### The adiabatic flame temperature

```Corso di Laurea Magistrale in Ingegneria Chimica/
Ingegneria Energetica
Formazione e Controllo di
Inquinanti nella Combustione
Impianti di trattamento
effluenti
Combustion Theory
Prof. L.Tognotti
Dipartimento di Ingegneria Civile e Industriale
Combustion: “Chemical reaction between fuel and oxidizer
involving significant release of energy as heat”
• Fuel is any substance that releases energy when oxidized, i.e.
methane
• Oxidized is any oxygen-containing substance, i.e. air, which can react
with the fuel
Combustion involves:
•
Thermodynamics
•
Chemical Kinetics
•
Fluid Mechanics and Turbulence
•
Energy and Mass Transfer
2
Combustion Theory
Outline:
1. Ideal gas behaviour
2. Thermo-chemistry
3. Chemical Kinetic
4. Premixed flames: Laminar vs. Turbulent
5. Diffusion flames : Laminar vs. Turbulent
6. Ignition and flame stabilization
Combustion Theory
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1. Ideal gas behaviour:
High temperatures associated with combustion generally results in sufficiently low
densities and make the ideal gas hypothesis suitable
•
Equation of State
pV  n tot R u T
•

pV  mRT

pV   RT
•
Ru is the universal gas constant, Ru=8.315 J/(mol K)
•
R is the specific gas constant, R=Ru/Mw (Mw is the gas molecular weight)
•
ρ is the gas density, ρ=m/V=v (v is the specific volume, m3 /kg)
Calorific Equation of State
•
Internal energy, u, is just a function of temperature, T:
du  c v dT
u: specific internal energy, J/kg cv: constant-volume specific heat (J/kg K)
•
Enthalpy, h, is just a function of temperature, T: dh  c dT
p
h: specific internal energy, J/kg cp: constant-pressure specific heat (J/kg K)
Combustion Theory
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•
The specific heats of gases are generally function of temperature. In general, the
more complex the molecule, the greater its molar specific heat.
Triatomic molecules: traslational, vibrational and
rotational components of internal energy
Diatomic molecules: traslational, vibrational and
rotational components of internal energy
Monoatomic molecules: only traslational,
component of internal energy
Combustion Theory
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•
Ideal gas mixtures
•
The mole fraction of species i is:
ni
Xi 
•
ni is the number of moles of species i, ntot is the total number of moles
n tot
The mass fraction of species i is:
Yi 
•
mi
mi is the mass of species i, mtot is the total mass
m tot
The mole and mass fractions sum up to unity:
N

N
Xi 1
and
i 1
•
i
1
i 1
The relation between mole and mass fraction is:
Yi  X i 
•
Y
M W ,i
MW
The mixture (mean) molecular weight is:
N
MW 

N
X i  M W ,i 
i 1
Combustion Theory
i

i 1
M W ,i
Yi
6/tot
•
The mole concentration of species i is:
Ci 
•
ni

X i  n tot
V
V
p
 Xi
R T
The total pressure, p, is equal to the sum of the partial pressures, pi:
p

pi
i
•
The partial pressure, pi, is equal to the total pressure times the mole fraction::
pi  X i p
•
Relations for ideal gases mixtures:
u mix 
Yh
i
i
u mix 
i
h mix 
Yh
i
ui
i
h mix 
X
i
hi
i
Ys
i
i
i
i
i
s mix 
X
i
 R  Yi ln Yi
i
s mix 
X
i
i
s i  R u  X i ln X i
i
u i , hi and s i are molar specific quantities, J/mol, J/(mol K)
Combustion Theory
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2. Thermochemistry
•
Combustion Stoichiometry
A hydrocarbon fuel can be completely oxidized if sufficient oxygen is available, i.e. the
stoichiometric quantity of oxidizer is available. Carbon, C, is converted to CO2 and
hydrogen to H2O.
The complete combustion of a hydrocarbon fuel (CnHm) can be expressed as:

 F C n H m  O  O2 
'
'
2


''
''
' ' 0 . 79
N 2    CO 2 CO 2  H 2 O H 2 O   O 2
N2
0 . 21
0 . 21

0 . 79
Dry air contents of O2 and N2 are 21% and 79% by vol., respectively.
