7.2 Flame stabilization and extinction
7.2.2 Flame stabilization: numerical results
The flame stabilization and structure characteristics of counterflow nonpremixed flames at low strain rates are further investigated by performing 2-D transient numerical sim- ulations in zero gravity. As mentioned earlier, the flame edge dynamics of counterflow nonpremixed flames at low strain rates is a key factor determining their stabilization and extinction [45,46], and hence, here we mainly focus on the dynamics of outer edge flames.
According to previous studies [138, 139], the outermost edge flame structure of coun- terflow nonpremixed flames exhibits a blunt shape, which is different from that of the conventional tribrachial edge flame structure in a mixing layer. For the counterflow flame, the direction of local flow velocity at the flame edge is from the burned to the unburned side, while it becomes opposite for the typical outwardly-propagating partially-premixed flame (e.g., lifted jet flame) [1], as shown in Fig. 7.6. The stabilization of a partially- premixed flame is attained by a balance between local flow velocity and the propagation speed of flame edge, and as such, the edge propagation speed of a steady counterflow non- premixed flame should be negative in a coordinate sense (or the edge flame propagates from unburnt to burnt mixture) to balance the local flow velocity [43, 44].
To estimate the edge flame speed in time, the displacement speed of the flame front relative to the flow velocity, Sd, is evaluated. Figure 7.7 shows the temporal evolution of the ignition and stabilization of counterflow nonpremixed flames of CH4/He versus air with XF,0 = 0.5 at two different ag of 10 and 30 s−1. Here, the counterflow nonpremixed flame at ag = 10 s−1 represents a flame at low strain rate, of which characteristics are compared with those at relatively-highagof 30 s−1. Several points are noted from Fig. 7.7.
First, after a successful ignition occurs by a high-temperature ignition source placed at the centerline, an ignition front emanates from the ignition source, exhibiting a bibrachial structure with positiveSe(see the first and second rows in Fig. 7.7). Note that the mixture
Figure 7.6: Heat release rate [J/m3s] isocontours for (a) laminar lifted jet flame from [1]
and (b) counterflow nonpremixed flame of CH4/He versus air with XF,0 = 0.5 at ag = 10 s−1. The dashed-dot line and solid lines with arrows represent stoichiometric mixture fraction isoline ξst, and the streamlines, respectively.
Figure 7.7: Temporal evolution of heat release rate [J/m3s] isocontours for counterflow nonpremixed flames of CH4/He versus air withXF,0 = 0.5 atag = 10 s−1 (left) andag = 30 s−1 (right). The solid and dashed-dot lines represent YOH = 4 × 10−4 and ξe isolines, respectively, at a given t.
fraction isoline passing through the flame edge,ξe, is slightly lower thanξst of 0.068, which may be attributed to the velocity gradient ahead of the flame edge [1, 111].
Second, as the ignition front propagates outward, it reaches its flammability limit and becomes an extinction front exhibiting a monobrachial structure with negative Seat r/R ∼ 1.10 and 1.55 for ag = 10 and 30 s−1, respectively. Note that we calculate the unstrained laminar flame speed, SL0, of CH4/He/air mixture along the ξe isoline based on the steady solutions of the nonreacting counterflow of CH4/He versus air with XF,0
= 0.5 at ag = 10 and 30 s−1. It is found that even for the nonreacting cases, the local fuel mole fraction along the ξe isoline keeps decreasing withr due to the dilution by the curtain flow, and as such, SL0 decreases withr along theξe isoline. Ultimately,SL0 cannot be determined beyondr/R∼1.18 and 1.65 for ag = 10 and 30 s−1, respectively, because the mixtures reach their flammability limit. The radial locations of the flammability limit predicted by SL0 are found to be nearly identical to those at which the edge flame becomes an extinction front with negative Se. This result indicates that the transition of the edge flame from an ignition front to an extinction front is primarily attributed to the increasing degree of He dilution by the curtin flow, while the effect of local strain rate, a, on the transition would be marginal because a is reduced along the r-direction near the flammability limit.
Third, there exists a period during which the edge flame still moves radially outward even after it turns into an extinction front with negative Se (see the third and fourth rows in Fig. 7.7). This is because Ue, of which magnitude is greater than that of Se, pushes the edge flame radially outward. During this period, the magnitude of Se keeps increasing with r, and hence, the counterflow flame starts to shrink once the magnitude of Se becomes greater than that of Ue. Finally, the edge flame is stabilized at a location where the magnitude of Se matches that of Ue.
