4.
Combustion mechanism of fuel gases
4.1
Reaction sequence
4.1.1 Reaction mechanism
Reactions like
CH 4 + 2O 2 → CO 2 + 2H 2 O
(4-1)
CO + 1 2 O 2 → CO 2
(4-2)
or
do not actually take place. These equations are the summarizing result of a number of
individual reactions. Consequently, they are called gross reaction equations. Actual reactions
(elementary reactions) proceed in the molecular range like for example the bimolecular
reactions.
H + O 2 → O + OH
(4-3)
CO + OH → CO 2 + H
(4-4)
and the unimolecular reaction
O2 → O + O .
(4-5)
The conversion is mainly effected by the radicals O, H and OH under formation of
intermediate products. Radicals are radiating in the short-wave visible range (ultraviolet
range). Therefore, the gas flames emit a bluish light. This effect is called luminescence.
The combustion of methane is the sum of some 400 elementary reactions. The kinetics of the
individual reactions must be known for exact description of the overall reaction mechanism.
The conversion speed of an elementary reaction is proportional to the product of molar
density concentrations of starting materials. For unimolecular reactions like (4-5) the
following shall apply:
d~
ρO2
1 d~
ρ
= − ⋅ O = −k ⋅ ~
ρO2
dt
2 dt
(4-6)
and correspondingly to a bimolecular reaction like equation (4-3)
~
d~
ρ H dρO 2
d~
ρ
d~
ρ
k
=
= − O = − OH = − ~ ⋅ ~
ρH ⋅ ~
ρO2 .
dt
dt
dt
dt
ρ
(4-7)
~⋅~
In case of time-constant overall density the following equation is obtained with ~
ρi = ρ
xi
~
d~
x H dx O 2
d~
x
d~
x
=
= − O = − OH = −~
ρ⋅ k ⋅~
xH ⋅ ~
xO2 .
dt
dt
dt
dt
(4-8)
The corresponding reverse reaction is
d~
xH ~ s ~ ~
= ρ ⋅ k ⋅ x O ⋅ x OH .
dt
(4-9)
The formation and disintegration rates are the same in the state of equilibrium. The
correlation of both reaction coefficients can be derived therefrom as follows:
s
k = k⋅K
(4-10)
with K = the equilibrium number according to paragraph 2.2.2.
The temperature dependence of the reaction coefficient is described by the Arrhenius
approach
E 

k = k 0 ⋅ exp −
.
 R ⋅T
(4-11)
The pre-exponential coefficient is slightly temperature-dependent in many cases which may
be approximately determined by
E 

k = k *0 ⋅ T n ⋅ exp −
.
 R ⋅T
(4-12)
The activation energy E corresponds to the energy threshold to be overcome for the reaction.
It reaches the value of bonding energies as maximum e.g. in case of dissociation reactions
but may even adopt very small values down to zero if new bonds are established
simultaneously with bond breaking.
The exponential term approaches 1 in case of extremely high temperatures so that the preexponential coefficient gives the maximum value of reaction coefficient. The latter has
different physical meanings in relation to unimolecular and bimolecular reactions. In case of
the unimolecular reaction the reciprocal value of k0 represents the mean life of the molecule.
The latter is determined by the oscillation frequency of atoms which participate in the
molecular compound. Application of the statistical thermodynamics results in k0 ≈ 1014 - 1015
· s-1. In case of bimolecular reactions the pre-exponential factor corresponds to a collision
number. In case of very high temperatures the reaction speed is limited by the time-wise
number of collisions between two molecules. Values amounting to k0 ≈ 1010 − 1011 m3 ·
kmol-1 · s-1 can be derived from the kinetic theory of gases. The activation energies and the
pre-exponential coefficient are given for a great number of elementary reactions in the
publication of Warnatz et al. 1996.
The reaction mechanism resulting from the calculation of the conversion kinetics of all
elementary reactions is shown as example for a premixed methane-air flame in Fig. 4-1. This
mechanism is shown in a simplified diagram in Fig. 4-2. As a result of this, one hydrogen
atom will be successively split off from the hydrocarbons and further transformed into water
steam. If only one or two hydrogen atoms are left, one oxygen atom is attached. Carbon
monoxide is formed by further splitting-off of hydrogen which is finally oxidized to carbon
dioxide.
The lowest reaction speeds are decisive for the overall combustion speed. Fig. 4-3 shows the
result of a sensitivity analysis of reaction speeds in a premixed methane-air flame according
to Nowak et al. 1988. Consequently, the reactions H + O2 → OH + O and
CO + OH → CO2 + H show the smallest speeds. These reactions are fuel-independent and
are applicable both to the combustion of oil vapours and the volatile matters of carbons.
Therefore, the OH concentration is preferentially measured for determination of shape and
burn-off of flames.
The number of reactions to be considered for the practical flame calculations is dependent on
the problem to be solved and the accuracy. The local distribution of radicals and temperature
and, consequently, the local heat release is of great importance for the calculation of NOx
emissions. In this case 20 to 40 of the slowest reactions must be considered (Görner 1991).
The mere conversion of fuel however may be approached with a much smaller number of
reactions especially in case of non-premixed flames where the conversion rate is mainly
determined by the degree of mixing. In the most simple case the reaction speed of fuel
components B may be approached by statements according to the gross reaction equations
d~
xB
a
~ ⋅ k ⋅ exp − E  ⋅ ~
= −ρ
x Ob 2 ,

 xB ⋅ ~
0
dt
 R ⋅T 
(4-13)
where the exponents of concentrations differ from 1. Table 4-1 gives such reaction equations
for a number of essential fuel components. The oxidation of carbon monoxide is largely
dependent on the water steam concentration in the air which must be considered through an
extra term. Therefore, a dry CO and O2 mixture is difficult to ignite since the OH radicals are
missing. The given equation is no longer applicable in case of water steam concentrations of
more than some 10 % since the conversion speed is now independent of this concentration.
Fig. 4-4 shows the measured values of the reaction coefficient of the CO oxidation as an
example. This makes evident that the values ascertained by different authors are extremely
differing from each other in some cases. Therefore, literature gives drastically differing
values for the reaction coefficients and the exponents of concentration.
