Accelerated flames and detonation in gases

The dynamics of accelerated flames in gases, and the transition to detonation are considered. It is shown that in the pre-detonation stage of an accelerated flame there is a fall in pressure and density behind the flame front, and that there the gas velocity is in the opposite direction to the motion of the flame. Increasing compression of the gas in front of the flame leads, after a time, to the development of a shock wave. The properties of this wave are calculated and it is proposed that detonation arises in this shock front which lies some distance ahead of the flame. The dynamics of the retonation wave, which is a shock wave thrown back into the hot gases at the onset of detonation, is examined and evidence is adduced to show that complete chemical reaction does not always occur in the front of an accelerated flame.