The stochiometric coefficients are:
F 1 O  n  m /4
'
'
2
Combustion Theory
 CO  1  H
'
'
2
2O
 m/2
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•
Stochiometric (mass based) Air to Fuel Ratio (AFR)

 O   M W ,O 2 
'
AFR
st
m 
  a  
 m F  st
2


 M W ,N 2 
0 . 21

0 . 79
M W ,F
for methane n=1 and m=4 → AFRst=17.2
for octane n=8 and m=18 → AFRst=15.1
Combustion Theory
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
m

n


4

0 . 79
 


M

 M W ,N 2 
  W ,O 2
0 . 21
 

M W ,F
•
Equivalence Ratio (Φ): it is commonly used to indicate if a mixture
is stoichiometric, fuel lean, or fuel rich
 
m a , st
ma
•

m a / m F st
m a / m F mix
Φ < 1 Fuel lean mixture, complete combustion

AFR st
Φ = 1 Fuel lean mixture, complete combustion
AFR mix
Φ > 1 Fuel rich mixture, CO and unburnts
The mixture fraction:
The mixture fraction is an extremely useful variable in combustion, in particular for
diffusion flames. Here we present it first for a homogeneous system. In a two-feed
system, where a fuel stream (1) with is mixed with an oxidizer stream (2), the mixture
fraction represents the mass fraction of the fuel stream in the mixture:
Z 
m1
m1  m 2
Combustion Theory
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•
First Law Analysis for reacting systems
 Closed system: exchange only energy with surrounding
Q  W   E   M  e 
Q is the heat supplied to the system, Q>0 if heat is added from the surroundings.
W is the mechanical work, W>0 if the system does work on the surroundings
e 
total
u
 1/ 
2w
 
internal
gz

kinetic
potential
2
u  1 / 2 w , gz
2
W
Q
Q  W  U
For a constant pressure system, the mechanical work is: W  p  V
Q  U  pV  H
Consider a process in which nF moles of fuel react with na moles of air to produce nP moles
of product:
Q  HP  HR 
 n h (T
i
P
Combustion Theory
i
p
)   n i h i (T R )
R
HP  HR

H  0
Exothermic reaction
HP  HR

H  0
Endothermic reaction
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 Open (steady) systems: exchange mass and energy with
surrounding
Q W 
 m
out
e out   m in e in
out
e flow 

total
in

u
internal
 1/ 
2w
 
gz

kinetic
potential
2
pv

flow work
(pressure)

h
 1/ 
2w
 
enthalpy
gz

kinetic
potential
2

h  1 / 2 w , gz
2
Q W 
 m
out
hout   m in hin
out
 m
out
hout 
out
 m
out
in
 m
Q , W
in
hin
Exothermic reaction
in
hin
Endothermic reaction
in
out
hout 
 m
in
Combustion Theory
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• Enthalpy of combustion:
Absolute enthalpy is the sum of two contributions: formation enthalpy (associated to
chemical bonds) and sensible enthalpy (associated only to temperature)
hi T 

 f H i T ref 
 

Absolute enthalphy
at tempera ture T
Standard enthalpy of formation
 h s , i T 




0
0
(T ref , P )
Sensible enthalpy change
Standard enthalpy of formation is the change of enthalpy that accompanies the
formation of 1 mole of a substance in its standard state from its constituent elements in
their standard states.
The standard enthalpy of formation is used in thermo-chemistry to find the standard
enthalpy of reaction. This is done by subtracting the sum of the standard enthalpies of
formation of the reactants from the sum of the standard enthalpies of formation of the
products:
cH F 
0

HP  fHR
0
f
P
0
R
Convention: Enthalpies of formation are zero for elements in their naturally occurring
state, at reference state temperature and pressure.