Oxidation of higher hydrocarbons may be defined by a three-stage reaction sequence in the
most simple case, i.e. the disintegration into CO and H2 in the first stage and the subsequent
oxidation into CO2 and H2O in the second and/or third stage (Görner 1991).
Finally it should be underlined once more that the conversion of fuel is effected by the
radicals. However, NOx emission is a secondary effect. Analogous to that, in human life the
reaction progress of established groups is only possible by means of radicals. Too much of
them, however, will have a detrimental effect.
4.1.2 Ignition
Ignition mechanism
The radicals OH, H and O are required for initiation of the reaction of a fuel with oxygen.
These radicals are initially generated by dissociation of hydrogen and oxygen according to
H2O → ΟΗ + Η
(4-14)
or
O2
→ O + O.
(4-15)
The equilibrium of these reactions is shown in Fig. 2-6. Consequently, H2O gets dissociated
at lower temperatures than O2. Therefore the air humidity has a decisive effect on the
generation of radicals. For instance, ignition of carbon monoxide in dry air takes place at
much higher temperatures than in humid air.
Therefore, for the generation of radicals it is sufficient to heat a small but sufficient gas
volume to a high temperature. The energy balance is applicable to the unsteady heating of a
gas volume as follows:
ρ ⋅ V ⋅ cp ⋅
dT &
& .
= QR − Q
α
dt
(4-16)
·
·
In this equation, QR is the heat flow generated by the reaction, and Qα is the heat flow
eliminated by convection and radiation. The following applies to both heat flows:
& =M
& ⋅ ∆h
Q
R
B
R
(4-17)
·
(MB = fuel mass flow, ∆hR = reaction enthalpy) with the reaction approach according to
equation (4-13):
2
& = ρ ⋅ V ⋅ dx B = ρ ~⋅ V ⋅ k ⋅ exp − E  ⋅ ~
M
x aB ⋅ ~
x Ob 2
B
0
dt
M
 R ⋅T 
(4-18)
and for pure convective heat dissipation:
& = α ⋅ A ⋅ (T − T )
Q
α
u
(4-19)
(TU = ambient temperature). The principle course of both heat flows as a function of
temperature is shown in Fig. 4-5. The heat flow caused by reaction has an S-shaped course in
compliance with the Arrhenius approach whereas the flow of lost heat shows a linear
·
progress. Let us initially consider the progress of QR1 for a large heat production. In case of
temperatures T < TZ the heat extraction is higher than the heat production. Ignition and
combustion are not possible. In case of T = TZ the equilibrium is established between heat
production and heat extraction. However, this equilibrium is unstable. If temperature lowers
slightly the loss of heat will exceeds the production of heat, i.e. the gas cools down and the
reaction is interrupted. In case of a slight temperature rise, however, the conversion speed
drastically increases and the gas is heated until a new equilibrium is established at the
combustion temperature TV. The temperature TZ as the initial point of automatic gas heating
forms the ignition temperature.
Ignition temperature and ignition limits
Lean gases have a low conversion rate due to their low concentration of inflammable
constituents according to equation (4-18) and, hence, a low heat production, as shown in Fig.
·
4-5 where the principle of the course of QR2 is demonstrated. Therefore, a higher ignition
temperature and a higher ignition energy would be required in this case. Consequently, they
have a bad ignition effect.
If fuel or oxygen take only a low concentration in a mixture, the conversion speed is very low
according to equation (4-18) again. Heat production can no longer exceed the heat dissipation
if the temperature falls below the so-called ignition limit, as it can be seen from the course of
·
QR3 in Fig. 4-5. The ignition limits are dependent on the kind of fuel, temperature, fuel and
oxygen concentration and a little dependent on the pressure. Fig. 4-6 shows the reference
values of ignition limits for natural gas.
4.2
Premixed flames
If fuel gas and air are mixed together prior to ignition, the burner and its associated flame are
called premixing burner and premixed flame. Examples are burners for short flames and
intensive combustion like ignition burners and overhead burners in industrial kilns, spark
ignition engines and gas turbines.
4.2.1 Flame length
Fig. 4-7 is a photograph of a turbulent premixed flame from a tubular burner, i.e. a long- time
photo and a short-time streak photo where the turbulent structures are clearly visible. Fig. 4-8
is the schematic view of the premixed flame. The typical flame shape is that of a cone. The
reaction front propagates in its surroundings with the speed vF. The_ so-called flame speed
may be determined by experiment through the mean outlet speed u of the burner and the
angle β of the cone
v F = u ⋅ sinβ .
(4-20)
The length of the flame may be approximately determined on the basis of the geometric
relation
LF =
d0 1
⋅
.
2 tanβ
(4-21)
The relation sinβ ≈ tanβ is applicable to small angles. Consequently, the following may be
derived from both equations above:
LF =
d0 u
.
⋅
2 vF
(4-22)
If the outlet speed is replaced by the volumetric flow
& = π ⋅d2 ⋅ u
V
0
0
4
(4-23)
the following will be finally obtained for the flame length:
LF =
& 1
2 V
⋅ 0⋅
.
π d0 vF
(4-24)
Consequently, the flame length is proportional to the emerging volumetric flow. The flame
gets longer if the burner diameter is made smaller. Flame length is furthermore dependent on
the flame speed to be explained in detail later. A difference is made between the laminar and
the turbulent flow.
4.2.2 Flame speed
Flame speed may be interpreted as the distance δFl to be passed by the flame front within the
time τ
vF ≈
δF
τ
(4-25)
The propagation of temperature front in a substance corresponds to the dimension-less style
of Fourier's differential equation
δF ≈ a G ⋅ τ ,
(4-26)
where a = λ /(ρ · cp) is the thermal diffusity of the gas. The following may be derived from
both equations for the flame thickness
δF ≈
aG
λG
=
.
vF ρ ⋅ cp ⋅ vF
(4-27)
Under conditions of ambient pressure the width δF of the flame front amounts to only a few
tenths of a millimetre. According to the equation stated above the flame width increases as a
function of declining density and declining pressure. Therefore, measurements of
concentration and temperature profiles in pre-mixture flames must be made under conditions
of negative pressure. Such measurements have been described in literature, for instance by
Braun in 1998.
