Analysis of nonequidiffusive premixed flames in obstructed channels

The impact of the Lewis number, $\mathrm{Le}$, on the dynamics and morphology of a premixed flame front, spreading through a toothbrushlike array of obstacles in a semiopen channel, is studied by means of the computational simulations of the reacting flow equations including fully compressible hydrodynamics and one-step Arrhenius chemical kinetics. The channels of blockage ratios $\alpha =1/3,1/2,2/3$ are considered, with the Lewis numbers in the range $0.2\le \mathrm{Le}\le 2$ employed. It is shown that the Lewis number influences flame evolution substantially. Specifically, flame acceleration weakens for $\mathrm{Le}>1$, inherent to fuel-rich hydrogen or fuel-lean propane burning. In contrast, $\mathrm{Le}<1$ flames, corresponding to lean hydrogen-air or rich propane-air mixtures, acquire strong folding of the front and thereby accelerate even faster. The latter effect can be devoted to the onset of the diffusional-thermal combustion instability.

Figure 1

An illustration of the Bychkov mechanism of flame acceleration in an obstructed channel [10, 11, 12, 13].

Figure 2

Resolution test: The scaled flame time position versus the scaled time for $\alpha =1/3$, $\mathrm{Le}=0.2$, and various square mesh sizes: $\left(0.1,0.2,0.4\right)L_f$.

Figure 3

Temperature snapshots taken at the same scaled time instant $\tau =S_{L}t/R=0.075$ for various $\alpha =1/3$, 1/2, and 2/3 and various $\mathrm{Le}=0.2$, 1.0, 2.0.

Figure 4

The scaled flame tip velocity $U_{\mathrm{tip}}/S_L$ versus the scaled time τ for $R/L_f=24$ and $\alpha =1/3$ (a), 1/2 (b), 2/3 (c). Panel (d) shows the scaled flame tip velocity $U_{\mathrm{tip}}/{S_L}_{}\mathrm{at}\tau =0.075$ versus Le for different values of $\alpha =1/3$, 1/2, 2/3.

Figure 5

The scaled flame tip velocity $U_{\mathrm{tip}}/S_L$ versus the scaled time τ for $R/L_f=24$ and various $\mathrm{Le}=0.2$ (a), 0.5 (b), 1.0 (c), 2.0 (d).

Figure 6

The scaled flame tip velocity $U_{\mathrm{tip}}/S_L$ versus the scaled time τ for $\alpha =2/3$ and various $\mathrm{Le}=0.2$ (a), 0.5 (b), 1.0 (c), 2.0 (d).

Figure 7

The exponential acceleration rate σ versus the Lewis number Le for $R/{L_f}_{}=24$ (a), 36 (b), and 48 (c), with $\alpha =1/3$, 1/2, and 2/3 in each panel.

Figure 8

The scaled flame tip position $\sigma Z_{\mathrm{tip}}/\mathrm{\Theta }R$ versus the scaled time $\sigma t{S}_L/R$ for various Le = 0.2 (dotted), 1.0 (dashed), and 2.0 (solid), with three different α = 1/3 (square markers), 1/2 (triangle markers), and 2/3 (without markers) for each given Le.