B URNING V ELOCITY
3.3. SIMPLE PROCESSES IN MILD COMBUSTION
3.3.3. HCDI IN C OUNTER -D IFFUSION F LOW R EACTOR
A fuel lean mixture outside the flammability (or inflammability) limit is defined as a mixture in which deflagration cannot be stabilized. Nevertheless, oxidation may occur when the mixture is heated by an external source by means of enthalpy and/or mass diffusion through the mixture. Several experimental studies have shown the occurrence of this process when the source is a heated wall or a high temperature inert flow in a laminar (Daribha et al., 1980; Smooke et al., 1990; Zheng et al., 2002) or turbulent (Blouch et al., 1998; Mastorakos et al., 1995) counter-diffusion reactor. These works were more focused on the ignition and extinction limit of the system rather than on their oxidation structure, even though they report many significant features of the
process. In particular, the peculiarity of oxidation under these conditions is not empha- sized. In the taxonomy of highly preheated combustion, however, it deserves a specific name in order to refer to it in an unambiguous way. An analogy to the HCCI process is suitable for this purpose. The first part of the acronym, HC, refers to the homogeneous charge of air and fuel and should be kept, while the second part of the acronym, CI (compression ignition), can be replaced with DI, which stands for diffusion ignition, to underline that they are similar in the autoignition of the mixture but differ in the cause of this process. In the first case, autoignition is due to compression heating, whereas in the second case it is due to enthalpy/mass diffusion, which mixes the HC with a high temperature inert flow. Hence, the acronym for the process is HCDI, that is Homogeneous charge diffusion ignition.
The main feature expected of this type of process consists of the whole oxidation structure which is placed inside the diffusive controlled mixture layer. Providing examples of this structure requires reference to the counter-flow configuration shown in Figure 3.6 for an oxygen, a methane, and a nitrogen system. As illustrated by the figure, two flows proceed along thexdirection, which is the coordinate axis with the origin at the stagnation point. The flows have defined velocities at infinite xon both the positive and negative sides and are characterized by a linear decrease of the velocity component on the symmetry axis coupled with a linear increase of the orthogonal component of the velocity. Therefore, the fluid dynamic pattern is characterized by a single parameter, that is the velocity gradient of the two velocity components.
In practice, this pattern is created around the stagnation point of two opposed flat (uniform velocity) jets, which flow through orifices placed at a fixed distance from each other. A mixing layer occurs around the stagnation point, in which the species of both jets are diffused into each other, yielding a continuous variation of the mixture fraction.
Reactions can also take place inside the mixing layer where suitable composition and temperature conditions are created. Figure 3.6 shows schematically the location of a reactive region by the shaded area. The region is deliberately shown away from the stagnation point in the symmetric plane in order to stress that the proper composition and temperature for reaction may be placed at any location.
The use of this counter-flow configuration allows for the illustration of a wide variety of HCDI structures as well as more invariant deflagration and diffusion flame structures by comparing a spatial or mixture fraction coordinate to different parameters involved in the controlling process. For instance, the role of the inert flow temperature is shown
y
x Hot products Lean fuel/air mixture
T0
Figure 3.6 Schematic of counter-flow configuration for flame stabilization.
in Figure 3.7. The plot reports three ensembles of spatial distributions of enthalpy production per unit mass. The three frames correspond to inert flow temperatures of 1400, 1600, and 1800 K, respectively, and the three curves in each frame correspond to three asymptotic strain rates,k(obtained ask¼2v0=L), of 20, 55, and 80 s 1.
The heat release values in Figure 3.7 for k¼20 s 1 at 1400 K are on the negative side, quite far from the stagnation point. This means that the reaction zone is placed in the homogeneous air–fuel mixture. The other two curves lie on the positive side with respect to the stagnation point. They are centered furthest from the stagnation point for the highest strain rate and are shifted toward the stagnation point for the intermediate strain rate. The bell-shaped curves are quite broad and extend for a large part of the diffusive layer.