Time is inversely proportional to the conversion speed of fuel
τ≈
1
.
~
d x B dt
(4-28)
Accordingly, equation (4-13) is applicable to the conversion speed
τ≈
1
.
k ⋅ ρG ⋅ x aB ⋅ x Ob 2
(4-29)
Consequently, the following is applicable to the flame speed:
vF ≈
λG
⋅ k ⋅ x aB ⋅ x Ob 2 .
cp
(4-30)
There with the flame speed is dependent through λ, cp and k on the kind of fuel, through k on
the temperature and through Π ∼
x on the product and, consequently, on the level of the
i
individual concentrations.
Fig. 4-9 shows the laminar flame speed for some hydrocarbons as a function of the fuel
concentrations. Consequently, the flame speed in close vicinity to the stoichiometric fuel-air
composition on the low-air side (unctuous mixture) reaches its maximum value. In case of
methane this values is about 45 cm/s. Table 4-2 summarizes the maximum and the
stoichiometric value of the laminar flame speed for three typical fuel gases. Hydrogen shows
the highest value. The value of carbon monoxide, however, is much lower and reaches only
some 50% of the value for methane.
Fig. 4-10 shows the influence of the O2 concentration on the flame speed by taking the
example of hexane as fuel (Chomiak 1990). Fig. 4-11 makes clear that the flame speed
increases as a function of air preheating and, consequently, the flame temperature (Chomiak
1990).
In case of turbulent flow no smooth cone shape will be produced. As shown in Fig. 4-7 the
formation of a rough cone surface takes place. As example, Warnatz et al. 1996 made visible
the OH concentration measured on the surface, i.e. on the reaction front. It is apparent that
the surface consists of a great number of small laminar flames. The co-called Flamelet model
serves as the basis for the mathematical description of such flames. The turbulent flame is
considered as an ensemble of many small laminar flames in a turbulent flow field.
The turbulent flame shape is shown in the schematic view in Fig. 4-12. The actual surface
with the laminar flames should be Alam whereas the mean surface should be Aturb. The latter
spreads with the turbulent flame speed vF turb. Consequently, the following relation may be
established:
v F lam ⋅ A lam = v F turb ⋅ A turb .
(4-31)
If the turbulent speed is replaced according to
v F turb = v F lam + v′
(4-32)
by the turbulent fluctuation speed v´, the following surface ratio will be established:
A lam
v′
= 1+
.
(4-33)
A turb
v F lam
Accordingly the turbulent flame speed is higher than the laminar flame speed:
v F turb
v′
= 1+
.
v F lam
v F lam
(4-34)
Fig. 4-13 shows the turbulent flame speed as a function of the fluctuation speed for a C3H8air mixture. Proceeding from the laminar value, the flame speed is initially subjected to a
strong increase as a function of the fluctuation speed and, consequently, the turbulence. After
that, flame speed passes a maximum that will be the higher the lower the air ratio will be. For
instance, if the air ratio is 1.1, the maximum turbulent flame speed will exceed the laminar
value by the factor 10. After that, the turbulent flame speed will decline again as a function
of turbulence until the turbulence finally will get so large again that the flame goes out.
The concentration gradients and, thus, the diffusion speed will increase as a function of rising
turbulence. Finally the kinematics of chemical conversion will be no longer rapid enough.
The reactive species are excessively thinned. Thus reaction heat will rapidly decline and the
local temperature will drop accordingly. Since reaction speed is exponentially dependent on
the temperature, the latter will decelerate drastically so that the flame goes out. Time required
for flame extinguishing is only in the range of 0.1 ms (Warnatz et al. 1996).
Extinguishing is described with the so-called stretching effect determined by the tangential
speed and concentration gradient (along the flame area). This gradient withdraws radicals
and reactands from the reaction zone in addition to the normal mass transport. This stretching
is described with the so-called Karlowitz number
Ka =
δ F du
⋅
.
v F dz
(4-35)
Extinguishing takes place if the value of this coefficient exceeds a value of about 1.
As shown in Fig. 4-13, mixtures are very easily extinguished at higher air ratios. This is one
of the reasons why engines running on lean fuel have relatively strong hydrocarbon
concentrations although the excessive O2 should rather promote the complete combustion.
Extinguishing takes place rather easily on the cold walls of engines (in contrast to furnaces).
By the way, the turbulent flame speed in engines is approximately proportional to the
rotational speed. Consequently, the combustion process gets accelerated. Otherwise the
combustion in engines would be limited to low speed ranges.
Lean gases (high inert share in the fuel) are extinguished very easily as well. Accordingly
they are difficult to ignite.
Contractions of gas caused by sudden extinguishing are to be considered as the source of
flame noises (together with the geometry-related resonance phenomena) (Warnatz et al.
1996).
4.2.3
Flame stability
If the outlet velocity of the burner exceeds the flame speed, the flame takes off and is thus
blown out. If the outlet velocity is too small, the flame flash back into the burner. Therefore
measures hast to be installed to stabilize the flame.
That a flame burns stably, the flow speed has to be equal to the flame speed in one position,
as is explained on the basis of Fig. 4-14. The flow speed rises from the wall to the centre of
the burner. The flame speed is very small at the rims of burner due to the calorific losses.
Therefore it goes through a maximum, which is in practical cases relatively close to the rims
of the burner. With the distance "2" should be alike the flow and the flame speed. If the front
of the flame induces itself from the rims to the distance "3" away, the flame speed becomes
larger than the flow speed and the flame returns to the distance 2. If the flame shifts to the
distance "1", the flame speed decreases and the flame is blown again to the distance 2. At
this distance thus the flame is stable. If the power of the burner and thus the outlet velocity
are reduced, thus the distance 2 can be shifted into the burner, the flame flashes back.
Against it if the achievement is shifted constantly increased to the point 2 behind the
maximum flame speed, then the flame is finally blown off.
The critical states for flash back and blow off depend with burners on the zone of flow and
on the distribution of the flame speed (Lewis, from Elbe 1987). For each burner a stability
diagram can be therefore provided as is schematically shown in fig. 4-15. The stability of the
flame depends according to fig. 4-15 on the speed gradients at the wall. In the case of a
laminar pipe flow we get for this gradient
du
dr
w
=
8⋅ u
,
d0
(4-35a)
whereby u the mean flow speed and d0 the nozzle diameter are. For a turbulent pipe flow the
empirical relationship applies
du
dr
w
≈ 0,023 ⋅
u
⋅ Re 0,8
d0
(4-35b)
with the Reynolds number
Re =
u ⋅ d0
ν0
.
