Defect and Diffusion Forum Vols. 273-276 (2008) pp 144-149
online at http://www.scientific.net
© (2008) Trans Tech Publications, Switzerland
Online available since 2008/Feb/11
Numerical Study of Propane-Air Mixture Combustion in a Burner
Element
C.E.L. Pinho1,a, J.M.P.Q. Delgado2,b, R. Pilão3,c, J. Conde1,d and C. Pinho2,e
1
INEGI − Rua do Barroco, nº 174; 4465-591 Leça do Balio, Portugal
CEFT − DEMEGI, Faculdade de Engenharia da Universidade do Porto
Rua Dr. Roberto Frias, s/n; 4200-465 Porto, Portugal
3
CIEA − Instituto Superior de Engenharia do Porto, Rua Dr. António Bernardino de Almeida
nº 341, 4200-072 Porto, Portugal
2
a
[email protected], [email protected], [email protected], [email protected], [email protected]
Keywords: Heat transfer, Combustion, Turbulence, Computer Fluid Dynamics.
Abstract. This study considers numerical simulations of the combustion of propane with air, in a
burner element due to high temperature and velocity gradients in the combustion chamber. The
effects of equivalence ratio (φ) and oxygen percentage (γ) in the combustion air are investigated for
different values of φ between 0.5 and 1.0 and γ between 10 and 30%. In each case, combustion is
simulated for the fuel mass flow rate resulting in the same heat transfer rate (Q) to the combustion
chamber.
Numerical calculations are performed individually for all cases with the use of the Fluent CFD
code. The results shown that the increase of equivalence ratio corresponds to a significantly
decrease in the maximum reaction rates and the maximum temperature increase with the increases
of oxygen percentage. Mixing hydrogen with propane causes considerable reduction in temperature
levels and a consequent reduction of CO emissions.
Introduction
When early commercial CFD packages became available more than 20 years ago, simulating the
complex physics inside combustion chambers was already one of the target applications. Of course,
projects were often limited by computer resources these days [1,2]. Therefore in most cases reaction
was taken into account using relatively simple approaches such as the Eddy Dissipation Model.
Today, with increasing maturity of CFD technique and computing power, one focus in numerical
simulation of combustion is in the area of non-equilibrium chemistry and multiphase flow. New
fields of application, such as the formation of pollutants in technical flames or the optimization of
combustion processes, can be tackled that way. Some of the elements contend by fuel form
dangerous combustion products. The amount of these products is related with their percentage in
the fuel. The complete combustion of the main elements of fuel increases the efficiency of the
boiler. The construction of burner defines the combustion efficiency.
Turbulent combustion of hydrocarbon fuels is an integral part of many segments of the chemical
and power industries, and also in hot water boilers usually used as heating source for residences.
Combustion phenomenon is a complex mixture of fluid dynamics and chemistry.
The primary objectives in burner design are to increase combustion efficiency and to minimize
the formation of environmentally hazardous emissions, such as CO, unburned hydrocarbons (HC)
and NOx. Critical design factors that impact combustion include: the temperature and residence time
in the combustion zone, the initial temperature of the combustion air, the amount of excess air and
turbulence in the burner and the way in which the air and fuel streams are delivered and mixed.
Therefore, CFD codes can serve as a powerful tool used to perform low cost parametric studies.
The CDF codes solve the governing mass, momentum and energy equations in order to calculate the
pressure, concentrations, velocities and temperatures fields.
This work considers the combustion of propane with air due to the high temperature and velocity
gradients in combustion chamber using a single burner element. In order to investigate the effect of
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Defect and Diffusion Forum Vols. 273-276
145
oxygen percentage on the combustion, the combustion of fuel with air is examined at various
oxygen percentages in the air by using Fluent CFD code [3].
Mathematical Model
In this work we used the following models for the numerical calculations: (a) turbulent flow, with
turbulent model of RNG k–ε applied [4] with a standard wall functions for near wall treatment; (b)
for the chemical species transport and reacting flow, the eddy-dissipation model with the diffusion
energy source option. The following assumptions are made: (a) the flow is steady, turbulent and
compressible; (b) the mixture (propane-air) is assumed as an ideal gas; (c) no-slip condition is
assumed at the burner element walls.
The governing equations for mass, momentum and energy conservation, respectively, for the
two-dimensional steady flow of an incompressible Newtonian fluid are:
Mass conservation equation
∇.( ρui Yi ) = −∇.J i + S i
(1)
with
J i = −(ρDi,m + µ t / Sc t )∇Yi
(2a)
and
Di,m =
1 - Yi
(2b)
∑Y / D
j
i, j
where ρ is the density, u i is the fluid velocity, Yi is the local mass fraction, J i is the diffusion flux,
S i is the rate of creation by chemical reaction, Di,m is the diffusion coefficient, µ t and Sc t are the
turbulent viscosity and Schmidt number, respectively.
