<qξ* > [J/m3 s]
0.0 0.2 0.4 0.6 0.8 1.0
0.0E+00 1.0E+01 2.0E+01 3.0E+01 4.0E+01
⋅
ξMR ξst
(a)
x ↑
Case H x = 0.1hL x = 0.2hL x = 0.3hL x = 0.4hL
<qξ* > [J/m3 s]
0.0 0.2 0.4 0.6 0.8 1.0
0.0E+00 5.0E+04 1.0E+05 1.5E+05 2.0E+05 2.5E+05
⋅
ξMR ξst
(b)
x ↑
Case Ig x = 0.1hL
x = 0.4hL x = 0.3hL x = 0.2hL
Mixture fraction, ξ*
<qξ* > [J/m3 s]
0.0 0.2 0.4 0.6 0.8 1.0
0.0E+00 1.0E+09 2.0E+09 3.0E+09 4.0E+09 5.0E+09
⋅
ξMR ξst
(c)
Case H
x = 4.0hL x = 1.0hL x = 1.5hL x = 3.0hL
Mixture fraction, ξ*
<qξ* > [J/m3 s]
0.0 0.2 0.4 0.6 0.8 1.0
0.0E+00 1.0E+09 2.0E+09 3.0E+09 4.0E+09 5.0E+09
⋅
ξMR ξst
(d)
Case Ig x = 1.0hL x = 2.0hL x = 3.0hL x = 4.0hL
Figure 6.5: Conditional Favre mean of heat release rate, ⟨q˙|ξ∗⟩, for Case H (left) and Case Ig (right) upstream of ¯hL (top) and (b) downstream ofh¯L (bottom).
is consistent with the results observed from Fig. 6.3. Within a jet width downstream of the flamebase (h¯L ≤ x ≤ 2¯hL), the profile of ⟨q˙|ξ∗⟩ shifts toward fuel-rich mixtures while the order of its peak magnitude remains nearly constant. Farther downstream of the flamebase (x >2.0¯hL/H), the vigorous heat release near the flamebase subsides, and is followed by heat release corresponding to a stoichiometric nonpremixed and fuel-rich premixed flames. Hence, the overall magnitude of ⟨q˙|ξ∗⟩ decreases exhibiting two peaks:
one centered near ξst and the other centered in the fuel-rich mixture.
Se/SL ≈ 1 indicates flame propagation [1, 34, 35, 96, 99]. We track the location of the flamebase by segmenting the data into z planes and then identify the local flamebase as the most upstream point on the YOH = 0.002 isoline. Although this is a simple segmentation method and contains some degree of uncertainty, it can effectively pinpoint outliers for whichSeis much greater thanSL. Note thatξof the flamebase,ξfb, is different from sample to sample such that Se of each sample is normalized by the corresponding SL for which ξ is identical to ξfb.
SL is estimated from 1-D transient reactive simulations as in [79, 90, 91, 96]. To aid understanding of the SL calculation, the temporal evolution of Sd∗ at the flame front of the 1-D combustion wave for the H2/air mixture is shown in Fig. 6.6a. Here, the initial mixture and temperature conditions are identical to those of ξMR for Case Ig.
The temporal evolution ofT and YHO2 farther upstream of the combustion wave are also shown in Fig. 6.6b to represent the spontaneous ignition of the unburnt mixture. It is readily observed from Fig. 6.6a that there exists a period during which Sd∗ of the flame front is nearly constant with the effect of initial forced ignition on the combustion wave vanishing (i.e., 0.2 < t/τig,0D < 0.8). Thus, Sd∗ during this period can be considered to be SL. It is worth mentioning that the significant increase of Sd∗ during the final stage of combustion (i.e., t/τig,0D > 0.8) coincides with the increase of temperature of the unburned mixture, while the formation of the intermediate species such as HO2, which precedes thermal runaway, marginally affects Sd∗. This implies that the enhancement of the flame propagation speed of the H2 lifted jet flame due to the partially-reacted mixture upstream of the flamebase is mainly attributed to the temperature increase of the unburnt mixture, rather than the accumulation of intermediate species.