(4-35c)
In the case of a stoichiometric composition a maximum gradient of approximately 2500 1/s
results according to this picture, before the flame is blown off. With diameters smaller than
10 mm (laminar flow) thus the maximum outlet velocities are in accordance with Eq. (4-3a)
below 3,1 m/s. Also with a large diameter of 100 mm (turbulent flow) one receives only
about 3.5 m/s from Gl. (4-35b) as maximum outlet velocity. With air numbers of one, and in
particular with air numbers more largely than one, with which the value of gradients steeply
drops, premixed burnes can be operated thus only with a relatively small outlet velocity and
thus power. Within the sub-stoichiometric range the critical gradient for the blown off rises
against it strongly. With an excess air number of 0.7 for example the gradient is about 3 time
higher as in the stoichiometric mixture. Premixed burners can be operated thus within the
sub-stoichiometric range with higher outlet velocities. Besides the danger of the flash back of
the flame is shorter in this range. The stability range is with air-poor mixtures thus larger
than with fuel-poor mixtures. For this reason with premixed burners mainly air-poor mixtures
are taken and led to the complete oxidation – later secondary air is added.
The smaller the flame speed is, the more highly is the blown off inclination of the flame.
Natural gas flames bend therefore rather to blown off as for example acetylene and hydrogen
flames. Accordingly the blown off inclination is the larger, the higher the air number is.
For safe ignition and thus stability different measures can be done with premixed burners. A
simple method is the installation of a small ignition flame, which possesses its own fuel
supply. A further method is the attach of pilotpushes into the zone of flow on the jet axle.
Thus an eddy develops with a back flow of hot gas already burned. To the physical
description of the effect is referred to the books of Chomiak 1990 and Guenther 1974.
4.2.4
Extinguish distance
In the proximity of walls the heat dissipation is very high, in particular if these are relatively
cold. If the flame is too close at such a wall, it can come to local extinguishes. The wall
distance, within the flame cannot burn, is called extinguish distance. The variables on the
extinguish distance can be deduced from the following consideration. The enthalpy q
generated in the flame zone has to be conduct within the extinguish distance dq to the wall
q ⋅δF ≈
λG
dq
⋅ (ϑF − ϑw ) .
(4-36)
Here in ϑF and ϑw are the flame and/or wall temperature and λ the heat conductivity of the
gas. The enthalpy has to warm up the gas in the flame zone from the initial or ambient
temperature outside of the extinguish distance to the flame temperature
q ⋅ δ F ≈ v F ⋅ ρ G ⋅ c p ⋅ (ϑF − ϑu ) .
(4-37)
From both equations follows
dq ≈
a G ϑF − ϑw
⋅
v F ϑF − ϑu
(4-38)
with aG as thermal diffusivity of the gas. The extinguish distance is thus the more largely,
the lower the wall temperature and the lower the flame speed is.
In Fig. 4-16 extinguish distances for different methane air mixtures are shown. According to
above equation the extinguish distances is the more largely, the more the mixture from the
stoichiometric composition deviates and the lower thereby the flame speed becomes.
Ignition electrodes has to lie apart at least the double of the extinguish distance, in order to
ensure an ignition. Wire nets with a mesh size, which is smaller than the double extinguish
distance, thus flames cannot pass through. Such nets are used as safeties for flash back.
4.2.5
Minimum ignition energy
In order to be able to ignite the fuel, one needs a minimum ignition energy ∆ H. This one
receives from the following consideration. For ignition a gas volume with the width of the
flame zone has to be warmed up to flame temperature
∆H = A ⋅ δ F ⋅ ρG ⋅ c p ⋅ (ϑF − ϑu ) .
(4-39)
The expansion of the cross-section area A must be larger in each direction than the
extinguish distance
A = d q2 .
(4-40)
With eq. (4-37) for the width of the flame zone arises then
∆H = d q2 ⋅
λG
vF
⋅ (ϑF − ϑu ) .
(4-41)
If one replaces the distinguish distance by eq. (4-38) with ϑw = ϑu , then follows finally
3
∆H =
aG
⋅ ρ G ⋅ c p ⋅ (ϑF − ϑu ) .
v3F
(4-42)
The ignition energy depends thus on the kind of fuel and with the flame speed on the
concentration and thus excess air number. From above equation one receives with the
material properties of air at 1000 °C for example for ϑF = 2000 °C and a flame speed of 1
m/s for the minimum ignition energy ∆ H = 0,03 mJ.
In Fig. 4-17 exemplarily minimum ignition energies are indicated for some fuels. One
recognizes that this possesses the lowest value according to the flame speed during
stoichiometric composition. According to the strong dependence on the flame speed the
minimum ignition energy with the deviation from the stoichiometric composition rises
strongly.
4.2.6 Swirling of flow
The flow and thus the form of a premixed flame can be affected by a Swirling of the mixture
before withdrawal from the burner. For this for example the mixture is led through a disk
with tangential rotated slots. Depending upon degrees of the tangential position the strength
of the swirl can be adjusted. The pattern of flow resulting from swirl is described with Fig.
4-18. In the left field the speed profile without swirl is represented. The mixture flowing out
of the burner results in a jet, which spreads approximately with 19°, as will be still explained
in the following section. The flame has the typical cone shape. If the mixture is swirled,
then it possesses a radial component after withdrawal from the burner due to the centrifugal
force. Starting from a certain swirl, the so-called critical swirl, the radial flow is so strong
that on the axle a back flow adjusts itself. In the radially leaking out reacting mixture a funnel
shaped flame is formed, as drawn in in the picture schematically. With very high swirl the
flame burns nearly to the wall. Such burners are called flat flame burners. To the promotion
of the radial flow the wall at the burner passage is funnel formed, as is suggested in the fig.
4-18. The back flow on the axle consists usually of burned out and thus hot gas. This hot gas
favours the ignition. Therefore swirl flames burn relatively stably, although their flow
exhibits high speed gradients and shearing stresses.
