B URNING V ELOCITY
3.3. SIMPLE PROCESSES IN MILD COMBUSTION
3.3.4. HDDI IN C OUNTER -D IFFUSION F LOW R EACTOR
lines in the upper part of the figure (temperature) show a steep variation at very low values of the mixture fraction. This means that oxidation takes place on the reactant side because the zero value is the mixture without any dilution. Figure 3.9 shows the same quantities that are reported in Figure 3.8 for a superadiabatic condition, in which, as shown by the dashed line, the adiabatic flame temperature of the fresh air–fuel mixture is 1500 K and the temperature of the inert gases is 1700 K. The adiabatic flame temperature corresponds to an air–fuel ratio slightly lower than the lean flammability limit, and the inert gases are close to the maximum temperature at which a metallic material can survive. In other words, the example is of some interest from the perspec- tive of practical applications.
In the same plot, the autoignition temperature is also reported as a function of the mixture fraction for minimum oxidation in a residence time of one second. This temperature is higher than the frozen mixture temperature, so the example pertains to an autoignited combustion regime. Furthermore, the maximum temperature increase is 1200 K, which is lower than the ignition temperature differential since the equivalence ratio of the mixture is above the flammability limit. Of course, it is possible to create superadiabatic combustion processes which are not MILD, but such processes are always at HiTeCo conditions because the inert gas temperature is higher than the adiabatic flame temperature, which is in turn higher than the autoignition temperature.
Under these conditions, it is possible to stabilize two kinds of processes: the develop- ment of a deflagration at Z ¼ 0, or an autoignition process in the range where the autoignition temperature is higher than the frozen mixture temperature.
In contrast, in the example of Figure 3.9, it is not possible to have a deflagrative premixed flame because the mixture is outside the flammability limit and only the autoignition structure can be stabilized. Thus, the temperature profiles reported with dash-dot lines and the enthalpy production reported with solid lines for three different stretch rates belong to the only possible regime, and the distinction between sub/
supercritical conditions is meaningless.
dilution of the oxidant. In the first case, the oxidant is also heated to high temperature, whereas in the second process, the fuel is heated. The last process is less interesting than the other three because the fuel is preheated to such temperatures that the fuel undergoes a classical pyrolysis, which may generate heavier and denser aromatic products. Con- sequently, the last process will not be discussed in this chapter because it would likely generate undesired pollutants.
The first process, on the other hand, has the potential to reduce several pollutants, such as nitrogen oxides and carbonaceous pollutants (Cavaliere and de Joannon, 2004).
It is analyzed here in detail when the oxidant is diluted to an oxygen molar fraction of 0.05 and is heated up to a temperature of 1300 K. The results are reported in Figure 3.10 with the same line conventions as those reported before. The temperature over the entire range of frozen mixture fractions, plotted as a solid line, is always higher than in standard conditions, and decreases continuously from 1300 to 300 K, which is the fuel temperature. The maximum and equilibrium temperatures are similar in their overall trend to those in standard conditions, but the maxima of both are shifted toward lean conditions and are lowered to values of 1800 and 1700 K. These two correlated features are of great interest because even in the case of a diffusion flamelet stabilized around the stoichiometric value, as is similar to standard combustion, a significant change takes place. The maximum occurs in conditions where the mixture fraction gradients are lower than those in standard conditions. As a result, the dissipation rate of the scalars is also lower which inhibits flame quench. In contrast, the autoignition temperatures (drawn with a dotted line) are higher than the frozen temperature over quite a large mixture fraction range. This means that whenever extinction occurs, a mixture is formed
Table 3.2Mild combustion configurations
Configuration Name Description
HODO Oxidant is hot and diluted
HFDO Fuel is hot and oxidant is diluted
HFDF Fuel is hot and diluted
HODF Oxidant is hot and fuel is diluted
2800
Tmax
Teq
Tfrozen
Tign 2300
1800 1300 800
3000 0.2 0.4
Mixture fraction, Z HODO = Hot oxidant-diluted oxidant
XO2= 0.05 p =1 bar t = 1s
Temperature (K)
0.6 0.8 1
Figure 3.10 Frozen inlet temperature, maximum temperature, autoignition temperature, and equilibrium temperature as a function of the mixture fractionZfor the hot oxidant-diluted oxidant (HODO) process.
