Cellularity and self-similarity of hydrogen expanding spherical flames at high pressures

The onset of transition to cellularity and self-similar propagation of centrally ignited, expanding spherical flames in a reactive environment of H-2/O-2/N-2 and H-2/O-2/He mixtures at initial pressures up to 15 bar were experimentally investigated using a newly developed, constant-pressure, dual-chamber vessel and were theoretically interpreted based on linear stability theory. The experiments were well-controlled to identify the separate and coupled effects of Darrieus-Landau instability and diffusional-thermal instability. Results show that the critical radius, r(cr), for the onset of cellular instability varies non-monotonously with initial pressure for fuel-lean and stoichiometric H-2/O-2/N-2 flames. This non-monotonous pressure dependence of r(cr) is well captured by linear stability theory for stoichiometric flames. The experimental critical Peclet number, Pe(cr) = r(cr)/d(f), increases non-linearly with the Markstein number, Ma, which measures the intensity of diffusional-thermal instability. However, a linear dependence of Pe(cr) on Ma is predicted by linear stability theory. Specifically, the theory shows well quantitative agreement with the experimental results for mixtures with near-unity Le(eff); however, it under-predicts the Pe(cr) for mixtures with off-unity Le(eff). In addition, there exists three distinct propagation stages for flames subjected to cellular instability, namely, smooth expansion, transition propagation, and self-similar propagation. The acceleration exponent, a, in the self-similar propagation stage was extracted based on the power-law of dr(f)/dt = aA(1/)(a)r(f)((1 - 1/a)), where r(f) is the instantaneous mean flame radius, and A is a constant. The values of a are located between 1.22 and 1.40, which are smaller than the suggested value (1.5) for self-turbulization.

Automated summary

This study experimentally investigated the transition to cellularity and self-similar propagation of flames in reactive environments. The results show that the critical radius for cellular instability varies non-monotonously with initial pressure, and the critical Peclet number increases non-linearly with the Markstein number. The theory provides a quantitative agreement with the experimental results and predicts the linear dependence of Pe(cr) on Ma.