4.3
Diffusion flames
The question if fuel and air are mixed before or after entering the combustion chamber is one
of the distinctive features of flames. In the first case the flames are called premixed flames.
In the second case the combustion intensity is decisively determined by the mixing speed
and, consequently, by the diffusion processes. An old slogan says: Mixed and immediately
burnt. Therefore such flames are even called "diffusion flames". The kinetics of combustion
of premixed flames are influenced as well by diffusion processes which however take place
in the microscopic range. These processes have influences on emissions and extinguishing.
Nevertheless the term "diffusion flame" is furthermore used since this term is well
established and a better terms is not known.
The majority of burners in industrial furnaces are diffusion burners used mainly for liquid
and solid fuels. Further examples for diffusion flames are the candle flame and the flames in
steam generators, diesel engines, aircraft engines and rocket propulsion units.
4.3.1 Mixing mechanism (free jet)
The fuel-air mixing mechanism in diffusion burners will be explained on the example of the
free jet. Fuel flows from a nozzle into a large air-filled compartment so that the walls cannot
influence the flow. The resultant flow field is shown in the schematic view in Fig. 4-18. In
case of a turbulent flow the jet is propagated in linear direction with an angle of some 18 to
20 degrees. By the way, this jet propagation is well visible on the outlet opening of power
station chimneys under conditions of qualm weather. During its propagation the fuel jet
draws air from the environment. Consequently, the speed in the jet is reduced continuously.
Speed reduction and the increase in mass flow should be considered now in detail.
Since the pressure is constant along the jet and no external forces are effective, the
momentum flow remains constant (Gersten et al. 1992 and Scholz et al. 1984). Consequently,
the following shall apply:
I O = I(z ) ,
(4-43)
where Io = the momentum flow of nozzle outlet flow. The momentum flow is defined as
follows:
& ⋅u ,
I=M
(4-44)
where u- = the mean flow velocity of the jet. The mass flow for round jets is defined as
follows:
& = ρ⋅ π ⋅d2 ⋅ u ,
M
4
(4-45)
where d = jet diameter and ρ = mean jet density. Use of those two equations and equation (443) result in:
ρ0
u d0
.
=
⋅
u0
d
ρ
(4-46)
As mentioned before, the jet gets wider by the angle α = 18° to 20° so that the following
equation can be established for its diameter:
d = d 0 + 2 ⋅ z ⋅ tan
α
.
2
(4-47)
With
tan 9° ≈ 0,16
(4-48)
and equation (4-46) the speed reduction may be calculated as follows
ρ0
u
1
=
⋅
u 0 0,32 ⋅ z d 0 + 1
ρ
.
(4-49)
Taking equations (4-43) and (4-49) the mass increase may be calculated as follows:
&

M
z
= 1 + 0,32
&
d
M0 
0
 ρ
 ⋅
.
 ρ0
(4-50)
Consequently, speed decreases in a certain distance reciprocally to the nozzle distance
whereas the mass flow shows a linear increase as shown in Fig. 4-18.
· takes the ambient air the more intensive the smaller the nozzle diameter is
The fuel flow M
0
according to equation (4-50). The length zst forms the measure for the intensity of
stoichiometric air volume to be taken by the jet. In this case the mass flow of jet amounts to
& =M
& +M
& ⋅L .
M
st
0
0
(4-51)
Thus the mixing length can be calculated from equation (4-50)
z st =

ρ
1 
⋅ (1 + L ) ⋅ 0 − 1 ⋅ d 0 .
0,32 
ρ

(4-52)
Consequently, the mixing length is proportional to the nozzle diameter. For instance, in case
of natural gas with L = 15 the mixing length of cold jets (ρ0/ρ ≈ 1) is in the order of 45
diameters and in case of hot jets (ρ0/ρ ≈ 4) in the order of 90 diameters. The stoichiometric
mixing length of the hot jet is shorter than the flame length. The flame length will be
discussed later.
The fuel concentration continuously decreases as a function of length due to the admixture of
air. The concentration profile of fuel gets wider and more flat as a function of nozzle distance
analogous to the speed profile. If fuel and air are in reaction with each other, they get into
each other only in a small reaction zone as shown in the schematic view in Fig. 4-19. The
reaction zone is very small as compared with the jet width. The reaction products CO2 and
H2O are diffusing both into the environment and even towards the jet centre. The reaction
zone and, consequently, the flame front are established in those areas where fuel and air are
in the stoichiometric ratio when cold mixing takes place.
L
CO
CH4
H2
2.47
17.3
34.5
ρ0 / ρ
28/29
16/29
2/29
zst/d0
7.53
39.3
26.0
zF/d0
52
187
113
The table above shows the stoichiometric mixing length for three typical fuel gases. The
flame length is given as well. It is obvious that the flame length of the individual fuel gases is
very different. Thus the flames of natural gas are the longest whereas the flames of carbon
monoxide are the shortest. Since the flame length is much longer than the stoichiometric
mixing length, the flame takes an air volume that corresponds to an excess air number of 2 3. Thus it may be stated that burners with diffusion flames but without air control (so-called
atmospheric burners) yield rather poor efficiency rates from the standpoint of fuel
engineering. Therefore, burners used in today's domestic heating systems are air-controlled in
order to reach excess air numbers of some 1.1 to 1.2.
4.3.6 Diffusion flame with partial premixing
Premixed flames are often sub-stoichiometrically operated, since, as described before, then
the stability range is larger. Usual air numbers lie in range about λ = 0,7. With smaller air
numbers the flame speed increases strongly and the flame length accordingly. Air for
premixing is called primary air. Air for the complete oxidation of the fuel has to be sucked
in as with the diffusion flame from the environment. This air is called secondary air. In this
case a form of the flame adjusts, as is represented in Fig. 4-24 in principle. Two flames are
formed out, an interior and an above external flame. The interior flame is conical like the
typical premixed flame. The above flame has the typical form of a diffusion flame. Also
with fuel concentrations more largely than the upper ignition limit one observes still an
interior flame. This is justified in the fact that at the flame root by the free jet effect
additional air is interfered.
