On deflagration-to-detonation transition

A reduced model for the reactive gas flow in a tube is proposed, where the nonlinear effects are discarded everywhere but in the reaction rate term. While ruling out the formation of shockwaves the model transpires to be rich enough to cover detonation-like phenomena with the sound waves acting as a driving agency. It is shown that depending on the ignition conditions, the detonation wave is evoked either immediately or gradually emanates from the low velocity deflagration by virtue of friction between the burning gas and the tube walls. At sufficiently strong friction the normal near-sonic detonation is found to undergo a hysteresic transition to a low speed quasi-detonation dominated by dissipative effects.