3.4 Effects of fuel composition and initial temperature RMS
3.4.3 Front speed and burning rate
(greenish region) becomes order of unity because the mixing process (χin Fig. 3-10d) shows the same order of magnitude as the chemical explosion process (λein Fig. 3-10a). These results also indicate that the reaction fronts of Case 3 are deflagrations rather than spontaneous ignitions.
It is also of interest to note from Fig. 3-10d that the reaction fronts mostly overlap with the strips with relatively large χ, a feature of deflagration waves propagating through unburned mixtures prior to the occurrence of auto-ignition.
3.4 Effects of fuel composition and initial temperature RMS most energetic length scale, le, in the two-dimensional DNS cases and the mean and RMS temperature, T0 and T0, also match the two-dimensional DNS cases. SL is estimated from a transient one-dimensional reactive simulation as in [53, 54]. The simulation was initialized with a high-temperature ignition source such that a combustion wave emanates from the source, propagating into the reactive mixture ahead of it. From the simulations, SL is found to be approximately 0.37 m/s for all PRF/air mixtures. It is readily observed from the figure that the mean front speeds of DNS cases exhibit a characteristic ‘U’ shape that is qualitatively consistent with previous studies [53, 54]. The occurrence of the ‘U’-shaped mean front speed is attributed to the initial thermal run-away in the nascent ignition kernel during the early phase of combustion and the burnout of the remaining charge due to compression heating during the last phase of combustion [53, 54, 86].
Figure 3-11 also shows that the mean front speed similar to SL develops earlier with in- creasing T0 and the duration of the region with a constant front speed at the bottom of the
‘U’ shape also increases with increasing T0. For cases with smallT0, however, the mean front speed is much greater thanSLand there is no region with a constant front speed. These results suggest the occurrence of different combustion modes depending on the degree of T0; for large T0 cases, deflagration represented by Sd∗ ∼ SL occurs at the reaction fonts, and for small T0 cases, simultaneous auto-ignition represented by Sd∗ SL occurs at the reaction fronts. It is revealed from Figs. 3-8 – 3-11 that for cases with small T0, the spontaneous ignition mode of combustion primarily occurs through the whole domain, resulting in an excessive rate of heat release within a very short time more like in the case of 0-D homogeneous auto-ignition. For cases with largeT0, however, the deflagration mode of combustion occurs at the reaction fronts while the spontaneous ignition mode of combustion also occurs upstream of the reaction fronts.
Note also that large T0 induces more locally hotter mixtures and local auto-ignition, hence, occurs and develops into a deflagration wave sooner than in cases with smallT0 such that the overall combustion starts sooner and persist longer than that of small T0.
To measure the occurrence of deflagration and spontaneous ignition modes systematically during combustion, the temporal evolutions of the fraction of heat release rate attributed to deflagration for Cases 1–9 are shown in Fig. 3-12. To distinguish between the two modes of propagation, the Damk¨ohler number,Da, defined by [78, 80, 87], is adopted:
Da= ω˙k
| − ∇ ·(ρYkVk)|, (3.4.4) where Yc is used for the Damk¨ohler number analysis. From a one-dimensional laminar simu- lation, it is found that Dain the diffusive limit is approximately 3.3, where the diffusive limit represents deflagration wave propagation without auto-ignition, i.e., where diffusion balances reaction. Note that the departure ofDain the diffusive limit from unity is a consequence of the
upstream mixture being highly reactive and hence, the reaction term is somewhat larger than the diffusion term [53]. Here, the delineation between the two propagation modes is defined by Da= 3.3 such thatDaless than 3.3 represents a deflagration wave.
FractionofHRR
-1.0 -0.5 0.0 0.5 1.0
t/τ0ig
MeanHRR(J/mm3 s)
0.0 0.2 0.4 0.6 0.8 1.0
0 20 40 60 80
30 K 60 K
T′= 15 K 30 K
60 K
PRF100 PRF80 PRF50
Figure 3-12: Temporal evolution of the fraction of the heat release rate from the deflagration mode and the mean heat release rate for Cases 1–9.
Several points should be noted from Fig. 3-12. First, the fraction of ˙q from the deflagration mode increases with increasing T0 regardless of the fuel composition as expected from the explanation above. Second, for cases with large T0 (Cases 3, 6, and 9), more than half of ˙q occurs by the deflagrations during most of the combustion process such that the total heat release from the deflagration mode for Cases 3, 6, and 9 are approximately 40 %. For cases with small T0 (Cases 1, 4, and 7), however, the fraction of ˙q from deflagrations is relatively small prior to the peak of ˙q and continues to increase until the end of the combustion. This observation is attributed to the fact that at the final stage of the ignition, all explosive modes die out and the correspondingDaalso vanishes such that the fraction of ˙qfrom the deflagration mode becomes unity. Note that the total heat release from the deflagration mode for Cases 1, 4, and 7 is approximately 1 %.
These results are qualitatively consistent with those in previous studies [50, 51, 53, 54]. In short, for cases with small T0, only a small fraction of combustion occurs by deflagration, verifying that spontaneous auto-ignition is predominant for the combustion with small T0, and for cases with largeT0, a relatively large fraction of combustion occurs by deflagration, indicating that both deflagration and spontaneous ignition occur for large T0. These results verify that the deflagration mode of combustion is attributed to the temporal spreading of the excessive rate of heat release and the vanishing of the effect of the fuel composition in HCCI combustion with largeT0 .