Self-similar propagation of spherically expanding flames in lean hydrogen–air mixtures

Abstract

The self-similar propagation of expanding spherical flames in lean hydrogen–air mixtures at elevated pressure was experimentally investigated using a dual-chamber apparatus with the quartz windows that enabled observing a flame radius of up to 110 mm. The flame images of the fully developed cellular structure were recorded, and the largest values of r/rc and Pe for the dual-chamber apparatus were estimated. The acceleration exponent, α, corresponding to the fractal dimension in lean hydrogen–air mixtures at elevated pressure was evaluated by plotting the experimental flame radius as a function of time. In this study, the experimental values of α (α = 1.25–1.43) occur within a wide range of r/rc (r/rc = 2–15). The observed trend of α to increase with a decrease in equivalence ratio, φ, and an increase in initial pressure, Pi, is owing to the effects of the diffusional–thermal and Darrieus–Landau instabilities. The value of α increased with an increase in r/rc and saturated at α = 1.43 at r/rc > 10, and the saturated values of the hydrogen–air flame are within α = 1.4–1.5. The results demonstrated that the flame propagation in lean hydrogen–air mixtures was classified as laminar (r/rc < 1), acceleration (r/rc > 1), transition (1 < r/rc < 10), and self-similar (r/rc > 10) regimes. Consequently, the practical three-dimensional fractal dimensions for accidental hydrogen–air explosions are D3 = 2.24–2.33.