(f) U > 7 m/s, z > ξst
Velocities
z along centerline
ξst
U Se
Ignition kernel
z
z
Stablez
U = Se,st
r
ξst(Se = Se,st) (a) U0≤ 6.5 m/s, z <
z
ξstξst
z
(b)
Stable
U
z along centerline
z
ξstVelocities
Se zξst Propagation
(b) U0≤ 6.5 m/s, z >
(d) 6.7 ≤ U ≤ 7 m/s, z > ξst Unstable
Stable
z along centerline
ξst
Velocities
z
Se U
z
Ignition kernel
Ignition kernel
z
U = Se,st
r
ξst(Se = Se,st)
z
ξst
ξst
z
r
U = Se,st ξst(Se = Se,st) (c) 6.7 ≤ U ≤ 7 m/s, z < zξst
(e) U > 7 m/s, z < zξst
(f)
Stable (d)
Figure 5.5: Schematic for the stabilization of autoignited laminar n-heptane lifted jet flames with T0 = 1025 K for (top) U0 ≤ 6.5 m/s, (middle) 6.7 ≤ U0 ≤ 7 m/s, and (bottom) U0 >7 m/s, and for (left) z < zξst and (right) z > zξst.
can exist farther downstream of zξst under this region (Fig. 5.5f).
Figure 5.6 shows the temporal evolutions of EIs of important variables for the 0-D ignitions of n-heptane/air mixtures with three different equivalence ratios. Overall, the temporal evolutions of EIs of important variables are qualitatively similar to one another regardless of ϕ. HO2 and H2O2 are found to be the most important variables to the CEM during the early stage of ignition while T dominates over other variables after the beginning of thermal ignition at which the EI of T becomes the largest (see red circles in Fig 5.6). For the extremely-lean mixture (ϕ = 0.10), however, its ignition has several distinct features compared to the relatively-rich mixtures. First, its relative importance ofn-heptane to the CEM is lower than those of the other mixtures. Second, the beginning of thermal ignition occurs faster than those of the relatively-rich mixtures although its overall ignition delay is longer than those of the other mixtures. As a result, it takes less time for the extremely-lean mixture to increase T by 10 K than the other mixtures.
Note that the mixture withϕ = 0.1 is not so explosive as compared to the relatively-rich mixtures during the later stage of ignition, and thus,τig0 for ϕ= 0.1 becomes longer than those for the other mixtures.
To further understand the ignition characteristics of the mixtures, the temporal evo- lutions of PIs of important reactions are shown in Fig. 5.7. During the early stage of ignition, n-heptane decomposition to small species including C2H5, HO2, H2O2, H2, and H via its unimolecular decomposition (R245–247) and/or two-body reactions (R248–265) are found to be predominant, and subsequently, C1 and/or C2 oxidation reactions (e.g.
C2H4 → C2H3 (R54, R55, and R86), C2H3 → HCO and/or CH2O (R13), CH2O→HCO (R29–R32 and R52), and HCO →CO (R11 and R44)) become important. Although not shown here, the chain branching reaction of H2O2 + M → OH + OH + M (-R49) also contributes to the CEM.
It is worth mentioning that as ϕ decreases, the two-body reactions of n-heptane molecules become less dominant during the early stage of ignition. Since some of these reactions are endothermic, their heat consumption is relatively small for the extremely- lean mixture during the early stage of ignition, resulting in the advance of its thermal runaway. Note that for the present XF,0 and T0 conditions, the decomposition of C3H7 via C3H7 + M → CH3 + C2H4 + M (R109), preceded by the conversion of n-heptane
Explosive Index, EI
0.00 0.02 0.04 0.06 0.08
0.0 0.2 0.4 0.6 0.8 1.0
C2H4 HO2
H2O2 T
nC7H16
φ = 0.10 (ξ = 0.09)
0.040
(a)
141 K
10 K ∇
∇ 0.040 s
Explosive Index, EI
0.00 0.02 0.04 0.06 0.08
0.0 0.2 0.4 0.6 0.8 1.0
C2H4 HO2
H2O2 T nC7H16
φ = 0.45 (ξMR = 0.3)
385 K
(b) ∇
0.016 10 K∇ 0.044 s
Time [s]
Explosive Index, EI
0.00 0.02 0.04 0.06 0.08
0.0 0.2 0.4 0.6 0.8 1.0
C2H4 HO2
H2O2
T nC7H16
φ = 1.00 (ξst = 0.494)
423 K
(c) ∇
0.012 10 K∇ 0.050 s
Figure 5.6: Temporal evolutions of EIs of important variables for the 0-D ignition of n-heptane/air mixtures with (a) ϕ = 0.1, (b) 0.45, and (c) 1.0. Red circles denote the start of thermal ignition of the 0-D ignitions.