Momentum conservation equation
∇.( ρu i u j ) = −∇.P + ∇.τ eff
(3)
with
(
)
τ eff = µ ∇u + ∇u T − 2/3∇.uδ
(4)
where τ eff is the stress tensor, µ is the molecular viscosity and δ is the unit tensor.
Energy conservation equation

∇.[u i ( ρE + P)] = ∇. k eff ∇.T −


∑j

h j J j + u jτ eff  + S h


(5)
with
E = h−
P
ρ
+
u i2
2
(6)
where E is the energy, P is the pressure, k eff is the effective conductivity, S h is the source of
energy and h is the sensible enthalpy.
In this work, the combustion of propane with air is modelled with one-step reaction mechanism.
The reaction mechanism takes place according to the constraints of chemistry and it is defined by
146
Diffusion in Solids and Liquids III
C3H 8 +
5
φ
O2 +
5 100 − γ
φ
γ
N 2 → 3CO 2 + 4H 2 O +
5 100 − γ
φ
γ
N2 + 5
1−φ
φ
O2
(7)
where φ ( = 5[M O2 + (100 − γ ) / γ M N2 m& fuel ] /( M fuel m& air ) ) is the equivalence ratio and m& fuel and m& air
are fuel and air mass flow rates, respectively and γ is the oxygen percentage in air.
Computational Model
A two-dimensional burner element (see Figure 1) was designed using Gambit package (v2.2.30,
Fluent Inc). The skewness of the cells was improved in Gambit and using the grid
refinement/adaptation procedure of the Fluent code it was refined.
In the numerical calculation, two
L= 0.5 m
calculation models, a laminar flow
model and a turbulent flow model, were
used because the Reynolds numbers
based on the hydraulic diameter and the
flow velocity vary from 500 to 3000. Air
r = 0.01 m
For flows of Reynolds number below
r = 0.01 m
Propane
r
= 0.006 m
r = 0.004m
1000, a steady laminar flow model was
used. For Reynolds numbers over 1000,
a turbulent model of RNG k–ε was
Figure 1 – Scheme of the burner analysed.
applied with a standard wall function
for near wall treatment.
air
out
fuel
wall
Geometry and Mesh Generation
Grid generation represents a major challenge for CFD analysis. It is a time-consuming task and, in
spite of steady advances in automatic mesh generation, it still requires the skill of a CFD
practitioner to yield a suitable mesh. The choice of the type of grid depends on geometrical
complexity and on physics. The skewness of the cells was improved in Gambit package and using
the grid refinement/ /adaptation procedure of the Fluent code it was refined. The grid was smoothed
using the swap/smooth options in both codes. Grid refinement was performed until further
refinement showed no noticeable effects. The final unstructured grid that had 50000 cells was used
in the simulation.
Gas Flow Simulation
For gas simulation a propane-air mixture was used with the following physical values:
hamb = 20 W/m 2 K , Tin = Tamb = Tref = 300 K ,
P = 101325 Pa and ρ air = 1.225 kg/m 3 and
ρC H = 1.91 kg/m3 at the air and fuel inlet, respectively. The thermal properties ( c p ,µ and λ) of the
3
8
propane and species are function of temperature. The propane density at the fuel inlet and the
molecular weights, enthalpies and lower heating values of reactant and product species are taken
from the material property database given by Fluent Inc. [3]. The ranges of the simulation values
are: Q& = 10000W , φ = 0.5, 0.7, 1.0 and γ = 10%, 20%, 30% .
Fluent Modelling
The Fluent modelling is based on the two-dimensional conservation equations for mass and
momentum. The differential equations are discretised by the Finite Volume Method and are solved
by the SIMPLE algorithm. As a turbulence model, the k–ε was employed [4]. The Fluent code uses
an unstructured non-uniform mesh, on which the conservation equations for mass, momentum and
energy are discretised. The k–ε model describes the turbulent kinetic energy and its dissipation rate
and thus compromises between resolution of turbulent quantities and computational time. No-slip
Defect and Diffusion Forum Vols. 273-276
147
condition is assumed at the burner walls. The model constants for the RNG k–ε model are
C µ = 0.0845 , C1 ε = 1.42 , C 2 ε = 1.68 , and wall Prandtl number of 0.85.
