in ξ rather than by T (i.e. dlog10(τig,0D) ≈ (∂log10(τig,0D)/∂ξ)|Tdξ). This is simply because the mixture under this condition is near its lean flammability limit such that the ignition of the mixture is more sensitive to the ξ variation. At ξ > ξMR, on the other hand, the change ofτig,0D is mainly attributed to the decrease ofT whereas the variation inξ shows a negligible impact on τig,0D (i.e. dlog10(τig,0D)≈(∂log10(τig,0D)/∂T)|ξdT).
Third, for Case H τig,0D increases significantly from τMR even with a small decrease of T. This trend is clearly different from that for Case Ig, whereτig,0D exhibits the same order of magnitude with τMR over a wide range of T (or ξ). This is because for Case H, Tc is slightly greater than the autoignition limit such that the reactivity of the mixture significantly decreases with the decrease of T (see Fig. 6.1), implying that the ignition process of a turbulent lifted flame in heated coflows near the autoignition limit (i.e. Case H) can be highly sensitive to temperature variation by turbulent mixing. The effects of turbulent mixing on the ignition of a turbulent lifted jet flame will be discussed later.
Figure 6.3: Instantaneous isocontours of (a) temperature (T), (b) heat release rate (q),˙ (c) scalar dissipation rate (χ), and (d) mass fraction of HO2 (YHO2) for the left branch of the lifted flame in the z = 0 mm plane for Cases L, M, H, and Ig (from left to right).
The solid and dashed lines represent the isolines of YOH = 0.002 andξst, respectively.
shear flow. Since ignition kernels for turbulent jet flames under autoignitive condition tend to form at relatively-lowχ [39, 115, 116], it is reasonable to expect that autoignition in the present DNSs is more likely to occur along theξMR isoline, where bothχ andτig,0D are sufficiently low.
On the other hand, the isocontours of q˙ and YHO2 upstream of the flamebase show distinct features depending on the case. For Cases L, M, and H, vigorous q˙ upstream of the flamebase is observed only within a narrow region near the flamebase, which is in contrast to Case Ig, for which vigorous q˙ occurs over a much broader region upstream of the flamebase (see Fig. 6.3b). Similar to the features of q, the formation of˙ YHO2 occurs farther upstream of the flamebase for Case Ig (see Fig. 6.3d). Since HO2 is one of the most predominant intermediate species generated during the ignition of a H2/air mixture [34, 80, 117–119], it is reasonable to consider that the characteristics of flame stabilization mechanism of the lifted flames near the autoignition limit (Case H) are more likely to be consistent with non-autoignitive turbulent jet flames (Cases L and M) than that of autoignitive turbulent jet flames (Case Ig).
The global characteristics of autoignition process occurring upstream of the lifted flames are now examined by computing the Favre mean of the variables obtained over 4τj and the entire range of z− planes. The profiles of averaged heat release rate,eq, and˙ mass fraction of HO2, YeHO2, along the mean ξst isoline are shown in Fig. 6.4. It is readily observed from Fig. 6.4a that the profiles ofeq˙ for Cases L, M, and H are nearly identical and peak only near their mean liftoff heights, consistent with the above discussion. In contrast, however,eq˙for Case Ig starts to increase from farther upstream of the flamebase, indicating that mixtures upstream of the flamebase for Case Ig are partially burned due to autoignition. It is also readily observed from the profile of YeHO2 in Fig. 6.4b that the accumulation of YeHO2 farther upstream of the flamebase is observed only for Case Ig.
Note that although the fluctuation in hL of the jet flames may influence the averaged profiles in Fig. 6.4, the variations in hL for all cases are found to be approximately 1.0 ∼ 1.5 H, and are similar to one another. Therefore, the distinct heat release and intermediate species formation characteristics upstream of the flamebase for Case Ig are a consequence of autoignition, while for the other cases, the effects of autoignition on the
-3 -2 -1 0 1 2 3 102
104 106 108 1010
Case Ig Case H Case M Case L
(a)
~ ⋅ q [J /m
3s]
x/H from hL/H
-3 -2 -1 0 1 2 3
10-8 10-7 10-6 10-5 10-4
Case Ig Case H Case M Case L
(b)
HO2
~ Y
~
Figure 6.4: Profiles of (a) Favre averaged heat release rate, eq, and (b) Favre averaged˙ mass fraction of HO2, YeHO2, along the mean ξst isoline for all DNS cases.
flame stabilization are marginal.
The flame characteristics for all cases are further elucidated by evaluating the cross- stream conditional Favre mean, ⟨ϕ|ξ∗⟩, of a variable, ϕ, where ξ∗ is the sample space of ξ. Figure 6.5 shows the conditional Favre mean of heat release rate, ⟨q˙|ξ∗⟩, for Cases H and Ig at several different axial positions. Upstream of their mean flamebase location,
¯hL (Fig. 6.5a and b), the peak value of ⟨q˙|ξ∗⟩ for Case H exhibits a non-monotonic be- havior along the axial direction whereas that for Case Ig continually increases. Although the overall magnitudes of ⟨q˙|ξ∗⟩ for both cases initially increase with x, showing their peaks near ξMR, those for Case H significantly decreases at x > 0.2¯hL. Note that q˙ for 0-D homogeneous ignition of H2/air mixture shows a monotonically increasing trend with residence time, and hence, the non-monotonic behavior of ⟨q˙|ξ∗⟩ cannot solely be explained by the homogeneous ignition characteristics of the H2/air mixture. The differ- ence in behavior is related to their ignition characteristics affected by turbulent mixing as previously mentioned.
Downstream of ¯hL, on the other hand, ⟨q˙|ξ∗⟩ for both cases exhibits a similar trend to each other. At x = ¯hL, the peak value of ⟨q˙|ξ∗⟩ occurs between ξMR and ξst, which
<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.