Transition from tribrachial edge flame to MILD combustion

5.1 Overall characteristics

5.1.2 Transition from tribrachial edge flame to MILD combustion

U₀ [m/s]

Se/SR,0 SR,0 [m/s]

5 6 7 8 9 10 11 12

1 6 11

0 1 MILD 2 (concave) Tribrachial MILD

(convex)

Figure 5.3: S_e/S_R,0 andS_R,0 for the autoignited laminarn-heptane lifted jet flames with X_F,0 = 0.02 and T₀ = 1025 K for various fuel tube exit velocities, U₀.

tribrachial edge flame mode follows the conventional stabilization theory for the non- autoignited lifted flames [12, 13]. Here, S_R,0 increases with increasingU₀ simply because the mixture condition at the flamebase,ξ_fb, becomes closer to the stoichiometric mixture, ξ_st (=0.494), with increasing U₀ (see Fig. 5.1a). For the lifted flame with the MILD combustion mode at U₀ = 6.7 m/s, S_e becomes significantly larger than S_R,0, which indicates that autoignition starts to contribute to its stabilization by enhancing S_e.

It is also readily seen thatS_e/S_R,0 increases slightly with increasing U₀ for the MILD combustion mode with a convex flame shape along the jet centerline while it significantly increases toO(10) for the MILD combustion mode with a concave flame shape along the jet centerline (see III and IV in Fig. 5.1b). This result implies that the effect of autoigni-

Figure 5.4: Temporal evolutions of T [K] (left half) and heat release rate [J/m³s] (right half) for autoignited laminar lifted n-heptane jet flames with (a) U₀ = 4.5 m/s and (b) U₀ = 8 m/s. The dashed line represents the stoichiometric mixture fraction isoline, ξ_st (= 0.494). The solid lines represent temperature isolines of which T = T₀+ ∆T, where

∆T = 10 and 40 K.

and 8.0 m/s cases, which represent the tribrachial edge flame and MILD combustion modes, respectively. To identify temperature increase upstream of the flamebase, two temperature isolines of which T =T₀+ ∆T are also plotted in the figure, where ∆T is 10 or 40 K.

It is readily observed from Fig. 5.4 that for both tribrachial edge flame and MILD combustion modes, an ignition kernel is first generated further downstream of z_ξst, from which a combustion wave emanates and propagates upstream. For the tribrachial edge flame, the combustion wave is found to first propagate upstream along the centerline since its S_e is large enough to overcome upcoming flow velocity,U, while traveling along the centerline. Then, it evolves into a tribrachial edge flame after passingz_ξst and finally

stabilizes at ξ_st isoline where S_e is balanced with U. For the MILD combustion mode, however, the combustion wave rarely propagates upstream, and hence, stabilizes nearly the same location where the ignition kernel develops, which implies that autoignition plays a critical role in stabilizing the lifted jet flame with MILD combustion mode.

The two different flame stabilization mechanisms may also be identified by examining temperature increase upstream of the flamebases. It is readily observed from Fig. 5.4 that for both flames, a noticeable increase of temperature occurs upstream of the lifted flames while propagating upstream. However, as the tribrachial edge flame approaches its stabilization location, temperature rarely increases upstream of the flamebase while there still exists a significant temperature increase upstream of the flamebase for the MILD combustion mode. These results imply that autoignition affects the stabilization of the lifted flame with MILD combustion mode. For the tribrachial edge flames, however, autoignition affects the propagation of the combustion wave but has no direct effect on its liftoff height.

It is worth mentioning that there exists a region downstream of z_ξst (‘A’ in Fig. 5.4b) where temperature increase by autoignition process is relatively small (i.e. ∆T < 40 K).

Although the pre-heating effect of the mixture on S_e may exist in this region, it is not significant to overwhelm the decreasing tendency of S_e along the axial direction due to the decrease of ξ (not shown here). In other words, the temperature increase in Region A is not large enough for the lifted flame to be stabilized by autoignition. However, the lifted flame cannot have a tribrachial edge flame mode in Region A because it is located downstream of z_ξst. Due to the existence of Region A under the present temperature condition, the lifted flame is stabilized either at ξ_st isoline as a tribrachial edge flame under the relatively-low U₀ or further downstream of z_ξst as a lifted flame with MILD combustion mode under the relatively-high U₀. The contribution of autoignition to the flame stabilization is predominant for the MILD combustion mode while it is marginal for the tribrachial edge flame mode.