4.3.7 Stability
Similar to the premixed flames criteria has to be kept also for the diffusion flames, so that
these burn stably. With a small outlet velocity of the fuel the flame touch the burner rim.
With rising outlet velocity increasingly holes form in the basis of the flame. The flame takes
off. It begins to burn only in a distance from some nozzle diameters. Starting from a certain
outlet velocity the flame is finally blown off. For safety reasons therefore the outlet velocities
may lie not too close to the blown off speed.
For the explanation of the flame distance three different theories (Turns 1996) exist. The
first theory means that the height of the flame is, where the flow speed at local stoichiometric
mixture is equal to the turbulent flame speed of a premixed flame. This is the oldest theory.
The second theory assumes the local shear stress speed (aspect ratio) exceeds the critical
extinguish speed of a laminar flamelets. The third theory contains: The time for the back
mixture of a turbulent eddy of hot combustion gas with the unreacted gas is smaller than the
critical time for the reaction, which is needed for an ignition.
In Fig. 4-25 taking off heights are shown as a function of the outlet velocity, for free jet
flames of the three gaseous fuels methane, progane and ethyls. It is remarkable that the
height is independent of the nozzle diameter and the height rises with decreasing flame
speed. According to fig. 4-9 the maximum flame speeds amount to that gases vF(CH4) = 40
cm/s and vF(C3H8) = 50 cm/s. This result is interpreted with the first theory. Kalghatgi 1984
gives the approximation for the taking off height of hydrocarbon flames
h ⋅ v F max
ν0
= 50 ⋅
u0
v F max
1, 5
ρ 
⋅  0 
 ρL 
(4-97)
whereby ρL the density of surrounding air is.
For the blown off of the flame one goes out with a similar mechanism as with premixed
flames. The basis and the edge of the diffusion flame are regarded as pre-mixed. The flame is
blown off therefore if the turbulent maximum flame speed with the distance drops faster than
the flow speed. For the critical speed of the blown off Kalghatgi 1981 gives the
approximation.
1, 5
ρ 
u 0crit
= 0,017 ⋅ Re L ⋅ (1 − 3,5 ⋅10 −6 ⋅ Re L ) ⋅  L 
v F max
 ρ0 
(4-98)
whereby the Reynolds number
Re L =
v F max ⋅ L
(4-99)
ν0
is defined. For the characteristic length L
L
1
=
d 0 0,25 ⋅ x st
ρ 
⋅  0 
 ρL 
0,5
− 1,5
(4-100)
is valid, what corresponds with the flame length. In Fig. 4-26 measured blown off speeds for
different gaseous fuel are depicted according to eq. (4-98), from which the applicability is
evident. From the three above equations for the critical outlet velocity follows concerning the
blown off
u 0 crit 0,017 ρ L v 2F max
≈
⋅ ⋅
d0
0,25 ρ0 ν 0 ⋅ x st
(4-101)
or
1, 5
 ρ  v2
u 0 crit
≈ 0,017 ⋅  L  ⋅ F max .
dL
ν0
 ρ0 
(4-102)
The blown off speed depends on the square of the flame speed. In Table 4-5 are for some
gases these on the diameter and/or on the flame length referred critical outlet velocity
specified. For acetylene and in particular for hydrogen these speeds lie substantially more
highly than concomitantly for methane and natural gas. Carbon monoxide and concomitantly
weak gases possess clearly lower critical speeds than natural gas. Therefore flames of these
gases are extremely stability sensitive.
Remarkable it is still that the blown off speed rises proportionally with the nozzle diameter.
Therefore it is so difficult to blow out flames of boreholes.
Measures to Stability
For stable burning of diffusion flames can be met several measures. For burners with large
power often small ignition burners are used, which always burn with a premixed flame. For
small and middle power in a small distance from the burner mouth on the axle a pilot disk are
attached. Thereby develops a flowing back eddy, which returns hot gas for ignition. One
reaches a back flow also by a swirling of the supplied combustion air.
4.4
Explosions and Detonations
The controlled combustion with constant pressure one calls deflagration. The explosion is
combustion with increase in pressure, e.g. combustion with constant volume. With a
detonation a progressive pressure wave is formed.
Explosions
Explosions takes place with combustion at constant volume, then an increase in pressure
follows. Due to this increase in pressure a damage can occur (exception engines), why
explosions are unwanted usually. With explosions fuel and air are pre-mixed, so that it comes
to a fast propagation of the flame front. So that an explosion can occur, three conditions must
be fulfilled:
-
enclosed room
defined fuel air mixture
ignition source.
Typical dangerous room for explosion are combustion chambers and boilers. In the cold
condition an explosive mixture can occur, e.g. by unburned remainder fuel after switching
off, or by leakages. By igniting the flame after the start of a burner it comes then to an
explosion. Such advices must be sufficiently rinsed therefore for safety reasons before
igniting the burner.
That an explosion is possible, the fuel air mixture must lie within the ignition limits. The
ignition limits were already treated in section 4.1.2. Further an ignition source must be
releases with sufficient energy. After Remenyi (1987) the explosion pressures can amount for
hydrogen and acetylene (C2H2) up to 16.5 bar, for methane up to 7.5 bar and for coal dust up
to 4.2 bar.
Measures to the explosion protection are therefore preventing possible ignition sources and
injecting of inert gas. For transportation and storage of oxidation able types of dust, e.g. coal
dust, therefore burned out gas, N2 or CO2 were used.
Detonations
For the explanation of a detonation a long pipe is regarded according to Fig. 4-4.1, in which a
pre-mixed fuel air mixture is contained. If the mixture at the open right side is ignited, then
an almost even burn front spreads to the left into the mixture. With this front a stationary
speed usually adjusts itself. The speed of this burn wave lies much below the speed of sound.
The burned and thus hot gas expands and flows to the right away. If the mixture is ignited
against it at the closed right end, then the pressure of the burned gas rises on the right side
strongly. This works then like a piston, which presses the reaction front into the unburned
mixture. The burn wave is accelerated and the speed can reach a multiple of the speed of
sound, what leads to a detonation. The structure of the detonation wave is described on the
basis Fig. 4-4.2, in that the axial change of the pressure is schematically represented. The
front of the detonation consists of a so-called shock wave, in which from the starting
situation the pressure, the density and the temperature rise steeply. The thickness of this layer
is very small and lies in the order of magnitude of few free distances of the molecules.