that can evolve spontaneously toward its oxidative state. In other words, whatever the local combustion regime may be, a reactive progression is always possible, and multiple combustion processes can take place by passing from the feedback mode, as occurs in diffusion flames to diffusion ignition oxidation. This is in contrast to events at standard conditions where multiple probable processes shift from the diffusion flame to the frozen condition with resulting noisy combustion. The local competition between these two processes should be evaluated case by case, taking into account the level of dilution and of oxidant preheating. In any case, the maximum temperatures in the MILD combustion examples are always lower than the maximum temperatures in the undiluted case, with the aforementioned positive effect in the reduction of both pollutant formation and of the temperature range in which the process advances.
Whether these characteristics are general for hot diluted oxygen conditions can be evaluated by analyzing Figure 3.11. This figure reports both the stoichiometric mixture fraction values, Zs, and the stoichiometric temperature reached by the system in this condition,Ts, as a function of the oxygen mass fraction in the oxidant with solid and dashed lines, respectively. The two curves represent plots of Equations (3.6) and (3.7):
Zs¼(1þnsYf1=Yox2) 1, (3:6) Ts¼ YfDHc
coxp Yoxþcdilp YdilþcpfYfþTfrozen=s, (3:7) whereTfrozen=sis defined as
Tfrozen=s¼(Yox2coxp þYdil2cdilp )T1þYox2=nscpfT2
1þYox2=ns
, (3:8)
andnsis the stoichiometric mass ratio,Yf1is the fuel mass fraction in the fuel stream, Yox2 is the oxidant mass fraction in the oxidant stream,Yf, Ydil, and Yox are the local mass fractions of fuel, diluent, and oxidant, respectively;DHcis the heat of combustion of the fuel, and thecpvalues are the specific heats of the different species.
0.06 0.05
0.05 0.1
Yox2
0.15 0.2 0.251300
1800 2300 2800 3300
0.04 0.03
Stoichiometric mixture fraction, Zs Stoichiometric temperature (K)
0.02 0.01 00
Figure 3.11 Stoichiometric mixture fraction (on the left axis) and the related temperature (on the right axis) as a function of oxygen mass fraction in the diluted stream.
The behavior described for such a configuration can be easily observed in the temperature and heat release profiles as a function of mixture fraction for a hot oxidant-diluted oxidant (HODO) case, as reported in Figure 3.12. The profiles refer to a methane flame at 10 bar with an initial velocity of 60 cm/s for a preheated, diluted oxidant stream of 1300 K and an undiluted fuel at 300 K. Clearly, the maxima of temperature (upper part of the figure) and heat release (lower part of the figure) occur at lower mixture fraction by increasing the dilution level, thus shifting toward the oxidant stream. At the same time, the flame structure also changes, as the shape of the heat release profiles show. In standard conditions, that is for an oxygen molar fraction of 0.21, two main regions can be recognized. The first flame zone lies between Z¼0 andZ¼0.07 where oxidation is the main reactive process, as the positive heat release rate testifies. In contrast, the second flame region forZhigher than 0.07 is found where, as the heat release rate demonstrates, an endothermic process overcomes the fuel oxidation. The extent of this second region decreases with decreasing oxygen content until it completely disappears, such as shown by the heat release profiles atXO2¼0:05 and 0.03. Moreover, the profiles atXO2¼0:21, 0:15, and 0.1 reach two maxima in the region where the heat release rate is positive, which is representative of the oxidation process occurring in two steps: fuel conversion principally to CO followed by oxidation to CO2.
The characteristics of MILD combustion change when diffusion ignition takes place in a structure where the diluted fuel diffuses into the non-diluted hot oxidant.