Combustion Theory
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Example: Evaluate the enthalpy of combustion of methane and
hydrogen fuels
The complete combustion of methane can be expressed as:
CH 4 ( g )  2 O 2 ( g )  CO 2 ( g )  2 H 2 O ( g )
The enthalpy of combustion of 1 mole of methane can be derived from reaction
stochiometry:
 c H CH 4   f H CO 2 ( g )  2  f H H 2 O ( g )   f H CH 4 ( g )  2  f H O 2 ( g )
0
0
0
0
 c H CH 4 ( 298 K )  - 802 kJ/mol
The complete combustion of hydrogen can be expressed as:
H2 
1
2
O 2  H 2O
The enthalpy of combustion of 1 mole of hydrogen can be derived from reaction
stochiometry:
cH H2   f H
0
H 2O ( g )
0
0
  f H H 2 ( g )  0 .5  f H O 2 ( g )
 c H H 2 ( 298 K )  - 242 kJ/mol
Combustion Theory
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Thermodymanics properties of selected substances
0
0
N. Specie Mw,i (kg/kmol)  f H i (kJ/mol) N. Specie Mw,i (kg/kmol)  f H i (kJ/mol)
1
H
2 HNO
3
OH
4
HO2
5
H2
6
H2O
7 H2O2
8
N
9
NO
10 NO2
11
N2
12 N2O
13
O
14
O2
15
O3
16 NH
17 NH2
18 NH3
19 N2H2
20 N2H3
21 N2H4
22
C
23
CH
24 HCN
25 HCNO
26 HCO
27 CH2
28 CH2O
29 CH3
Combustion Theory
1.008
31.016
17.008
33.008
2.016
18.016
34.016
14.008
30.008
46.008
28.016
44.016
16.000
32.000
48.000
15.016
16.024
17.032
30.032
31.040
32.048
12.011
13.019
27.027
43.027
29.019
14.027
30.027
15.035
217.986
99.579
39.463
20.920
0.000
-241.826
-136.105
472.645
90.290
33.095
0.000
82.048
249.194
0.000
142.674
331.372
168.615
-46.191
212.965
153.971
95.186
715.003
594.128
130.540
-116.733
-12.133
385.220
-115.896
145.686
15/tot
30 CH2OH
31
CH4
32 CH3OH
33
CO
34
CO2
35
CN
36
C2
37
C2H
38 C2H2
39 C2H3
40 CH3CO
41 C2H4
42 CH3COH
43 C2H5
44 C2H6
45 C3H8
46 C4H2
47 C4H3
48 C4H8
49 C4H10
50 C5H10
51 C5H12
52 C6H12
53 C6H14
54 C7H14
55 C7H16
56 C8H16
57 C8H18
58 C(solido)
31.035
16.043
32.043
28.011
44.011
26.019
24.022
25.030
26.038
27.046
43.046
28.054
44.054
29.062
30.070
44.097
50.060
51.068
56.108
58.124
70.135
72.151
84.152
86.178
98.189
100.205
112.216
114.232
12.011
-58.576
-74.873
-200.581
-110.529
-393.522
456.056
832.616
476.976
226.731
279.910
-25.104
52.283
-165.979
110.299
-84.667
-103.847
465.679
455.847
16.903
-134.516
-35.941
-160.247
-59.622
-185.560
-72.132
-197.652
-135.821
-223.676
0.000
• Adiabatic flame temperature:
Consider a constant pressure adiabatic
system in which combustion takes place.
Combustion process can be represented by
the general equation:
N

i 1
i e i
'
N
'
i
  i     i
''
i
i 1
''
are the stochiometric coefficients of Mi
The first law, for both closed and opens systems, reduces to:
hu  hb
the subscripts u and b refer to burn and unburnt mixture, respectively.
