Inward-propagating cylindrical flames under different ignition conditions

Inward-propagating cylindrical flames are studied numerically by high-resolution simulations using a one-step Arrhenius kinetics. Emphasis is placed on the effect of shock waves on the flame propagation by setting initial ignition conditions with and without shock wave. It is found that without initial shock wave, the inward-propagating flame propagates initially at a constant speed, while in the later stage of the propagation, it shows a small-amplitude oscillatory motion. When the shock wave initially introduced is medium, a large-amplitude oscillatory motion is caused by the interaction of shock waves with the inward-propagating flame. Moreover, autoignition occurs at the center and develops outwardly into a cellular flame. However, as the introduced shock wave is strong, autoignition created at the center evolves outwardly a cellular detonation.