Explosive combustion in a closed channel revisited

This work investigates the mechanism of deflagration-to-detonation transition (DDT) in a closed channel filled with a stoichiometric hydrogen–air mixture under knocking-relevant conditions (10 atm, 1100 K). We first revisit the low-Mach-number model for a planar flame propagating towards an inert end-gas, deriving an analytical solution that reveals a finite-time singularity in temperature, which remains physically irrelevant without end-gas reactions. The core analysis demonstrates that the transition is triggered by the breakdown of the low-Mach-number approximation due to weak heat release during the end-gas autoignition induction period. The extreme thermal sensitivity of the induction delay to a small increase in temperature (resulting from both adiabatic compression and autoignition reactions) causes a drastic reduction in the time scale of flame dynamics. This leads to acceleration-induced compression waves which quickly steepen into shocks propagating in a combustible gaseous mixture prompt to detonate. A thermal feedback loop between the self-accelerating flame and the compression waves culminates in the catastrophic breakdown of the laminar flame structure associated with the spontaneous onset of a detonation burning quickly the end-gas in a shorter time than the bulk thermal explosion by autoignition. Supporting numerical simulations, in which the induction chemistry is artificially modified without modifying the chemical kinetics controlling the flame propagation, confirm that the DDT is intrinsically linked to the high thermal sensitivity of the reaction scheme controlling the induction delay in the end-gas.