Critical conditions for flame acceleration in long adiabatic channels closed at their ignition end

The propagation of premixed flames in long adiabatic channels is investigated when a combustible mixture is ignited at their close end while the other end remains open to atmospheric pressure. This constraint conditions the flow produced by gas expansion near the flame. The burned gas trapped between the flame and the closed end comes eventually to rest, while the flow sets in the fresh mixture escapes freely at the far end of the channel. Seeking for traveling wave solutions, we find that two possible solutions, corresponding to slow and fast steadily propagating flames, exist under appropriate conditions. The critical conditions are determined when the two solutions merge, and depend on the channel width, the heat release and the Lewis number. Beyond criticality, steadily propagating flames in channels closed at their ignition end are not possible. Numerical simulations of the time-dependent equations in sufficiently long channels confirm the existence of a steady propagation mode, always corresponding to the slow flame solution. Beyond criticality, the flame always accelerate as it travels down the channel.