N
Y
N
i ,u
i 1
h i ,u 
Y
i ,b
h i ,b
i 1
With the temperature dependence of specific enthalpy, this may be written as:
N
N
 Y
 Y i , b   f H i T ref  
0
i ,u
i 1
Tb
Tu
 c p ,b  dT 
 c p ,u  dT
T ref
T ref
c p ,b 
where
c pi ( T )
i ,u
c pi ( T )
N
Y
i 1
16/tot
i ,b
i 1
c p ,u 
Combustion Theory
Y
For a one-step global reaction (Yi,u-Yi,b) may be calculated as:
Y i ,u  Y i ,b  Y F ,u  Y F ,b 
 i M W ,i
 F M W ,F
where νi and νF are the net stochiometric coefficients, defined as:
 i   i  i
''
 i   i  i
'
''
'
Assuming cp constant and Tu=Tref we get:
Y
F ,u
 Y F ,b 
 F M W ,F

Y
F ,u
N
   i M W ,i   f H i T ref
0
i 1
 Y F ,b 
 F  M W ,F
Tb
 c
Tu
p ,b
 dT 
T ref
  c H F  c p , b Tb  T ref

c
p ,u
 dT
T ref
N
where
 c H F     i M W , i   f H i T ref
0

i 1
The adiabatic flame temperature for a lean (Φ<1) and stochiometric (Φ=1) mixture,
i.e. complete combustion of the fuel, is:
T b  T ref 
Y F ,u   c H
  M W , F  c p ,b
'
F
Combustion Theory
being
'
 F   F and Y F , b  0
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Adiabatic flame temperatures for lean methane, acetylene and propane flames
as a function of the equivalence ratio for Tu = 300 K
Combustion Theory
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The adiabatic flame temperature for a rich (Φ>1) mixture, i.e. incomplete
combustion of the fuel, is:
T b  T ref 
Y O 2 ,u   c H

'
O2
 M W ,O 2  c p , b
being  O   O' and Y O
2
2
2
,b
0
Adiabatic flame temperatures for rich flames
as a function of the equivalence ratio for Tu = 300 K
Combustion Theory
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• Chemical equilibrium
i.
From the standpoint of thermodynamics, the assumption of complete
combustion is incorrect because it disregards the possibility of dissociation of
major species (CO, CO2, H2O, N2, O2) into minor species, i.e. radicals, such as H,
N, O, OH, NO. In that context complete combustion represents the limit of an
infinite equilibrium constant
ii.
A more general formulation is the assumption of chemical equilibrium. Both
approximations, chemical equilibrium and complete combustion, are valid in the
limit of infinitely fast reaction rates only. In most combustion cases, however,
chemical reactions occur on time scales comparable with that of the flow and the
molecular transport processes. Only for hydrogen diffusion flames complete
chemical equilibrium is a good approximation, while for hydrocarbon diffusion
flames finite kinetic rates are needed.
iii. Nevertheless, since the equilibrium assumption represents an exact
thermodynamic limit, it shall be considered here.
Combustion Theory
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 The chemical potential and the law of mass action
The partial molar entropy of a chemical species in a mixture of ideal gases depends on the
partial pressure:
s i  s  R ln
0
i
T
Pi
where
P0
P0  1 atm
s s
0
i
and
0
i , ref


T ref
c p ,i
dT
T
The partial molar entropy may now be used to define the chemical potential:
 i  hi  T s i  hi , ref  T s i , ref 
0

T
T ref
T
c p ,i
T ref
T
c p , i dT  T 
dT  RT ln
The condition for chemical equilibrium is given by:

i
i  0
   i  i  RT ln
0
i
i

i
 pi 


 p 
 0
i
Defining the equilibrium constant by:
RT ln K P     i  i
0
i
We obtain the Law of Mass Action
 p
K P T     i
Combustion Theory
i  p0




i
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pi
p0
  i  RT ln
0
pi
p0
 Calculation of full equilibrium products of combustion
Two approaches:
i.
Assuming no dissociation: i.e. ignoring
the presence of minor species in
combustion products.
ii.
Adiabatic flame temperature e
composition of combustion products can
be obtained by solving (1) first law of
thermodynamics, (2) chemical equilibrium
criteria and (3) element-conservation
simultaneously.
 F C n H m   O ( O 2  3 . 76 N 2 )   CO CO 2   H O H 2 O   N N 2   O O 2   CO CO   H H 2
'
'
''
2
''
2
''
2
''
2
''
2
2
  H H   O O   OH OH   NO NO   N N  
''
''
''
''
Computer programmes can be used for these calculations:
http://www.wiley.com/college/mechs/ferguson356174/wave_s.html
Combustion Theory
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''
''
Adiabatic flame temperature, major and minor species distributions
for constant pressure propane combustion with air
Constant pressure combustion of propane, C3H8, with air, assuming that the products are
CO2, CO, H2O, H2, H, OH, O2, O, NO, N2, and N:
Combustion Theory
23/tot
 Full equilibrium calculation example 3:
Constant pressure combustion of methane, CH4, with air. Equilibrium composition of CO
and CO2 in the products’ mixture as a function of the equivalence ratio.