Starting from a certain temperature, which depends on the kind of the mixture, the fuel
ignites. The ignition range is called induction zone. The temperature rises due to the low
reaction rate still slowly. Pressure and temperature rise according only little. Afterwards in
the so-called reaction zone the temperature rises steeply to very high values. If the reaction is
ended, temperature, pressure and density have nearly reached the equilibrium state. The
distance from the shock front to the burn off lies in the magnitude of 1 cm.
On the mechanism of the acceleration of the reaction front which first spreads with the
laminar flame speed and then exceeds the speed of sound is not dealt with here. For this is
referred to the book of Kuo 1986. In the following however the height of the detonation
speed is regarded still briefly. In the Fig. 4-4.3, this speed is shown for the two fuels propane
and acetylene as a function of their concentration in the mixture. The detonation speeds lie
within the range of 1500 to 3000 m/s and amount to thus a multiple of the speed of sound. It
is remarkable that the maximum value arises not with the stoichiometric concentration, but
within the range with substantially higher fuel concentration. The maxima lie somewhat
above the stoichiometric concentration for the conversion to CO and H2O. This can be
explained thereby that the reaction time is too short with a detonation, to convert the CO
completely to CO2. This reaction is as well known relatively slow. So that a detonation can
occur, the mixture must lie within certain limits similar to the ignition. In Table 4-6
experimentally determined limits for the detonation and ignition of some fuels are
confronted. From this it is evident that the limits for a detonation are closer than for
combustion.
Fig. 4-30: Ignition of fuel-air-mixture in a long pipe
Fig. 4-31
Structure of a detonation wave
Fig. 4-32
Detonation speeds in dependence on fuel concentration in oxygene
Mixture
Combustion
Detonation
lower limit
in Vol % fuel
H2-O2
H2-air
CO-O2 (wet)
(CO + H2) – O2
(CO + H2) – air
NH3 – O2
C3H8 – O2
C2H2 – O2
C4H10O – air
Tab. 4-6:
4,6
4
15,5
12,5
6,05
13,5
2,4
2,8
1,85
Detonation
Combustion
upper limit
in Vol % fuel
15
18,3
38
17,2
19
25,4
3,2
3,5
2,8
Ignition and detonation limits due to Kuo (1986)
90
59
90
91
59
75
37
92
4,5
93,9
74
93,9
92
71,8
79
55
93
36,5
CH4
+H
C2H6
+H,O,OH
+H
CH3
+H,O,OH
+CH3
C2H5
+H,O,OH
+M
CH3CHO
CH3CO
+O
CH3
+CH3
+CH3 +H +M,O 2
+O
C2H4+O,OH CH ,CH O,CHO
3
2
CH2O
+H
+H,O,OH
C2H3
CHO
+O
+M,O 2,H
+H
+OH
C2H2
CO
CH2CO +H
CH3
+OH
CH
+H
CH2
+O,O2
CO
Fig. 4-1:
CH2O,CHO
+O,O2
CO,CO2
Integral reaction-flow analyse in a premixed stoichiometric CH4-air-flame at
1 bar and 298 K (Warnatz 1984)
CH4
C2 H6
CH3
C2 H5
CH2O
C2 H 4
CHO
C 2 H3
CO
C2 H2
CO2
CH2
CH
Fig. 4-2:
Schematic mechanism of oxidation of carbon-hydrogen (Warnatz 1981 a)
Lean flame
Stoichiometric flame
Fat flame
Relative sensitivity
1
H+O2 OH+O
0,5
CO+OHCO2+H
0
OH+OH+O 2
H + CH3CH4
Reaction
1 2 3 5 6 7 8 11 15 38 39 51 6184 93 102
-0,5
H+O2+MHO2+M
H2-Ox
Fig. 4-3:
CO-Ox
C1-Ox
Analysis of sensitivity of the reactions in a premixed methane flame
(Warnatz 1984)
10
1500
2000
2
1200
1000
K
0.5
f
f 0.5 f
CO O2 H2 O
101
1
10-1
.
2
N(RT/P) x10
-9
ml / mole sec
CO+1/2 O2 CO2
10-2
10-3
4
5
6
7
8
9
10
-4
11 12x10
Inverse temperature 1/T
Fig. 4-4:
Standardized reaction rate of the CO burning (Howard 1973)
.
Qα
.
Q
.
QR1
.
Q
.
Qα 1
.
QR2
.
Qα 2
.
QR3
Tz1 Tz2
Fig. 4-5:
.