1300K
750
500
250
−250 0
2800 2300 1800 1300 800 300
0.15 0.1
0.05
Oxidant Mixture fraction, Z
Heat release (cal/s/cm3) Temperature (K)
Fuel 0.15
0.15
CH4/Air p = 10 bar vo = 60 cm/s
0.05
0.05
0.03
0.03
XO2 = 0.21
XO2 = 0.21
0.1
0.1
0
Figure 3.12 Temperature and heat release rate as a function of the mixture fractionZfor fixed strain rates in a HODO configuration.
The temperature-mixture fraction plot reported for this case in Figure 3.13 shows this change when the oxidant is heated up to the same temperature as before and the fuel molar fraction is 0.1 due to dilution in nitrogen. The frozen temperature profile is the same as that in Figure 3.9, whereas the maximum temperature profile is altered significantly with the shift of its maximum toward the richer region. In this specific case, the location of the maximum is atZ¼0.5, at which the maximum temperature is 1900 K, but both quantities depend on the dilution level, as is illustrated in Figure 3.14.
Similar to Figure 3.11, and according to Equations (3.6) and (3.7), Figure 3.14 illus- trates the dependence of the stoichiometric mixture fraction and the maximum tempera- ture on the dilution level of the fuel. The shift of the stoichiometric value is toward the rich side, and is therefore in the direction of decreasing frozen temperature. This means that, jointly with the moderate temperature increase due to dilution, the variation in maximum temperature is not very steep. In fact, for this condition, there are two concurrent factors that both depend on large amounts of dilution. The first is the decrease in temperature increment, and the second is that the temperature increment has to be added to the initial frozen value, which has also decreased. This peculiar trend can be extended to a condition where the maximum temperature at the stoichiometric value is lower than the value on the oxidant side. In any case, there is a tendency toward a strong homogenization of the temperature over a wide mixture fraction range. This means that the oxidation process is controlled by the temperature since the kinetic characteristic times are the same for both the very lean side and the stoichiometric condition. In other words, the ignition diffusion process and feedback combustion have the same probability to occur. It is also of interest that the equilibrium temperature is nearly the same in this condition. This temperature closely follows the maximum temperature in Figure 3.13 for mixture fraction values up toZ¼0.5 and is only slightly lower for richer conditions. This means that, regardless of the kinetics involved in the process, maximum oxidation is favored over the formation of pyrolytic partially endothermic compounds.
Comparing profiles of the ignition and frozen temperatures is also informative. The crossover of the two curves occurs at a mixture fraction of 0.4 and is expected to occur at lower mixture fractions by increasing the dilution. This means that richer conditions
Temperature (K)
2800 2300 1800 1300 800 300
Mixture fraction, Z Tmax
Teq
Tfrozen
Tign
HODF = Hot oxidant-diluted fuel t = 1s
p = 1 bar Xf = 0.1
0 0.2 0.4 0.6 0.8 1
Figure 3.13 Frozen inlet temperature, maximum temperature, autoignition temperature, and equilibrium temperature as a function of the mixture fractionZfor the hot oxidant-diluted fuel (HODF) process.
than this value cannot spontaneously react and that in limiting conditions, autoignition is favored relative to the oxidation process at stoichiometric conditions. This is particu- larly true for processes in very turbulent regimes where quenching extinction of the diffusion flame may occur so that the only possible oxidation takes place at a mixture fraction lower than the stoichiometric condition; that is, only lean or super lean combustion takes place with enhanced inhibition of partial oxidation species.
The example reported in Figure 3.13 is relative to conditions in which the mass flow rate of the fuel is comparable to the mass flow rate of the oxidant. This is an advantage for the mixing of the two streams because they can be injected in the reactor with comparable momentum, but it can be a disadvantage because it is difficult to dilute the fuel to a high degree. For instance, these results were obtained with a mass diluent-fuel ratio on the order of ten, corresponding to an overall heating value on the order of 1000 kcal/kg. On the other hand, low dilution may be required anyway in the event a low heating fuel must be burned.