Residence Time [s]
Participation Index, PI
0.00 0.02 0.04 0.06 0.08
0.0 0.2 0.4
(a)0.6
C2H5 → C2H4 + H (-R14) H + O2 → O + OH (R7)
HCO → CO nC7H16 - two body
C2H4 → C2H3 → HCO nC7H16 - unimolecular
φ = 0.10 (ξ = 0.09)
Participation Index, PI
0.00 0.02 0.04 0.06 0.08
0.0 0.2 0.4
(b)0.6 φ = 0.45
(ξMR = 0.3)
nC7H16 - unimolecular nC7H16 - two body
H + O2 → O + OH (R7) C2H5 → C2H4 + H (-R14) C2H4 → C2H3 → HCO HCO → CO
Residence Time [s]
Participation Index, PI
0.00 0.02 0.04 0.06 0.08
0.0 0.2 0.4
(c) 0.6φ = 1.00
(ξst = 0.494)
nC7H16 - unimolecular nC7H16 - two body
H + O2→ O + OH (R7) C2H5 → C2H4 + H (-R14) C2H4 → C2H3 → HCO HCO → CO
Figure 5.7: Temporal evolutions of PIs of important reactions for 0-D ignitions of n- heptane/air mixtures with variousϕ of 0.1, 0.45, and 1.0.
to C3H7, is found to be the most dominant heat consumption reaction during the early stage of ignition. It is also found that the contribution of C2H5 → C2H4 + H (−R14) and the chain branching reaction of hydrogen via H + O2 → O + OH (R7) to the CEM increases with decreasing ϕ such that the relatively-high PI values of −R14 and R7 can be good markers for the ignition of the lean n-heptane/air mixtures. As the residence time increases, HCO + O2 → CO + HO2 (R44) and subsequent CO to CO2 conversion via CO + OH → CO2 + H (R6; not shown here) are two major exothermic reactions under the present condition.
In this time, we perform the CEMA of autoignited laminar liftedn-heptane jet flames with U0 = 6, 8, and 12 m/s and identify their ignition characteristics by comparing the 0-D and 2-D CEMA results. Figure 5.8 shows the EI isocontours of several important variables for the lifted flames with three differentU0, which represent the tribrachial edge flame and MILD combustion modes for relatively-low and high U0, respectively. Several points are noted.
First, it is readily observed from Fig. 5.8a that for the tribrachial edge flame mode (U0 = 6 m/s), the EI of T exhibits relatively-small value upstream of the flamebase as compared to those for the MILD combustion, and hence, there is no temperature increase upstream of the flamebase (see temperature isolines in Fig. 5.8f). Second, the overall contributions of EIs to the CEM have characteristics similar to those in the 0- D simulations, and their 2-D profiles are just spatially elongated with increasing U0. Although the characteristics of autoignition remain nearly invariant with respect to U0, its contribution to flame stabilization changes depending on the location of the flamebase.
Third, while EIs of n-heptane, CH2O, and C2H4 are predominant at a wide range of ξ near the nozzle exit (see Fig. 5.8b, d, and e), the thermal runaway of the lifted flame with MILD combustion starts at very lean mixtures of whichξ is much smaller than that of the most reactive mixture, as shown in Fig. 5.8f. This is consistent with 0-D CEMA results in Fig. 5.6, which indicates that the thermal ignition of n-heptane jet is mainly developed by the lean mixtures at the outside of the jet shear layer, and thus, the coflow velocity could play an important role in determiningHL of the autoignited laminar lifted jet flame as compared to that of the non-autoignited ones.
Figure 5.8: Isocontours of EIs of (a) T, (b) nC7H16, (c) H2O2, (d) CH2O, and (e) C2H4, and (f) temperature for autoignited laminar lifted n-heptane jet flames with U0 = 6, 8, and 12 m/s (XF,0 = 0.02 andT0 = 1025 K). The dashed and dash-dot lines represent the stoichiometric mixture fraction and isolines of Re(λe) = 0, respectively. The solid lines in (f) denote∆T of 10 and 40 K.
Figure 5.9 shows the PI isocontours of several important reactions for the cases in Fig. 5.8. Overall, n-heptane decomposition and C2H5 → C2H4 + H reactions become important to the CEM right after the fuel jet is issued from the nozzle as shown in Fig. 5.9a and 5.9b, which is spatially followed by H + O2 → O + OH (R7; Fig. 5.9c) upstream of the flamebases and in the coflow side. As the flow moves further downstream, H2O2 + M→OH + OH + M (−R49; Fig. 5.9d), C2H4 →C2H3 →HCO (Fig. 5.9e), HCO
→CO (Fig. 5.9f), and CO to CO2 conversion via CO + OH→CO2 + H (R6; not shown here) are found to simultaneously and/or sequentially become important to the CEM at relatively-low ξ. All of the results reveal that the spatial ignition characteristics of the 2-D n-heptane jets are very similar to those of temporal evolution of the 0-D ignition.
However, for the tribrachial edge flame (U0 = 6 m/s), the contribution of each reaction to the CEM is relatively marginal compared to the MILD combustion mode (U0 = 8 and 12 m/s), which verifies that the effect of autoignition on the flame stabilization of the tribrachial edge flame is marginal even if it may exist. Meanwhile, the mixture composition upstream of the lifted flames with MILD combustion is lean (< ξst) such that the ignition process of the MILD combustion can take place in a wide range of radial directions (see Fig. 5.8f). Thus, the flamebase of a lifted flame with MILD combustion mode is determined by competition between local flow velocity and local progress of autoignition, which ultimately lead to a convex or concave flame shape as shown in Fig. 5.1b.