7.2 Flame stabilization and extinction
7.2.3 Flame stabilization: transport budget analysis
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].
Transport budget [kg/m3 s] YOH
0.90 0.95 1.00 1.05 1.10
-0.4 -0.2 0.0 0.2 0.4
0.0E+00 3.0E-04 6.0E-04 9.0E-04
XF,0 = 0.5, a = 10 s-1 (a)
D + R R
Dt
Dn C
r/R along ξe
Transport budget [kg/m3 s] YOH
1.65 1.70 1.75 1.80 1.85
-0.2 -0.1 0.0 0.1 0.2
0.0E+00 3.0E-04 6.0E-04 9.0E-04
(b)
D + R
Dt C
Dn
R XF,0 = 0.5, a = 30 s-1
Figure 7.10: Profiles of convection, diffusion in tangential and normal directions, and chemical reaction terms along the ξe isoline for steady counterflow nonpremixed flames of CH4/He versus air with XF,0 = 0.5 at ag = (a) 10 and (b) 30 s−1.
study, hydroxyl radical (OH) is adopted for the analysis since it is often used as a flame marker [30, 34, 35].
Figure 7.10 shows the profiles of C,Dt,Dn, andR along theξe isoline for the steady counterflow nonpremixed flames of CH4/He versus air with XF,0 = 0.5 at ag = 10 and 30 s−1 . It is readily seen that the net value of D + R is negative at the flame edge region (see the grey area), indicating that the diffusive loss of heat and radicals is greater than the chemical reaction at the reaction zone, which consequently induces a negative Se at the flame edge. However, the flame stabilization is achieved by the balance between the positive C and the negative D + R. In other words, the stabilization of the edge flame in a counterflow burner is mainly achieved by the convection of heat and radicals from the trailing diffusion flame to the outer edge flame, which is consistent with the results of a previous study with a 3-step global chemical mechanism [46]. It is also found that the relative contribution of C to the species transport budget increases with increasing ag, and as such, the radial stabilization location of the edge flame is also increased with ag. The diffusive loss in the normal direction is the major loss mechanism of OH, which is also consistent with [46].
XHe
Transport budget [kg/m3 s] re/R
0.45 0.50 0.55 0.60
-0.2 -0.1 0.0 0.1 0.2
0.85 0.90 0.95 1.00 1.05
D + R
ag = 10 s-1 R
C re/R
D
Figure 7.11: Variations of convection, diffusion, chemical reaction terms at the flame edge, and re/R as a function of XHe for steady counterflow nonpremixed flames of CH4/He versus air at ag = 10 s−1.
Note that C exhibits a relatively-large positive value at the flame edge in Fig. 7.10 because local gas flow moves from burnt to unburned mixture, which is a distinct feature of the counterflow nonpremixed flame. For outwardly-propagating flames such as a 1-D premixed flame [17] and a laminar lifted flame in a jet [18, 96, 110], the role of convective flow is to de-stabilize the flame front such that the relative contribution of C to the species transport equation is generally negative at the flame front.
The edge flame stabilization characteristics of counterflow nonpremixed flames at low strain rates are further examined in terms of XHe. Figure 7.11 shows the variations of re/R, and C, D, and R at the flame edge as a function of XHe for steady counterflow nonpremixed flames of CH4/He versus air atag = 10 s−1. It is readily observed thatre/R decreases with the increase of He dilution or XHe, which implies that the counterflow flame may achieve its stabilization by reducing the flame length as the flame intensity is reduced with increasingXHe, as will be discussed below.
As the flame length decreases with increasing XHe, R at the flame edge increases while both D and C decrease. The local mole fractions of reactants at a given ξ isoline increases with decreasingr due to the finite nozzle size of the burner and the dilution by the curtain flow, and hence, the reactivity of the mixture represented by R is enhanced with decreasing re/R, which plays a positive role in stabilizing the flame. However, since the diffusive loss term at the flame edge is inversely proportional to the flame length [143], the magnitude of negativeDalso increases with decreasingre/R. Meanwhile, the contribution ofCto the species transport equation slightly decreases with decreasing
re/Rbecause the radial velocity is linearly proportional tor (see Fig. 7.4). Therefore, the counterflow flame achieves flame stabilization by shrinking its flame length toward the center of the flow where the reactivity of the mixture is high enough to sustain the flame.
However, this is feasible only when the positive effect (i.e., increasing reactivity of mixture at the flame edge) can compensate for the negative effects (i.e., increasing/decreasing conductive/convective heat and mass transfer) with decreasing the flame length.