. [5] O2
0,30 Exp. [5] CO2
4-step (JL)
1-step (WD)
0,25
Mass Fraction

0,20

0,15

0,10

0,05

0,00
0,000 0,003 0,006 0,009 0,012 0,015

Radial distance (m)

Figure 6. Radial profiles of the species mass fractions at x=2.4cm

0,40
Exp. [5] O2
0,35 Exp. [5] CO2
Exp. [5] H2O
0,30 Cal. 4-step (JL)
Cal. 1-step (WD)

0,25
Mass Fraction

0,20

0,15

0,10

0,05

0,00
0,000 0,003 0,006 0,009 0,012 0,015
Radial distance (m)

Figure 7. Radial profiles of the species mass fractions at x=5cm.

71


0,05

Reduced mechanism (J-L)[25]
Cal. x=5 cm
0,04 Cal. x=2.4 cm
Cal. x=1.2 cm
Exp. [5] x=1.2 cm
Exp. [5] x=2.4 cm
Mass Fractio of H2

0,03 Exp. [5] x=5 cm

0,02

0,01

0,00
0,000 0,003 0,006 0,009 0,012 0,015
Radial Distance (m)

Figure 8. Radial H2 mole fraction profiles.

0,05

Reduced mechanism (JL)[25]
Cal. x=2.4cm
0,04 Cal. x=1.2cm
Cal. x=5cm
Exp. [5] x=2.4cm
Mass Fraction of CO

Exp. [5] x=1.2cm
Exp. [5] x=5cm
0,03

0,02

0,01

0,00
0,000 0,003 0,006 0,009 0,012 0,015

Radial distance (m)

Figure 9. Radial CO mole fraction profiles.

72


2500
x=1.2cm
Exp. [5]
Cal. 4-step (JL)
2000
Temperature (K) Cal. 1-step (WD)

1500

1000

500

0
0,000 0,003 0,006 0,009 0,012 0,015

Radial Distance (m)

Figure 10. Radial temperature profiles at x=1.2cm

2500

x=2.4 cm
Exp. [5]
2000 Cal. 4-step (JL)
Cal. 1-step (WD)
Temperature (K)

1500

1000

500

0
0,000 0,003 0,006 0,009 0,012 0,015

Radial Distance (m/s)

Figure 11. Radial temperature profiles at x=2.4 cm

73


2500

x=5 cm
Exp. [5]
2000 Cal. 1-step (WD)
Cal. 4-step (JL)
Temperature (K)

1500

1000

500

0,000 0,003 0,006 0,009 0,012 0,015

Radial Distance (m)

Figure 12. Radial temperature profiles at x=5cm.

3,0
Exp. [5] x=1.2 cm
Exp. [5] x=5 cm
2,5 Cal. 4-step (JL)
Cal. 1-step (WD)
Cal. 4-step (JL)
Cal. 1-step (WD)
Axial Velocity (m/s)

2,0

1,5

1,0

0,5

0,0
0,000 0,003 0,006 0,009 0,012 0,015

Radial Distance (m)

Figure 13. Radial profiles of axial velocity.

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7. CONCLUSION

Numerical computations of axisymmetric laminar diffusion flame for methane in air
have been carried out to examine the nature of flame, distributions of velocity, temperature,
and different species concentrations in a confined geometry. Different conservation equations
for mass, momentum, energy and species concentration for reacting flows are solved in an
axisymmetric cylindrical co-ordinate system. The 1-steps and 4-step chemical reaction of
methane and air has been considered to capture some of the features of chemical reaction
mechanisms. The CFD model based on SIMPLE algorithm predicts velocity, temperature and
species distributions throughout the computational zone of the cylindrical burner.

The predictions from the model match well with the experimental results available in
the literature [5, 28]. That in the general, in the 4-step mechanism, the presence of CO and H2
lowers the total heat release and the adiabatic flame temperature is below the values predicted
by the 1-step global mechanism and the smallest flame is predicted by the global reaction,
whereas the largest flame is predicted by the 4-step mechanism. The results are much closer
to the real situation. With engineering consideration for calculation time (or cost) and
accuracy, it recommended to adopt the 4-step mechanism.

This study constitutes the initial steps in the development of an efficient numerical
scheme for the simulation of unsteady, multidimensional combustion with stiff detailed
chemistry.

Nomenclature

Ai Chemical symbol denoting species i
Ak Pre-exponential factor
Cp Specific heat [J kg-1K-1]
Cj' Molar concentration of each reactant or product species j’ (Kmol m-3)
Di,m Diffusion coefficient for species i in the mixture
djet Diameter of gas jet [mm]
da Diameter of air jet [mm]
E Energy total
Ek Activation energy [Kj mol-1]
gx Acceleration of gravity [m s-2]
hi0' Standard-state enthalpy
hi Enthalpy of species i [J kg-1]
Ji Diffusive flux of species i[mol m-2 s-1]
Jq Heat flow caused by the diffusive flux [J m-2 s-1]
k k Equilibrium constant for the k-th reaction
kb,k Backward rate constant for reaction k
kf,k Forward rate constant for reaction k
Le Lewis number
Mw Molecular weight [Kg mol-1]
Mw,I Molecular mass of species i
N Number of species in the reaction
P Absolute pressure [Pa]
75


qr Heat radiation [J]
r Axial coordinates [mm]
R Universal gas constant [J Kmol-1K-1]
Ri Rate chemical reaction of species i
Si Rate of creation by addition from the dispersed phase [mol m3s-1]
S i0' Standard- state entropy
T Temperature [°K]
U Axial velocity [m s-1]
V Radial velocity [m s-1]
x Radial coordinates [mm]
Yi Mass fraction of species i

Greek symbols
µ Dynamic viscosity [kg m-1 s-1]
υi’ ,k Stoichiometric coefficient for reactant i in reaction k
υj’’,k Stoichiometric coefficient for product i in reaction k
ρ Density [Kg m-3]
λ Thermal conductivity [Wm-1K-1]
βk Temperature exponent
Γ Net effect of third bodies on the reaction rate
η' j',k Rate exponent for reactant j’ in reaction k
η"j',k Rate exponent for product j’ in reaction k

Abbreviations
UDF User Defined Functions
SIMPLE Semi-Implicit Method for Pressure-Linked Equations
WD Westbrook and Dryer
JL Jones Lindstedt

ACKNOWLEDGMENTS

We thank the research laboratory CNRS combustion and reactive systems (CNRS
Orléans, France) for the interest, support and assistance they have brought to this work.

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