Self-acceleration and global pulsation in expanding laminar ${\mathrm{H}}_2\text{−}{\mathrm{O}}_2\text{−}{\mathrm{N}}_2$ flames

We report herein the quantitative data and physical insights acquired on the self-acceleration and global pulsation of spherically expanding ${\mathrm{H}}_2\text{−}{\mathrm{O}}_2\text{−}{\mathrm{N}}_2$ flames, propagating in a constant-pressure environment and subjected to hydrodynamic and diffusional-thermal instabilities over a wide range of pressures and equivalence ratios. Results show that the critical radii for the onset of the transition stage and global pulsation stage have a similar variation with pressure and equivalence ratio and can be collapsed by plotting the nondimensional values normalized by the planar flame thickness. Furthermore, through experiments with fixed flame temperature achieved by adjusting the amount of ${\mathrm{N}}_2$ in air, it is demonstrated that the global pulsation frequencies dominated by the diffusional-thermal instability increase with its intensity, which is consistent with the hypothesis that the global pulsation behavior of cellular flames arises from the continuous cell growth and splitting during the flame propagation. The global pulsation frequencies of ${\mathrm{H}}_2$-air flames, subjected to the coupled hydrodynamic and diffusional-thermal instabilities, show a nonmonotonic trend with the equivalence ratio; while their nondimensional values, normalized by the flame time, collapse and decrease with increasing equivalence ratio, in that the pressure and flame temperature effects are properly scaled out through the normalization. The acceleration exponents of the transition stage and global pulsation stage are also determined, with the latter slightly smaller than the critical value of 1.5 suggested for self-turbulization.

Figure 1

Schlieren images from the spherical flame propagation of ${\mathrm{H}}_2$-air flames at different pressures and equivalence ratios.

Figure 2

Flame-fronts of ${\mathrm{H}}_2$-air flames at different equivalence ratios. $P=3.0$ atm. (a) $\varphi =0.6$, (b) $\varphi =0.8$, (c) $\varphi =1.0$.

Figure 3

Propagation of cellular flames with pulsatory behavior for ${\mathrm{H}}_2$-air flames at $P=3.0$ atm and $0.6\le \varphi \le 1.1$. $T_u=298\mathrm{K}$. (a) Dimensional flame speed, $S_b$, vs flame radius, $R_f$; (b) normalized flame speed, ${\overline{S}}_b=S_b/S_b^0$, vs normalized flame radius or Péclet number, $\mathrm{Pe}=R_f/{\delta }_f$, where ${\delta }_f=\left(T_{b-}{T}_u\right)/{\left(dT/dx\right)}_{\max }$ is the flame thickness; (c) ${\overline{S}}_b$ vs Pe for ${\mathrm{H}}_2$-air flames at $\varphi =0.8$ and pressures from 1.0 atm to 5.0 atm.

Figure 4

Critical radius for the onset of the transition stages for ${\mathrm{H}}_2$-air flames at $2.0\mathrm{atm}\le P\le 5.0\mathrm{atm}$. $0.6\le \varphi \le 1.0$. (a) Dimensional critical flame radius, $R_{\mathrm{ct}}$; (b) nondimensional critical flame radius, $\mathrm{P}{\mathrm{e}}_{\mathrm{ct}}=R_{\mathrm{ct}}/{\delta }_f$, where ${\delta }_f=(T_b-T_u)/{\left(dT/dx\right)}_{\max }$ is the flame thickness.

Figure 5

Critical nondimensional critical flame radius $\left(\mathrm{P}{\mathrm{e}}_{\mathrm{ct}}=R_{\mathrm{ct}}/{\delta }_f\right)$ for the onset of the global pulsation stages for ${\mathrm{H}}_2$-air flames at 2.0 atm ≤ $P$ ≤ 5.0 atm. 0.6 ≤ ϕ ≤ 1.0.

Figure 6

Propagation of cellular flames with pulsatory behavior for ${\mathrm{H}}_2\text{−}{\mathrm{O}}_2\text{−}{\mathrm{N}}_2$ flames at $T_u=298$ K and $P=3.0$ atm. The experimental conditions are listed in Table 1. The burned flame temperature is fixed at 1800 K by varying the ${\mathrm{N}}_2$ amount in air. (a) Dimensional flame speed, $S_b$, vs flame radius, $R_f$; (b) normalized flame speed, ${\overline{S}}_b=S_b/S_b^0$, vs normalized flame radius or Péclet number, $\mathrm{Pe}=R_f/{\delta }_f$.

Figure 7

Frequency, $f$, for global pulsation in ${\mathrm{H}}_2\text{−}{\mathrm{O}}_2\text{−}{\mathrm{N}}_2$ flames at $P=3.0$ atm. The experimental conditions are listed in Table 1.

Figure 8

Global pulsation frequency for ${\mathrm{H}}_2$-air flames. 0.6 ≤ ϕ ≤ 1.0 and 2.0 atm ≤ $P$ ≤ 5.0 atm. (a) Dimensional frequency, $f$; (b) nondimensional frequency, $\overline{f}=f·{\delta }_f/S_b^0$.

Figure 9

The flame propagation speed along a certain angle, $S_b\left(\theta \right)=d{R}_L\left(\theta \right)/dt$. The experimental condition is stoichiometric ${\mathrm{H}}_2$-air flame. $P=3.0$ atm. $G^{*}=3.0$ and $n_c=7.0$ for both $\varphi =1.0$ and 1.1 in panel (b).

Figure 10

Acceleration exponent for ${\mathrm{H}}_2$-air flames at 0.6 ≤ ϕ ≤ 1.0 and 2.0 atm ≤ $P$ ≤ 5.0 atm. (a) Transition stage, ${\alpha }_t$; (b) global pulsation stage, ${\alpha }_p$.