QR
Tv1
Tv2 T
Tz2Tz1
Tv1
Tv2
Mechanism of ignition
30
Upper ignition limit
Vol. %
20
Rapid ignition
CH4
10
Lower ignition limit
0
Fig. 4-6:
0
500
1000
Temperature
Ignition temperature of methane (Zelkowski 1969)
o
C
1500
T
Fig. 4-7:
Short duration schlieren photographs of turbulent premixed propane-air flames
(Tsuji 1979)
ϕ
LF
u
ϕ
uo
do
vF
Fig. 4-8:
Length of premixed flames
1.0
-1
m. s
0.8
VF
0.6
C3H8
C4H30
N-C7H16
C2H6
C2H2(vF/2)
CH4
0.4
0.2
0
Fig. 4-9:
0
5
10 Vol %
Fuel concentration
15
Laminar flame velocity in dependence on concentration of fuel-air-mixtures at
bei 1 bar (Warnatz 1993)
2.8
-1
m.s
2.4
100 %O2
80 %O2
2.0
67 %O2
1.6
VF
51 %O2
40 %O2
1.2
28 %O2
0.8
20 %O2
16 %O2
0.4
0
0
2
4
6
8
10 12 14 16 Vol.% 20
XC H
6 14
Fig. 4-10:
Laminar flame velocity of hexane-O2-nitrogen mixtures (Shchetinkov 1965)
2.0
-1
m.s
1.5
Kerosene
Naphtalene
vF 1.0
0.5
0
0
100
200
300
o
C 400
Temperature
Fig. 4-11:
Influence of the initial velocity on the laminar flame velocity during the
stoichiometric burning of kerosene and naphthalene (Shchetinkov 1965)
Alam
Aturb
Fig. 4-12: Actual and mean flame surface
6
λ = 0.9
-1
m.s
λ = 1.1
4
λ = 1.25
Extinction
vF
λ = 1.4
2
0
0
4
8
v´ in m/s
12
Fig. 4-13: Turbulent flame velocity in dependence on turbulent intensity of C3H8-air
mixture (Abdel-Gayed et al. 1984)
16
z
r
1
2
3
Burner
flow
vF1 < vF2
< vF3
Burnerrim
Fig. 4-14: Stability of flames
Velocity gradient at the boundary 1/s
Blow-off region
Region of stable flame
Flash-back
region
rec. Excess air number 1/λ
λ
Fig. 4-15: Flame stability diagram for natural gas-air-mixture (Merzhanov et al. 1988)
10
mm
O2/(O2+ N2)
6
0.35
0.21
0.5
0.65
1
Extinction distance
4
2
1
0.8
0.6
0.4
0.2
0.1
0
10
20
30
40
50 % 60
Vol.-conc. of Methane
Fig. 4-16: Distance of extinction for mixtures of methane, O2 and N2
(Lewis and Ebbe 1951)
6
4
mJ
2
n-Pentane
Butane
Propane
Minimum ignition energy
1
0.6
0.4
0.2
0.1
0.06
0.04
H2/O2/He
H2/O2/N2
Acetylene
0.02
0.01
0.5
H2/O2/Ar
1
1.5
2
2.5
3
Fuel concentration fraction of stoichiometric
Fig. 4-17: Minimum ignition energies for various fuel-air-mixtures. H2(II)-hydrogen and
air; H2(I)-hydrogen and air with N2 replaced by argon; H2(III)-hydrogen and air
with N2 replaced by helium (Calcote et al. 1952)
r
19
d0
o
z
r
1,0
u/uo
0,8
0,6 Core
region
0,4
Transition
region
0,2
0
0
5
Similarity
region
10
15
20
25
30
25
30
z / do
. .
M / Mo
12
8
4
0
0
5
10
15
20
z / do
Fig. 4-18: Turbulent open jet (Scheme) with velocity field and axial profile
Mass increasing in a round free jet
d0
z/d0
Fig. 4-19: Principle forming of free jet flame
X
B
O2
r
rst
rst
0
r
X
B
CO2, H2O
O2
r
0
rst
r
Reaction
zone
Fig. 4-20: Radial concentration profile with a fuel jet in air without (above) and with
reaction (below)
Fig. 4-21: Photo of a free jet flame
250
CH4
Lift
Liftof
ofheight
heighthhininmm
mm
200
C3H8
150
100
C2H4
50
0
0
50
100
150
d0in mm
4.06
6.1
8.3
200
Jet exit velocity u0 in m/s
Fig. 4-23: Lift of heights of free jet flames
250
1000
800
U0
vF
1.5
ρ 
⋅  0 
 ρL 
600
Methane
Propane
Ethylene
Butane
Acetylene
X Hydrogen
400
200
0
0.017 ReL (1-3.5 10-6 ReL)
0
20000
40000
60000
80000
ReL
Fig. 4-24: Blow out velocities of free jet flames
unburnt gas
ρ1, p1, T1
burnt gas
combustion front
u
Fig. 4-30: Ignition of a fuel-air-mixture in a long pipe
Fig. 4-31: Structure of a detonation wave
ρ2, p2, T2
Fig. 4-32: Detonation speeds in dependence on fuel concentration in oxygen
CH4 + 2 O2 → CO2 + 2 H2O
d~
x CH4
dt
0, 7
= −~
ρ1 / 2 ⋅ k ⋅ ~
x CH
⋅~
x O0,28
4
3
 202kJ / mol   m 
k = 5,0 ⋅10 ⋅ exp −
⋅

R ⋅T

  kmol 
11
1/ 2
⋅
1
s
Dryer et al. 1973
CO + ½ O2 → CO2
d~
x CO
~⋅k⋅~
= −ρ
x CO ⋅ ~
x1O/22 ⋅ ~
x1H/22O
dt
3
 125kJ / mol  m 1
k = 1,3 ⋅1011 ⋅ exp −
⋅

R ⋅ T  kmol s

Howard et al. 1973
Table 4-1: Global approaches for fuel reactions
Fuel
Symbol
Hydrogen
H2
Carbon monoxide
CO
Methane
CH4
Acetylene
C2H2
Ethylene
C2H4
Ethane
C2H6
Propylene
C3H6
Propane
C3H8
n-Butane
C4H10
n-Pentane (*)
C5H12
n-Hexane (*)
C6H14
Top gas
Coke gas
Naturel gas L
Naturel gas H
(*) condensate at standard condition
Ignition
temperature in
air
°C
530
610
645
335
540
530
460
510
490
285
240
630
560
640
640
630
Table 4-2: Ignition temperature and limits of gaseous fuels
Ignition limit in air (20 °C)
lower
upper
Vol.-%
4,1
19,6
5,1
2,3
3,0
3,1
2,6
2,1
1,5
1,3
1,2
33
5
5
4
Vol.-%
72,5
72,9
13,5
82,0
17,7
11,7
10,0
9,5
8,5
7,6
7,4
70
30
15
16
Methane CH4
Hydrogene H2
Carbonmonoxide CO
v max [m/s
0,43
3,64
0,195
~
x max [%]
10,2
42,5
41,5
~
x st [%]
9,5
29,6
29,6
vFst [m/s]
0,42
2,37
0,174
Table 4-2: Laminar flame speeds
Gas
ν O2
~
MB
 kg O2 
O

 kg B 
 kg 
x st  B 
 kg G 
H2
CO
CH4
C3H8
1/2
1/2
2
5
2
28
16
44
8
0,57
4
3,6
0,028
0,29
0,055
0,060
 m3 
 kg 
~
x st  3B  L  L 
 mG 
 kg B 
0,296
0,296
0,095
0,40
34,5
2,5
17,3
15,7
λ F ( x st )
 MJ 
hu 

 kg B 
2,1
2,8
2,1
2,1
120
10,1
50,0
46,4
Table 4-3: Gas data to the evaluation of the flame length and the excess air number