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 H₂/O₂/N₂ and H₂/O₂/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 H₂/O₂/N₂ 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/δ_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, α, in the self-similar propagation stage was extracted based on the power-law of dr_f/dt = αA^1/αr_f^{(1 − 1/α)}, where r_f is the instantaneous mean flame radius, and A is a constant. The values of α are located between 1.22 and 1.40, which are smaller than the suggested value (1.5) for self-turbulization.