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

Abstract

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, rcr, 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 rcr is well captured by linear stability theory for stoichiometric flames. The experimental critical Peclet number, Pecr = rcr/δf, increases non-linearly with the Markstein number, Ma, which measures the intensity of diffusional–thermal instability. However, a linear dependence of Pecr on Ma is predicted by linear stability theory. Specifically, the theory shows well quantitative agreement with the experimental results for mixtures with near-unity Leeff; however, it under-predicts the Pecr for mixtures with off-unity Leeff. 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 drf/dt = αA1/αrf(1 − 1/α), where rf 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.