CH4/Air To
k, s−1
Tdil
Tdil = 1400 K
Tdil = 1600 K P = 1 atm
P = 1 atm
Tdil = 1800 K P = 1 atm 20
N2 δ80
δ55
δ20
55 80
Heat release (cal/s/cm3)
−0.5 −0.25
x (cm)
0.5 0.25
0 70
50
30
10
50
30
10
50
30
10 0 0 0
Figure 3.7 Spatial distribution of heat release in a counter-flow configuration at 1400, 1600, and 1800 K.
The enthalpy production at 1600 K for k¼55 s 1 and 80 s 1 is positioned on the opposite side of the stagnation point with respect to the position at 1400 K, which is the side from which the air–fuel mixture enters. These two curves are different from those in the previous case as they are quite thin, and are shifted closer to the stagnation point.
The same trend is also confirmed at the higher temperature of 1800 K, even though the profiles are nearer the stagnation point. Notably, the peak of the enthalpy production is comparable in amplitude for the last two cases, whereas it is quite low for the process at 1400 K.
On top of the figure, the mixing layer thicknesses are reported for the three strain rates in the form of dark bars which extend in the range of the spatial axis, shown as the abscissa of the plots. Note that the heat release profiles are approximately inside the corresponding mixing layer thicknesses.
In summary, the figure demonstrates that a great variety of oxidation structures may be stabilized in HCDI processes, but there is an unequivocal localization of the structure inside the mixing layer. In other words, the presence of the oxidation process is related to the diffusion between the inert and the air/fuel charge. Therefore, the acronym seems appropriate, but the structures do not share any characteristics with diffusion flames, neither in the provenance of the reactants nor in the invariance properties which are known for classical diffusion flames.
In order to give a reference framework for the analysis of these processes, two ensembles of plots, which refer to examples of two regimes identified in the literature
2400
1800
1200
600
p = 1 atm
Heat release (cal/s/cm3) 1700
t = 0.4 s
0 1250 1000 750 500 250 55 cm/s
Φstoich
5 cm/s
5 cm/s
Tign
55 cm/s
Mixture fraction, Z
0 0.2 0.4 0.6 0.8 1
Temperature (K)
Figure 3.8 Frozen inlet temperature, maximum temperature, autoignition temperature, and heat release rate as function of the mixture fractionZfor different strain rates for a subadiabatic case.
(Libby and Williams, 1983; Puri and Seshadri, 1987) are reported in Figures 3.8 and 3.9.
In Figure 3.8, the frozen inlet temperature, maximum temperature, and autoignition temperature are reported as a function of the mixture fraction with solid, dashed, and dotted lines, respectively. The mixture fraction in this case is the mass fraction of the inert species, and is thus zero for the air–fuel mixture and unity for the diluents, so the fractional values are percentages based upon the presence of the diluents in the mixture.
The example refers to an adiabatic flame temperature of 2004 K and an inert temperature of 1700 K. Consequently, the maximum temperature is a decreasing linear function of the mixture fraction, as it is obtained from the weighted average of the enthalpies of the undiluted, reacted charge and the inert flow. This condition has been classified in the literature as the subadiabatic regime, since the enthalpy of the inert gases is lower than the enthalpy of the reactants (Libby and Williams, 1983). It refers to conditions which are used in some experimental works (Puri and Seshadri, 1987; Smookeet al., 1990) and in some theoretical studies (Libby and Williams, 1982, 1983; Seshadri, 1983) in order to analyze the behavior of a counter-flow reactor with homogeneous air–fuel flow impin- ging on a hot inert flow.
The most important result of these papers is that they show the occurrence of premixed flame extinction. Furthermore, an abrupt displacement of the reaction zone from the reactant side to the inert side is also related to this transition (Libby and Williams, 1982), which separates the subcritical and supercritical regimes. In Figure 3.8, the vertical black bar in the lower part of the figure (heat release) and the dash-dot
2400
Tign
t = 0.4 s 1800
1200 600
25 cm/s
100 cm/s 55 cm/s
Mixture fraction, Z
0 0.2 0.4 0.6
p = 1 atmΦlean
0.8 1
Heat release (cal/s/cm3)
1700
20 40 60 80 100
0
Temperature (K)
Figure 3.9 Frozen inlet temperature, maximum temperature, autoignition temperature, and heat release rate as function of the mixture fractionZfor different strain rates for a superadiabatic case.
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.