Combustion Theory
24/tot
3. Chemical Kinetics:
i.
First and Second Laws of thermodynamics are used to predict the final
equilibrium state of the products after the reaction is complete
ii.
Thermodynamics describe the system locally if one assumes that chemical
reactions are fast compared to other transport processes
iii. Nevertheless, information is needed about the rate of chemical reactions.
Chemical reaction rates control pollutant formation, ignition, and flame
extinction in most combustion processes.
• Global reaction mechanisms: “Black-box” approach
Global reaction mechanisms describe the initial and final state of a combustion system
kG
d F 
dt
F  aOx  b Pr
 k G T    F   Ox 
x
 E 
k G T   A exp   a 
 RT 
Combustion Theory
y
•
[ ] denotes molar concentration
•
k(T) is the global rate constant expressed in the
Arrhenius form
•
x and y are the reaction order with respect with the fuel
and oxidizer, respectively. (x+y) is the overall order.
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 Example: The overall oxidation reaction of a hydrocarbon fuel is:
CnH m
kG
m
m

 n 
O

nCO

H 2O
 2
2
4 
2

The overall reaction rate is:
d C n H m 
  AT
n
dt
 E 
x
y
exp   a  C n H m  O 2 
 RT 
Rate coefficients for global hydrocarbon oxidation (units: kcal, mol, cm, s)
Hydrocarbon
A
Ea
x
y
Hydrocarbon
A
Ea
x
y
CH4
1.3E+08
48.4
-0.3
1.3
C8H18
7.2E+12
40
0.25
1.5
CH4
8.3E+05
30
-0.3
1.3
C9H20
4.2E+11
30
0.25
1.5
C2H6
1.1E+12
30
0.1
1.65
C10H22
3.8E+11
30
0.25
1.5
C3H8
8.6E+11
30
0.1
1.65
CH3OH
3.2E+12
30
0.25
1.5
C4H10
7.4E+11
30
0.15
1.6
C2H5OH
1.5E+12
30
0.15
1.6
C5H12
6.4E+11
30
0.25
1.5
C6H6
2.0E+11
30
-0.1
1.85
C6H14
5.7E+11
30
0.25
1.5
C7H8
1.6E+11
30
-0.1
1.85
C7H16
5.1E+11
30
0.25
1.5
C2H4
2.0E+12
30
0.1
1.65
C8H18
4.6E+11
30
0.25
1.5
C2H2
6.5E+12
30
0.5
1.25
Combustion Theory
26/tot
• Elementary reactions
i.
Use of global reactions to express chemistry does not provide a basis for
understanding what is actually happening. For example, the overall reaction
equation for hydrogen combustion:
2 H 2  O 2  2 H 2O
implies that two moles of hydrogen molecule react with one mole of oxygen to
form one mole of water. This is unrealistic to believe since it would require
breaking several bonds and subsequently forming many new bonds.
ii.