Grid independence/solution adaptive refinement
While finer meshes would yield more accurate results, we were limited to this number of elements
because of the computer speed and memory. However, doubling the total number of elements
yielded less than 2% change in overall pressure drop and the solutions were considered basically
grid-independent. The standard k–ε model was used with non-equilibrium wall functions. Nonequilibrium wall functions were preferred to the standard wall functions because non-equilibrium
wall functions are better to deal with complex flows involving separation, reattachment, other nonequilibrium effects and strong pressure gradients (see Fluent User’s Guide [3]).
Results and Discussion
Numerical modelling of the burner element was performed at different stoichiometric mixture ratios
and oxygen percentage in the air. Table 1 shows the inlet velocities of air and stoichiometric air/fuel
ratios for Q = 10000 W and u fuel = 2.247 m/s , with Rsto and u air given by:
Rsto = 5
u air =
M O2 + (100 − γ ) / γ M N2
(8)
M C3 H 8
Rsto ρ fuel Afuel
u fuel
φ ρ air Aair
(9)
Table 1 – Inlet velocities of air and stoichiometric air/fuel ratios, for Q = 10000 W .
56.436
28.614
19.340
φ = 1.0
28.218
14.307
9.670
0.05
0.04
0.04
0.04
0.03
0.03
0.02
0.01
0
0.4
0.2
0.01
0.1
0.05
0.1
x (m)
0.005
0.02
0.01
0.05
0.01
0.005
0
0.0
05
0.2
0.15
( φ = 0.5 and γ = 10% )
0.2
0
r (m)
0.05
r (m)
0.05
0
0.2
1
0.0
0.05
0.03
00
5
10
20
30
r (m)
φ = 0.5
Rsto
32.22
16.34
11.04
0.02
1
0.0
0.01
0.2
0.05
0.1
x (m)
0.15
( φ = 1.0 and γ = 10% )
0.2
0
0
0.
γ (%)
uair (m/s)
φ = 0.7
40.312
20.439
13.814
0.05
0.1
0.05
0.1
x (m)
0.15
0.2
( φ = 1.0 and γ = 30% )
Figure 2 – Reaction rates contours for different equivalence ratios and oxygen percentage.
Figure 2 presents the distributions of reaction rates in the burner element for γ = 10% to 30% in
the case of φ = 1.0 . The numerical results showed that the maximum reaction rates decrease
significantly with the increase of equivalence ratios and with the increase of oxygen percentage in
air, these regions contract in the axial direction whereas they expand in the radial direction. The
maximum reaction rate profiles obtained were R = 1.14, 0.55 and 0.41 kmol/m3s in the cases of
φ = 0.5 / γ = 10% , φ = 1.0 / γ = 10% and φ = 1.0 / γ = 30% , respectively.
Figure 3 shows the temperature distribution in the burner element for the cases of
γ = 10%, 20%, 30% and φ = 0.5, 1.0 . The numerical results illustrates an increase of temperature
148
Diffusion in Solids and Liquids III
with both increases of γ and φ . The maximum temperature level was about 2701 K ( φ = 0.5 and
γ = 30% ). The average temperatures of the burner element increased from 1322 to 2701 K and
from 1251 to 2652 K in the cases of φ = 0.5 and φ = 1.0 , respectively, with the increase of γ from
10 to 30, i.e., the results shows that γ has more effect in temperature than φ . Temperature level is
decreasing considerably from the maximum zone trough the burner exit.
0.05
0.05
r (m)
0.02
13
0.02
0.01
00
0
0.1
0
0.2
x (m)
0.3
0.4
0.5
0
0.2
x (m)
0.3
0.4
0.02
1240
0
0.1
500
1500
0.04
1700
0.03
1900
0.02
1950
0.2
x (m)
0.3
0.4
0.5
1100
0.3
0.4
0.5
0
0.1
0.2
x (m)
0.3
0.4
0.5
1700
2100 1900
1100
2300
26
0.02
0
( φ = 1.0 and γ = 20% )
( φ = 1.0 and γ = 10% )
x (m)
0.03
13
00
1990
0
0.2
900 1300
700
0.01
0.01
1200
0.1
00
25
0.01
2700
0
( φ = 0.5 and γ = 30% )
r (m)
11
00
0.03
900
110
1300 0
0.04
1000
r (m)
600
700
900
800
0.04
900
00
19
0
2100 0
2500
0.05
500
500
17
0.02
0
0.5
0.05
0.05
r (m)
2100
0.03
( φ = 0.5 and γ = 20% )
( φ = 0.5 and γ = 10% )
0
0.1
700
0
130
0
1500
0.01
1900 1700
11
10
0
130 1200 0
0
00
00
15
90
0
0.01
0.03
0.04
0
70
0.03
11
00
r (m)
700
500
500
600
900
900
r (m)
0.05
0.04 500
800
700
0.04
0
23
190 210 0 0
0 0
1700
0.1
0.2
00
2650
x (m)
0.3
0.4
0.5
( φ = 1.0 and γ = 30% )
Figure 3 – Temperature distribution for φ = 0.5 and φ = 1.0 at different values of γ .