Figure 6.7 shows the scatter plot ofSe/SL as a function ofχfor all cases. The number of samples for all cases is equal to 6000. The conditional mean of Se/SL denoted by a dashed-dot line is also shown in the figure. The samples for whichSe/SL>3are denoted by a diamond symbol to highlight that Se is much greater than the corresponding SL. In general, the mean values of Se/SL exhibits a decreasing trend with χ consistent with previous studies [120–122]. Note that at relatively-large χ, Se/SL generally exhibits a large negative value. This is because the flamebase situated at large χ typically resides
Sd
* [m/s]
0.0 0.2 0.4 0.6 0.8 1.0
20 40 60 80 100
ξMR for Case Ig
Diffusive limit (Sd* ≈ SL) At flame front
(a)
(T = 1066 K, ξ = 0.05)
t/τig,0D
T [K]
0.0 0.2 0.4 0.6 0.8 1.0
1070 1085
0.0E+00 8.0E-05
HO2Y (b) ξ
MR for Case Ig (T = 1066 K, ξ = 0.05)
Ignition process of unburned mixture
Figure 6.6: Temporal evolution of (a) Sd∗ at the flame front and (b) T and YHO2 farther upstream of the flame front for the 1-D premixed H2/air flames. The initial mixture and species conditions are the same as those at ξMR for Case Ig.
in a developing shear layer such that it recedes toward the burnt mixture [43].
It is also of interest to note that for Case Ig, the magnitude of the conditional mean of Se/SL at moderate χ (i.e. 10 ∼ 100 1/s) is approximately unity, similar to those for the other cases. This is in contrast to the previous DNS results of DME [38] and n-dodecane [123] jet flames under autoignitive conditions, from which it was found that Se under autoignitive condition is significantly larger than SL due to partially-reacted mixture upstream of the flamebase. This difference may be attributed to peculiarities of the ignition process of H2/air mixtures which undergo ignition largely through chain branching reactions at nearly isothermal conditions, and therefore, have little effect on the enhancement ofSe. This has already been demonstrated in Fig. 6.6 that the propagation speed of the combustion wave is nearly constant until the temperature of unburnt mixture starts to increase after t/τig,0D = 0.8. However, during the ignition of DME/air and n- dodecane/air mixtures under high pressures, the increase of temperature occurs much earlier than τig,0D due to the multi-stage ignition characteristics of hydrocarbon fuels.
Thus, it is reasonable to expect that the enhancement of Se for turbulent H2 jet flame assisted by a partially-reacted mixture is not as remarkable as that for turbulent DME
χ [1/s]
Se/SL
100 101 102 103
-10 -5 0 5 10
χ [1/s]
Se/SL
100 101 102 103
-10 -5 0 5 10
χ [1/s]
Se/SL
100 101 102 103
-10 -5 0 5
10 Case Ig
D
(d) E
Case L A
(a) Case M
B (b)
χ [1/s]
Se/SL
100 101 102 103
-10 -5 0 5
10 Case H
C (c)
Figure 6.7: Scatter plot ofSe/SL as a function of χ for (a) Case L, (b) Case M, (c) Case H, and (d) Case Ig. Samples with Se/SL > 3 are highlighted by diamond symbols. The dashed-dot lines represent the conditional mean ofSe/SL.
orn-dodecane jet flames, and consequently, the conditional mean value ofSe/SL for Case Ig is similar to the other cases.
Nonetheless, it is worth mentioning that for Case Ig, the number of samples with Se/SL > 3 is notably larger than for the other cases, which implies that both flame propagation and autoignition modes contribute to the flamebase stabilization, and co- exist for Case Ig. For Cases L, M, and H, however, there also exist a few samples where Se/SL>3, and hence, it is needed to clarify that autoignition cannot significantly affect their flame stabilization. For this purpose, we select five samples (A – E) in Fig. 6.7 and investigate their flamebase dynamics.
Figure 6.8 shows the snapshots of flame fronts of A – E represented by the isosurface of YOH = 0.002 at three different times. The isosurfaces are colored by Sd to highlight the local acceleration of Se. It is readily observed from the figure that the acceleration of Se for all the samples in Cases L, M, and H is primarily attributed to flame merging by the spanwise movement of the flame fronts: at first, two separate flame fronts develop along the spanwise direction (the first row of Figs. 6.8a–c), and then, they approach each other (the second row of Fig. 6.8a–c), consequently leading to flame merging. When two flame fronts merge, the gradient of YOH between them vanishes, resulting in a significant
Figure 6.8: Temporal evolution of the flame front for the five selected samples in Fig. 6.7, represented by the isosurface,YOH = 0.002. The isosurfaces are colored by Sd.
increase in Sd (the third row of Fig. 6.8a–c). Thus, autoignition does not contribute to the flame stabilization for Cases L, M, and H. For Case Ig, however, two ignition kernels pinched-off from flame fronts first develop, and then, evolve into another flame fronts (see Fig. 6.8d). Therefore, it can be concluded that for Case Ig, the lifted flame is stabilized by local intermittent autoignition together with flame propagation from the base of the lifted jet flame.