Examples of flame structures obtained in the hot oxidant-diluted fuel (HODF) configuration are reported in Figure 3.14. As with the HODO configuration, tempera- ture (upper part of the figure) and heat release rate (lower part of the figure) profiles refer to a methane flame at a pressure of 10 bar and an initial velocity of 60 cm/s. As is also implied in Figure 3.15, the stoichiometric mixture fraction and heat release profiles shift toward the fuel side with increasing fuel dilution. Moreover, the flame structure changes with the fuel molar fraction. ForXf ¼0:5, the heat release rate is positive up to
1600
1200
800
400
−400 0
2800 2300 1800 1300 800 300
0.8 1
0.4 0.6 0.2
Oxidant Mixture fraction, Z
Heat release, cal/s/cm3 Temperature, K
Fuel 0.15
0.15
CH4/Air p = 10 bar
0.05 0.05
0.03 0.03 Xf = 0.5
Xf = 0.5 0.2 0.1 0.2
0.3 0.3
0.1
0
Figure 3.14 Temperature and heat release rate as a function of the mixture fractionZfor fixed strain rates in a HODF configuration.
Z¼0.18 and two maxima are present. These maxima are related to the successive steps of the oxidative process. For higher mixture fraction, the heat release rate becomes negative. By decreasingXf, the maxima move toward the fuel side and become closer until they merge into a single peak. Simultaneously, the region corresponding to negative heat release rates reduces its size until it disappears.
The last HDDI process analyzed is obtained when the fuel is injected at high temperature and is diluted. This process is classified as a hot fuel-diluted fuel (HFDF) process. Figure 3.16 shows the behavior of the characterizing temperatures for an inlet fuel temperature of 1300 K and a fuel molar fraction of 0.1. The trend of the maximum temperature is different from previous cases: it increases steeply on the lean side, whereas it decreases gradually on the rich side. The inlet–ignition differential shows the opposite behavior where it is negative on the lean side and is positive on the rich side. In some respects these conditions are not favorable for diffusion ignition oxidation because the conversion should be restricted to the rich side. Nevertheless, the conditions
Stoichiometric mixture fraction, Zs 1 0.8 0.6 0.4 0.2 0
Yf
0 0.2 0.4 0.6 0.8 1
Stoichiometric temperature (K)
3500
2700
1900
1100
300
Figure 3.15 Stoichiometric mixture fraction (on the left axis) and the related temperature (on the right axis) as a function of fuel mass fraction in the diluted stream for HODF configuration.
2800 2300 1800 1300 800 300
Temperature (K)
Mixture fraction, Z
HFDF = Hot fuel-diluted fuel Xf= 0.1 t= 1s p = 1 bar Tmax
Teq
Tfrozen
Tign
0 0.2 0.4 0.6 0.8 1
Figure 3.16 Frozen inlet temperature, maximum temperature, autoignition temperature, and equilibrium temperature as a function of the mixture fractionZfor a hot fuel-diluted fuel (HFDF) configuration.
are better than those in traditional combustion. The temperatures do not attain high values of feedback combustion, and reforming of the fuel on the rich side can be achieved which helps in the complete oxidation of the fuel. In particular, this feature can be exploited for nitrogen oxide reduction in a reburning process, and in the suppression of recombination kinetics which are ter-molecular in nature because they reduce the concentration of any reactive species due to dilution.
This behavior is general for a wide range of preheat and dilution conditions, but is different from previous cases since the stoichiometric mixture fraction shifts with dilution toward the rich side where the frozen temperature also increases. These trends can be better analyzed with the aid of Figures 3.16 and 3.17, which shows the same quantities as Figures 3.13 and 3.15. The only difference is that the diluted fuel is preheated instead of the oxidant. In Figure 3.17, the curve related to the stoichiometric mixture fraction is the same as that in Figure 3.15. Figure 3.16 shows that in the HFDF case the maximum temperature increases for low values of dilution and, only for values higher than 0.5, starts to decrease.