Self-acceleration and global pulsation in hydrodynamically unstable expanding laminar flames

The cellularly unstable laminar flame is of fundamental and practical interest because of its intrinsic ability to accelerate without any external sources, as demonstrated previously for the spherically expanding flame. In this work, enriched physical insights and useful quantitative data on the subject phenomena are obtained by employing stoichiometric H₂/O₂/N₂ flames and focusing on the individual roles of pressure, P, and the burned flame temperature, T_b, on the flame speed acceleration. Specifically, we first demonstrate that the propagation speed of the self-accelerating cellularly unstable flames at various pressures, including the state of the critical radius at which the flame becomes unstable, can be collapsed by plotting the flame speed, normalized by the planar flame speed, versus the normalized radius, or the Peclet number. Furthermore, through experiments with reduced burned flame temperature achieved by increasing the amount of N₂ in air, the normalized flame speed with lower T_b is found to be larger than that with higher T_b. We have also found that instead of continuing with steady acceleration after its attainment, the unstable flames exhibit a global pulsatory acceleration mode in that stages of strong and weak acceleration are cyclically repeated. Mechanistically and confirming results from previous studies, while the flame is globally expanding, the local cascading process in the cellular structure could cause phases of faster and slower growth in the surface area. Such an intermittent local burning rate or flame speed consequently translates to oscillatory global propagation, even after global averaging, due to nonlinear coupling. The frequency and acceleration exponent of the pulsatory multi-stage acceleration are also determined, with the latter slightly smaller than the critical value of 1.5 suggested for self-turbulization.