2700
γ = 20%
2100
2300
1800
1900
1500
T (K)
T (K)
γ = 10%
Series1
γ = 20%
Series2
γ = 30%
Series3
1200
φ = 0.5
Series1
φ = 0.7
Series2
φ = 1.0
Series3
Series4
φ = 1.0 (50%H2+50%C3H8)
900
600
1500
1100
700
φ = 0.5
300
300
0
0.1
0.2
x (m)
0.3
0.4
0.5
0
0.1
0.2
x (m)
0.3
0.4
Figure 4 – Axial temperature variation at different (a)-equivalence ratio and (b)-oxygen percentage.
Figure 4 illustrates the axial temperature, along the axis of the burner, for different equivalence
ratios and oxygen percentage in air, on propane combustion. In general, increasing the oxygen
percentage increases the temperature. This trend is as expected and similar to the works developed
by other authors [5,6].
Moreover, this computational fluid dynamics study also considered the combustion of hydrogen–
propane mixture fuel with 50%H2+50%C3H8. It is known [2] that hydrogen reduces the emission of
some pollutants, pure hydrogen fuel combustion does not give CO or unburned HC emissions.
Figure 4(a) shows that mixing hydrogen with propane causes considerable increase in
temperature levels. The predicted maximum temperature level, for pure propane combustion with
an equivalence ratio of 1.0 and an oxygen percentage in air of 20%, was about 1992 K, whereas the
0.5
Defect and Diffusion Forum Vols. 273-276
149
predicted temperature distributions for hydrogen–propane (50%H2+50%C3H8) mixture combustion,
at the same conditions, showed a predicted high temperature of 2195 K.
The overall flame temperature increases as hydrogen is added to the fuel due to the higher
energy input and lower flame radiation. It must be stressed that although a higher combustors
temperature will reduce CO and unburned HC emissions it will, on the other end, raise NO
emissions through the thermal or Zeldovich mechanisms [7].
Conclusions
The combustion of propane with air was analyzed in a burner element and the effect of the
equivalence ratio and oxygen percentage in air investigated, for different numerical values.
Combustion was simulated for the fuel mass flow rate resulting in the same heat transfer rate to the
combustion chamber in each case.
The results shown that the increase of equivalence ratio corresponds to a significantly decrease
in the maximum reaction rates and the maximum temperature increase with the increases of oxygen
percentage. Mixing hydrogen with propane causes considerable reduction in temperature levels and
a consequent, expected, reduction of CO and unburned HC but higher NOx emissions are expected.
Acknowledgment
J.M.P.Q. Delgado wishes to thank FCT for the grant Nº SFRH/BPD/11639/2002.
Notation
A
cp
Cµ
Area
Constant-pressure specific heat
Coefficient in k-ε turbulence model
Rsto
Sct
Sh
Stoichiometric air/fuel ratio
Turbulent Schmidt number
Source of energy
C1 ε
C2 ε
Di,m
E
h
Ji
keff
m&
M
P
Q&
R
Coefficient in k-ε turbulence model
Coefficient in k-ε turbulence model
Molecular diffusion coefficient
Energy
Sensible enthalpy
Diffusion flux of species
Effective conductivity
Mass flow rate
Molecular weight of species
Pressure
Heat transfer rate
Reaction rate
Si
T
u
Yi
Rate of creation by chemical reaction
Temperature
Velocity
Local mass fraction of each specie
Oxygen percentage in air
Unit tensor
Equivalence ratio
Thermal conductivity
Molecular viscosity
Turbulent viscosity
Density
Stress tensor
γ
δ
φ
λ
µ
µt
ρ
τ eff
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
G. Wecel and R.A. Białecki: Combust. Sci. and Tech. Vol. 178 (2006), p. 1413
M. Ilbas, I. Yılmaz and Y. Kaplan: Int. J. Hydrogen Energ. Vol. 30 (2005), p. 1139
Fluent Incorporated: FLUENT User’s guide version 6.2 (2005).
V. Yakhot and S.A. Orszag: J. Sci. Comput. Vol. 1 (1986), p. 151
M. Ilbas: Int. J. Hydrogen Energ. Vol. 30 (2005), p. 1113
M. Ilbas: Studies of ultra low NOx burner (PhD thesis, Cardiff, University of Wales, 1997).
S.R. Turns: An introduction to combustion - Concepts and application (McGraw Hill, Inc.,
New York, 1996).