Self-similar propagation of expanding spherical flames in large scale gas explosions

This paper presents the experimentally observed onset of self-acceleration and self-similarity of flame propagation during a large-scale gas explosion. Specifically, the critical Peclet number (flame radius relative to flame thickness) at which self-acceleration begins, Pec=r/δ, the experimental acceleration exponent, α, and the fractal excess, d, are evaluated from the results of field experiments of hydrogen/air, methane/air, and propane/air explosions at various concentrations. Experimental results show that Pec for the onset of self-acceleration correlates with Markstein number, Ma, of the mixture that measures the intensity of diffusional–thermal instability. This result demonstrates that the onset of self-acceleration depends on the intensity of hydrodynamic instability as well as that of diffusional–thermal instability. The value of power law exponent of flame radius, α, calculated from r∼tα, increased in Pe, and then it reached a limiting value when (Pe−Pec)/Pec≫1, from which the fractal dimension is calculated. The results suggest that a self-acceleration (α>1) and a self-similarity (α=constant) regimes exist for an expanding spherical flame. The experimental three-dimensional fractal dimension for real flames is found in the range of D3≈2.2–2.35 in the present study. It is confirmed that the fractal dimension is affected by the intensity of instabilities. The present results are expected to help improve the accuracy of the risk assessment of explosion hazards.