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.
6.2 Ignition dynamics upstream of turbulent lifted
radical diffusion to the CEM, which are expressed as:
ϕω =be·ω; ϕs=be·s. (6.2)
The ratio of ϕs to ϕω is then defined as a local combustion mode indicator, α ≡ ϕs/ϕω, which represents the relative importance of diffusion to chemical reaction in an ignition process and describes three different local combustion modes: 1)α >1: a local diffusion (or assisted-ignition) mode where diffusion dominates the chemical reaction; 2) |α| < 1 : a local ignition mode where chemistry plays a dominant role; 3) α < −1 : a local extinction mode where the diffusion dominates and works against the chemical reaction process [112].
To understand the fundamental characteristics of the local combustion mode, we test two 1-D laminar premixed H2/air flames with different inlet temperatures, T0, of 850 and 950 K, of which inlet mixture compositions are specified as the stoichiometric H2/air mixture with XF,0 = 0.65, similar to those of 3-D DNS cases (i.e. Cases M and H). Figure 6.9 shows the profiles of ϕω, ϕs, and T colored by α for the two laminar flames with inlet velocity, U0, and induction length, L. Here, L denotes the distance from the inlet to the fixed flame position where T = T0 + 400 K as in [89, 112]. In previous studies [89, 112], it was revealed that the flame stabilization mechanism of 1-D premixed flames can be changed by variations in T0, U0, and L. In the present study, these parameters are systematically varied such that the combustion wave in Fig. 6.9a represents an ignition front (T0 = 950 K, L = 0.02 m, U0 ≫ SL) whereas that Fig. 6.9b represents a conventional deflagration wave with negligible contribution from autoignition (T0 = 850 K, L = 2 m,U0 ≈SL).
Upstream of the ignition front in Fig. 6.9a, the magnitude of ϕω is greater than that of ϕs such that a local ignition mode prevails with |α| < 1. On the other hand, α indicates a local diffusion mode with α > 1 upstream of the conventional deflagration wave (Fig. 6.9b) except for the location near the flame front, which implies that the initial mixture with T0 = 850 K is forced to ignite by back-diffusion of heat and radicals from the flame. In this regard, the local combustion mode analysis with α is useful for
T/1000 [K] Projections to CEM
-10 -5 0 5
1.0 1.2 1.4
-1.0 -0.5 0.0 0.5 1.0
φs
φw
ignition front
Diff
λe = 0 Ign
(a) T
0 = 950 K, L = 0.02 m
x from xf [mm]
T/1000 [K] Projections to CEM
-2 -1 0 1
0.8 1.0 1.2 1.4
-1.0 -0.5 0.0 0.5 1.0
φs φw
T0 = 850 K, L = 2 m
Diff
λe = 0 Ign
(b)
deflagrative wave
Figure 6.9: Profiles of T, ϕω, and ϕs for 1-D H2/air laminar premixed flames with (a) T0 = 950 K, L = 0.02 m, U0 ≫ SL and (b) T0 = 850 K, L = 2 m, U0 ≈ SL. The profile of T is colored byα, and the non-explosive region with λe <0 is excluded.
elucidating the ignition characteristics upstream of turbulent lifted flames as in [124,125].
Figure 6.10 shows the instantaneous isocontour of α in the z = 0 mm plane for all DNS cases, corresponding to those in Fig. 6.3. Note that α at weak or non-explosive regions (i.e. λe≤1) is excluded from the figure. For Case L, the CEM first appears just upstream of the flamebase sinceTc for Case L is considerably lower than the autoignition limit. For Case M, although CEM exists at lean mixture, its Tc is still not high enough such thatα shows either the local diffusion (α >1) or extinction modes (α <−1). Note that the isocontours of α for Cases L and M exhibit a local ignition mode (|α|<1) near the flamebase, which is primarily attributed to the thermal and radical diffusion from the flame, similar to the characteristics ofαin a conventional deflagration shown in Fig. 6.9b.
Therefore, these results substantiate that there is no contribution of autoignition to the flame stabilization for Cases L and M.
For Case Ig, α exhibits a local ignition mode with |α| < 1 along fuel-lean mixtures upstream of the flamebase as expected [34]. This is simply because Tc for Case Ig is much higher that the autoignition limit. For Case H, however, even though its Tcslightly exceeds the autoignition limit, the characteristics ofαupstream of the flamebase resemble
Figure 6.10: Instantaneous isocontours ofαin thez = 0 mm plane for all 3-D DNS cases.
The solid and dashed lines represent the isolines of YOH = 0.002 and ξst, respectively. α with λe ≤1is excluded.
those in Case M rather than those in Case Ig, which indicates that autoignition may not affect the flame stabilization of Case H. It is worth mentioning that for Case H, the local ignition mode with |α| < 1 appears in the near field of the jet and rapidly disappears as it is convected downstream (see ‘I’ in Fig. 6.10c), which consequently causes the non- monotonic behavior of heat release near the inlet as shown in Fig. 6.5a.
