Oscillatory flame propagation: Coupling with the acoustic field

An analysis is presented of flame acceleration in a tube filled with flammable mixture, closed at one end and open to the atmosphere at its second end. Ignition takes place near the closed end; experiments then show that the flame accelerates, slows down and moves back, accelerates again, and may eventually reach considerable speeds. The one-dimensional analysis is based upon the assumption that the flame front propagates at a speed that is small compared to the speed of sound, and that depends upon the temperature and pressure perturbation due to acoustics that it encounters. A complete unsteady solution is constructed. The tube acoustics are set in motion by the expansion of the fluid due to ignition at the closed end. Subsequently, both spectrum and amplitude evolve because of the motion of the temperature interface, and because of forcing by the flame front, which itself depends upon the effect of acoustics on the state of the fluid that it encounters. Oscillations in the front position are stronger than in a previous study in which the flame propagation speed was taken to be constant. With the additional feedback now included, it is strong enough to result in strong flow reversal.