Flame evolution in shock-accelerated flow under different reactive gas mixture gradients

The interaction between a planar shock wave and a spherical flame is studied numerically for an ethylene-oxygen-nitrogen gas mixture. Influences of different initial reactive gas mixture gradients on the shock-flame interaction are investigated by using high-resolution computational simulations. The results show that the different reactive gas mixture gradients can greatly affect the flame evolution in shock accelerated flow. A detonation only emerges in the homogenous reactive gas mixture case, but a distinct shock bifurcation can be found in the inhomogeneous cases where the leftward reflected shock wave propagates in a reverse flow with a high transverse velocity gradient in the inhomogeneous cases. Also, the flame volume and heat release rate increase when the distribution of the reactive gas mixture is uniform or with a positive gradient in this paper, but decrease when the distribution of the reactive gas mixture is with a negative gradient, however, the ratio of unburned to burned regions in the flame zone shows just the opposite trends. Furthermore, the factors affecting the vorticity generation are also analyzed. It is found that the compression term has a relatively stronger influence on the vorticity generation in all the three cases except the period before the reflected shock wave impinges on the distorted flame in the homogeneous case, wherein the baroclinic effect dominates the vorticity generation in the flame zone.

Figure 1

Schematic of the computational setup.

Figure 2

Comparison between experimental Schlieren images [4] and computational Schlieren images at the selected time instants (a) $t=143\mu \mathrm{s}$, (b) $t=194\mu \mathrm{s}$, (c) $t=443\mu \mathrm{s}$, and (d) $t=494\mu \mathrm{s}$.

Figure 3

Reactive gas mixture distributions in the three different cases.

Figure 4

Computational density and reactive gas mixture mass images (Case 1) (a) $t=75.7\mu \mathrm{s}$, (b) $t=148.7\mu \mathrm{s}$, (c) $t=204.7\mu \mathrm{s}$, (d) $t=210.3\mu \mathrm{s}$, (e) $t=222.0\mu \mathrm{s}$, (f) $t=231.2\mu \mathrm{s}$, (g) $t=251.4\mu \mathrm{s}$, and (h) $t=263.0\mu \mathrm{s}$.

Figure 5

Computational density and reactive gas mixture mass images (Case 2) (a) $t=204.8\mu \mathrm{s}$, (b) $t=222.8\mu \mathrm{s}$, (c) $t=263.0\mu \mathrm{s}$, (d) $t=330.4\mu \mathrm{s}$, (e) $t=410.6\mu \mathrm{s}$, and (f) $t=529.0\mu \mathrm{s}$.

Figure 6

Computational density and reactive gas mixture mass images (Case 3) (a) $t=205.8\mu \mathrm{s}$, (b) $t=229.9\mu \mathrm{s}$, (c) $t=231.4\mu \mathrm{s}$, (d) $t=252.1\mu \mathrm{s}$, (e) $t=340.5\mu \mathrm{s}$, and (f) $t=480.9\mu \mathrm{s}$.

Figure 7

Evolution of the flame volume.

Figure 8

Evolution of the ratio of unburned to burned regions in the flame zone.

Figure 9

Evolution of the total heat release rate of flame.

Figure 10

Evolutions of the different transport terms for different cases (a) case 1, (b) case 2, and (c) case 3.