To further investigate the characteristics of the local combustion mode of Case H especially in the near field of the jet, the instantaneous 3-D snapshots ofα, the magnitude of vorticity,|ω|, andT near the region ‘I’ are shown in Fig. 6.11. Instantaneous streamlines are also shown in Fig. 6.11a to identify vortex structures. The regions with λe ≤ 1 are excluded from the figure. It is apparent from the figure that the transition of α from the local ignition to local extinction mode coincides with the roll-up of vortex in the jet shear layer, which is also identified by the streamlines in Fig. 6.11a and by the significant increase of |ω| in Fig. 6.11b. It is also of importance to note that the development of vortices leads to an approximately 20 K temperature drop of the reactive mixture as shown in Fig. 6.11c. As discussed above (see Fig. 6.2), Tc of Case H is slightly greater than the autoignition limit such that τig,0D significantly increases from τMR even with a small drop in temperature. Under the present condition, the vortex structure readily develops in the jet shear layer due to the shear-driven Kelvin-Helmholtz instability, which subsequently leads to the entrainment of relatively-cold fuel into the reactive mixture.
The overall ignition process is then suppressed by the decrease of local temperature in the
Figure 6.11: Instantaneous snapshots of (a)α, (b) the magnitude of vorticity,|ω|, and (c) temperature profiles for Case H. The solid lines with arrows in (a) represent instantaneous streamlines.
near field of the jet, and thus, the contribution of autoignition to the flame stabilization becomes marginal for Case H.
To statistically evaluate the effect of vortices on the ignition process of Cases H and Ig, the joint probability density functions (PDFs) of the local ignition and extinction modes conditioned on |ω| and χ over the time ranges of 4τj are shown in Fig. 6.12. Note that the regions, where local mixture features a weak or non-explosive (i.e. λe <1) and it is affected by temperature or species diffusion from the flame front (i.e. q >˙ 105 J/m3s), are excluded from the PDF evaluation. Although not shown here, the overall result shows qualitatively a similar trend even with an order of magnitude variation in the threshold value ofq.˙
It is readily observed from Figs. 6.12a and b that for Case H, the local ignition mode with |α|<1is concentrated on relatively-low |ω|of ∼O(104)1/s andχ of < O(10) 1/s, while the extinction mode with α < −1 is distributed over a wide range of |ω| and χ.
Considering the order of magnitude of|ω|within vortices is much larger thanO(104)(see an example in Fig 6.11b), the joint PDF ofα verifies that for Case H, vortices generated within the jet shear layer continually inhibit the development of ignition kernels upstream of the flamebase, and hence, the turbulent lifted flame of Case H is stabilized by flame propagation rather than autoignition.
Figure 6.12: Joint probability density functions (PDFs) of the local ignition mode with
|α|<1 (left) and the local extinction mode with α < −1(right) conditioned on |ω| and χ over the period of 4τj for Case H (top) and Case Ig (bottom).
For Case Ig, however, the local ignition mode with |α|<1 exists within a wide range of |ω| and χ (see Fig. 6.12c) while the local extinction mode is more concentrated on relatively-large values of|ω|compared to that of Case H (see Figs. 6.12b and d). This is nearly opposite to that of Case H. Furthermore, the joint PDF of the local ignition mode exhibits its peak at relatively-high values of|ω|of∼O(106), which indicates that for Case Ig, mixing in vortical regions is favorable to autoignition unlike Case H in the near field of the jet. It is also worth mentioning that for Case Ig, both local ignition and extinction modes co-exist within the vortices depending on the magnitude ofχ. At|ω|= 106 1/s, for instance, the mixture is more likely to exhibit a local ignition mode at relatively-low χ.
Conversely, it is more apt to exhibit a local extinction mode when the order of magnitude of χ becomes greater than O(103) 1/s. This indicates that ignition is favorable within a vortex with relatively-lowχ, consistent with previous studies [39, 126–129].
In summary, vortices generated in the jet shear layer play a different role in the autoignition of H2/air mixture depending on their thermochemical condition. Especially,
vortices are found to inhibit the ignition of H2/air mixture when Tc approaches the autoignition limit. Nevertheless, it is of importance to note that the thermochemical conditions of turbulent H2 jet flames vary depending onT0, Tc, and mixture composition at the inlets, and hence, the ignition dynamics of H2/air mixture within vortices may differ from this study. Moreover, the variations of the jet Reynolds number or turbulence intensity can directly affect the vortex structure generated in the shear layer of turbulent jets, thereby influencing the ignition dynamics of H2/air mixture within vortices. Thus, it is reasonable to expect that the rate at which vortices interact with the mixture would also play a key role in determining ignition dynamics within vortices.
To extend the present result to the different conditions, therefore, we perform an additional parametric study of the ignition dynamics of a nonpremixed H2/air mixture within a rolled-up vortex by varying air temperature (Ta), vortex intensity (Umax), and the timing at which a vortex is introduced in the domain (τv). Note that this additional study adopts a simple 2-D domain instead of using the 3-D jet configuration, not only for computational expediency, but also because the roll of vortices on the ignition of the mixture can effectively be investigated by simple 2-D simulations.