In reality the global reaction proceeds through elementary reactions in a chain
process that involve several intermediate species
iii. Hydrogen oxidation proceeds via elementary reactions, collectively known as a
reaction mechanism:
Combustion Theory
27/tot
• Hydrogen-oxygen reaction mechanism
Rate constants for H2 oxidation detailed mechanism (units: kJ, mol, cm, s)
N
Reaction
A
n
Ea
N
1.1 H2/O2 Chain Initiation
0f
H2+M’→H+H+M’
4.580E+19
Reaction
A
n
Ea
1.2 HO2 Formation and Consumption
-1.40
436.73
1.1 H2/O2 Chain Reactions
7
HO2+H→H2+O2
2.500E+13
0.00
2.90
8
HO2+OH→H2O+O2
6.000E+13
0.00
0.00
1f
O2+H→OH+O
2.000E+14
0.00
70.30
9
HO2+H→H2O+O
3.000E+13
0.00
7.20
1b
OH+O→O2+H
1.568E+13
0.00
3.52
10
HO2+O→OH+O2
1.800E+13
0.00
-1.70
2f
H2+O→OH+H
5.060E+04
2.67
26.30
2b
OH+H→H2+O
2.222E+04
2.67
18.29
11
HO2+HO2→H2O2+O2
2.500E+11
0.00
-5.20
3f
H2+OH→H2O+H
1.000E+08
1.60
13.80
12f
OH+OH+M’→H2O2+M’
3.250E+22
-2.00
0.00
3b
H2O+H→H2+OH
4.312E+08
1.60
76.46
12b
H2O2+M’→OH+OH+M’
1.692E+24
-2.00
202.29
4f
OH+OH→H2O+O
1.500E+09
1.14
0.42
13
H2O2+H→H2O+OH
1.000E+13
0.00
15.00
4b
H2O+O→OH+OH
1.473E+10
1.14
71.09
14f
H2O2+H→H2+HO2
1.700E+12
0.00
15.70
14b
H2+HO2→H2O2+H
1.150E+12
0.00
80.88
1.2 HO2 Formation and Consumption
1.3 H2O2 Formation and Consumption
5f
O2+H+M’→HO2+M’
2.300E+18
-0.80
0.00
5b
HO2+M’→O2+H+M’
3.190E+18
-0.80
195.39
15
H+H+M’→H2+M’
1.800E+18
-1.00
0.00
6
HO2+H→OH+OH
1.500E+14
0.00
4.20
16
OH+H+M’→H2O+M’
2.200E+22
-2.00
0.00
17
O+O+M’→O2+M’
2.900E+17
-1.00
0.00
Combustion Theory
28/tot
1.4 H2/O2 Recombination Reactions
 Example: Simplified reaction mechanism for hydrogen oxidation
derived from the detailed reaction scheme
k0, f
H2  M  H  H  M
Chain initiation
•
•
k1 , f
H  O 2  OH  O
k2, f
Chain branching
reactive and short lived.
•
OH  H 2  H 2 O  H
Radicals have unpaired valence
electrons which make them very
H 2  O  OH  H
k3, f
Species such as H, O, OH and HO2
Chain branching reactions lead to a
net production of radicals which
Chain propagation
causes reaction to proceed extremely
fast, i.e. chemical explosion.
k1 5
H  H  M  H2  M
k1 6
Chain termination
•
The reaction comes to completion
through chain termination reactions:
H  OH  M  H 2 O  M
the radicals recombine to form the
M is any species which acts as collision
partner
Combustion Theory
29/tot
final products.
Stochiometric H2-O2 mixture explosion limits
1st explosion limit: At low pressures molecular mean free
path is long enough for O, H, OH radicals to reach and be
3000
destroyed at walls before reacting with other species, resulting
in the quenching of the chain propagating reactions. As the
pressure increases: molecular mean free path decreases and O,
H, OH radicals begin to react with other species. At some
pressure (~1.5mmHg for 500°C), chain-propagating reactions
prevail over wall destruction and the mixture can explode.
2nd explosion limit: As pressure is increased past the 1st
explosion
50
limit, reaction (5f) begins to compete with (1f) for H atoms.
HO2 radical is relatively inert and can reach and be destroyed
at walls. At some pressure (~50mmHg for 500°C), reaction
(5f) prevails over reaction (1f), and terminates the explosion
process.
3rd explosion limit: At higher pressure (~3000mmHg for
1.5
500°C), the mean free path becomes short enough for HO2
radicals to react with other species, i.e. reactions (6)-(10).
Combustion Theory
30/tot
•
How to express net production rate of each species in a complex system
The compact notation for a system of elementary reactions is:
N
N

'
ik
i 1
  i    ik   i
k  1, 2 ,..., m
''
i 1
•
ν’ik: stochiometric coefficients of reactant i in k-th elementary reaction.
•
ν’ik: stochiometric coefficients of product i in k-th elementary reaction.
•
Mi: Chemical species i
•
m: total number of elementary reactions
•
N: total number of species.