It is of interest to note that even though the radial locations of two flame edges of I and II in Fig. 7.7 are nearly the same, the flame structure changes from a bibrachial edge flame with positive Se to a monobrachial edge flame with negative Se, indicating that there exists a transition of the flame behavior during the ignition and stabilization process. To investigate such a transition of flame behavior, the profiles of several species
Mass fractions
0.7 0.8 0.9 1.0 1.1 1.2 1.3
0.0E+00 1.0E-01
OH × 100
CH4 H2O
XF,0 = 0.5, ag = 10 s-1 t = 60 ms CO2
(a)
r/R along ξe
Mass fractions
0.7 0.8 0.9 1.0 1.1 1.2 1.3
0.0E+00 1.0E-01
OH × 100
CH4 H2O
XF,0 = 0.5, ag = 10 s-1 Steady state CO2
(b)
Figure 7.8: Profiles of CH4, CO2, H2O, and OH mass fractions for CH4/He versus air counterflow nonpremixed flames with XF,0 = 0.5 and ag = 10 s−1 along the ξe isoline at two different t: (a) t = 60 ms, and (b) steady state. The vertical dashed line represents the radial flame edge position.
mass fractions along the ξe isoline for the two edge flames are shown in Fig. 7.8. When the edge flame is an ignition front (see Fig. 7.8a), the mass fractions of reactants ahead of the edge flame are large enough such that the edge flame can propagate radially outward with positive Se. Once the edge flame reaches its flammability limit, however, a large amount of combustion products is convected toward the unburned region such that the fuel concentration ahead of the edge flame is reduced by the addition of combustion products (Fig. 7.8b). Consequently, the mixture composition ahead of the flame edge consists of relatively-small amount of reactants and relatively-large amount of combustion products such that the edge flame turns into an extinction front with negative Se.
For a partially-premixed flame propagating toward reactants such as a lifted flame in a jet and a flame spread in a mixing layer [14, 107], the mixture composition upstream of the flame is not generally affected by combustion product such that local flow and mixing information upstream of the flame can be uniquely determined as a function of its spatial coordinates [14, 140, 141]. For nonpremixed flames in a counterflow burner, however, a large amount of combustion product is transported into the unburned mixture such
Speed [cm/s] re/R
50 100 150 200
-20 -10 0 10 20
0.0 0.5 1.0 1.5
-Ue,n
XF,0 = 0.5, ag = 10 s-1 re/R
Se
III I
II (a)
Time, t [ms]
Speed [cm/s] re/R
20 40 60 80 100
-30 -15 0 15 30
0.0 0.5 1.0 1.5 XF,0 = 0.5, ag = 30 s-12.0 Se
-Ue,n
re/R
I
II III (b)
Figure 7.9: Temporal evolutions of Se, −Ue,n, and re/R for counterflow nonpremixed flames of CH4/He versus air with XF,0 = 0.5 at (a) ag = 10 and (b) 30 s−1. Three different regimes are denoted by: (I) outwardly-propagating bibrachial edge flame, (II) outwardly-propagating monbrachial edge flame, and (III) retreating-monobrachial edge flame.
that the mixture composition ahead of the flame edge cannot be uniquely determined, resulting in the transition of flame behavior such as flame structure and Se for r.
To quantitatively understand the characteristics of the edge flame dynamics, the tem- poral evolutions of re/R, Se, and −U⃗e·⃗n for the two cases are shown in Fig. 7.9. Here, re/R and ⃗n represent the normalized radial location of the flame edge and the flame surface normal vector at outward direction, respectively. Thus, −U⃗e ·⃗n indicates the projected local gas velocity at the flame edge toward the inward direction (i.e., from unburned to burnt side), which is henceforth denoted as −Ue,n. As such, the difference between Se and −Ue,n orSe+Ue,n at a given t represents the net displacement speed of the edge flame toward the outward direction.
The characteristics of the flame edge structure can be classified into three different regimes: (I) an outwardly-propagating bibrachial edge flame regime whereSeandSe+Ue,n are both positive; (II) an outwardly-propagating monobrachial edge flame regime where Se is negative and Se+Ue,n is still positive; (III) a retreating-monobrachial edge flame
regime where both Se and Se+Ue,n are negative. As discussed earlier, the edge flame initially exhibits a bibrachial structure and propagates toward the unburned mixture (Regime I), which is consistent with the typical partially-premixed flame structure with large fuel concentration gradient [107]. As the edge flame reaches its propagation limit due to dilution, the bibrachial edge flame structure changes to a monobrachial edge flame structure andSebecomes negative. However, the magnitude ofSeis still smaller than that of−Ue,nsuch that the edge flame moves radially outward (Regime II). SinceSeat Regime II keeps decreasing with r and eventually its magnitude becomes larger than −Ue,n, the edge flame starts to retreat (Regime III). The magnitude of Se tends to decrease with decreasingr such that the edge flame is finally stabilized at a location where Sebalances
−Ue,n.
Note that Regime III nearly vanishes for the case at ag = 30 s−1. The flame edge moves to relatively-large r by relatively-high Ue (see Fig. 7.7), where the mixture is affected by the curtain flow, and hence, the degree of dilution and the resultant value of Se can significantly change with r such that the balance between Se and −Ue,n can be quickly attained.
The sensitivity of the edge flame propagation characteristics to the ignition source is also examined by performing additional 2-D simulations for several different ignition source temperatures, Tign. A uniform temperature profile within the ignition source is adopted for the simulations. The result demonstrates that the characteristics of the edge flame propagation do not change much withTign once the ignition successfully occurs by the ignition source. Note that the effects of the temperature profile of the ignition source and the ignition energy deposition time on the qualitative trend of the edge flame prop- agation characteristics are expected to be marginal, similar to the results of a previous study [142].