Based on the above results, we schematically describe in Fig. 5.5 the flame stabilization mechanism for autoignited laminar liftedn-heptane jet flames atT₀ = 1025 K, which can provide a heuristic argument for the liftoff height characteristics of the jet flame including

the hysteresis. Note that the figures on the left represent the iso-velocity and iso-mixture fraction lines on the r −z space upstream of z_ξst, which are based on the well-known stabilization criterion for laminar lifted jet flames with Sc_F > 1 under non-autoignitive condition [12–14]. The figures on the right represent the edge flame speed, S_e, and the upcoming flow velocity, U, profiles downstream of z_ξst along the centerline. It is of importance to note thatS_e downstream ofz_ξst is found to exhibit a ‘U-shape’ profile with respect toz. This is because S_einitially decreases with z where the effect of autoignition on the enhancement of S_e is marginal (i.e., region A shown in Fig. 5.4), whileS_estarts to increase withzfarther downstream where the effect of autoignition on the enhancement of S_e becomes significant. It is also noted thatU downstream ofz_ξst continuously decreases with z along the centerline.

For U₀ ≤ 6.5 m/s (Figs. 5.5a and 5.5b), the lifted flame can be stabilized along the ξ_st isoline due to the relatively-low U₀ (Fig. 5.5a). As discussed in Fig. 5.4a, an ignition kernel generated downstream ofz_ξst can approachξ_st isoline under this condition because S_e is always larger than U downstream of z_ξst (Fig. 5.5b).

For 6.7 ≤ U₀ ≤ 7 m/s in which the hysteresis curve of H_L is observed (Figs. 5.5c and 5.5d), the lifted flame still does not reach its conventional blow-off criteria based on non-autoignitive condition. Therefore, a stationary lifted flame can exist along the ξ_st isoline when U₀ is increased from a lower value (Fig. 5.5c). It also indicates that S_e is larger than U at z_ξst. Based on this, we can predict S_e and U profiles downstream of z_ξst (Fig. 5.5d), from which it is expected that there are two possible flame stabilization points downstream of z_ξst; one is unstable and the other is stable. For instance, when lifted flames are perturbed to move downstream from these points, one at the unstable point would continue to move toward downstream (S_e < U) whereas one at the stable point is pulled back to its original position (S_e > U). In this regard, we observe two stable lifted flames under this region depending on the direction of change of U₀.

ForU₀ >7 m/s (Figs. 5.5e and 5.5f), the lifted flame already approaches its conven- tional blow-off criterion under non-autoignitive condition such that no stationary lifted flame can exist upstream ofz_ξst without the assistance of autoignition (Fig. 5.5e). Again, this indicates that U is higher than S_e at z_ξst. Thus, only one stable stabilization point

(f) U > 7 m/s, z > ξ_st

Velocities

z along centerline

ξ_st

U S_e

Ignition kernel

z

z

^Stable

z

U = S_e,st

r

ξ_st(S_e = S_e,st) (a) U₀≤ 6.5 m/s, z <

z

_ξst

ξ_st

z

(b)

Stable

U

z along centerline

z

ξ_st

Velocities

S_e zξ_st Propagation

(b) U₀≤ 6.5 m/s, z >

(d) 6.7 ≤ U ≤ 7 m/s, z > ξ_st Unstable

Stable

z along centerline

ξ_st

Velocities

z

S_e U

z

Ignition kernel

Ignition kernel

z

U = S_e,st

r

_ξ

st(S_e = S_e,st)

z

_ξ

st

ξst

z

r

_{U = S}

e,st ξ_st(S_e = S_e,st) (c) 6.7 ≤ U ≤ 7 m/s, z < zξ_st

(e) U > 7 m/s, z < zξ_st

(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 < z_ξst and (right) z > z_ξst.

can exist farther downstream of zξst under this region (Fig. 5.5f).