The net production rate of each species in a multi-step mechanism is:
i 
d M i 
dt
wi  W i
kf
k
m

 
'
i ,k

''
i ,k
k 1
d M i 
dt
m

 Wi  
k 1
'
i ,k

k f



N
M i 
k
''
i ,k
ik
'
i 1

k f



N
 k r k  M i 
ik
''
i 1
ik



Mole basis
'
N
k

i 1
  Yi

 W
 i




ik
''
N
 kr k 
i 1
  Yi

 W
 i





 Mass basis


and k r k are the forward and backward elementary reaction rate constants
Combustion Theory
31/tot
• Carbon monoxide (CO) oxidation mechanism
i.
Oxidation of CO is very important in hydrocarbon combustion. From a very
simplistic point-of-view, hydrocarbon combustion can be characterized as a twostep process:
ii.
•
breakdown of fuel to CO
•
oxidation of CO to CO2
CO oxidation is extremely slow in the absence of small amounts of H2 and H2O
If H2O is the primary hydrogen-containing species, CO oxidation can be
described by:
CO  O 2  CO 2  O
O  H 2 O  OH  OH
O 2  H  OH  O
CO  OH   CO 2  H
Combustion Theory
Chain initiation
Chain branching
Chain propagation
32/tot
Key step in CO oxidation
i.
In presence of H2 the following step are included:
O  H 2  OH  H
OH  H 2  H 2 O  H
CO  HO 2  CO 2  OH

IMPORTANT: In presence of H2, the entire H2-O2 kinetic
mechanism should be taken into account to describe CO oxidation
Combustion Theory
33/tot
• Alkanes oxidation mechanism
Steps:
i.
Fuel is attacked by O and H; breaks down to H2 and olefins (double-bonded
straight hydrocarbons). H2 is oxidized to H2O.
ii.
Unsaturated olefins form CO and H2. Almost all H2 is converted to water.
iii. CO burns to CO2 releasing almost all of the heat associated with combustion

1.
Example: Propane (C3H8) oxidation mechanism
A C-C bond is broken in the original fuel molecule
C 3 H 8 M  C 2 H 5  CH 3  M
2.
Two resulting hydrocarbon radicals break down further to olefins
C 2 H 5 M  C 2 H 4  H  M
CH 3  M  CH
3.
2
H M
H atoms from Step 2 starts a radical pool
H  O 2  OH  O
Combustion Theory
34/tot
4. With the development of a radical pool, attack on the fuel molecule intensifies
C3H 8  H  C3H 7  H 2
C 3 H 8  O  C 3 H 7  OH
C 3 H 8  OH  C 3 H 7  H 2 O
5. Hydrocarbon radicals decay to olefins and H atoms
C 3 H 7 C 2 H 4  CH
3
C 3 H 7 C 3 H 6  H
6. Oxidation of olefins created in steps 2 and 5 with production of formyl radicals
(HCO) and formaldehyde (H2CO)
C 3 H 6 O  C 2 H 5  HCO
C 3 H 6  O  C 2 H 4  H 2 CO
7. Methyl radicals (CH3), formaldeydhe (H2CO), and methylene (CH2) oxidize
8. Carbon monoxide oxidizes
35/tot
Combustion Theory
• Methane oxidation mechanism
i.
Methane displays some unique characteristics not common with higher alkanes
ii.
The detailed reaction mechanism is actually very complex. GRI-Mech 3.0
(http://www.me.berkeley.edu/gri-mech/releases.html) consists of 325
elementary chemical reactions involving 53 species
iii. Methane is attacked by H, O, OH radicals and chain initiation occurs
CH
4
 H  CH 3  H 2
CH
4
 O  CH 3  OH
CH
4
 OH  CH 3  H 2 O
iv. Lean mixtures (Φ<1): CH3 is oxidized to radicals, H2O, H2, and CO which burns
slowly to CO2.
v.
Rich mixtures (Φ>1): two CH3 radicals combine to start a reaction path which
leads two ethylene, acetylene and C3 compounds.
Combustion Theory
36/tot
 Example 1: Methane oxidation reaction path
Combustion Theory
37/tot
Combustion Theory
38
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