Numerical analysis of the flame piston-model for acceleration runaway in thin tubes

A one-dimensional model is developed and studied to explore the flame acceleration runaway mechanism for deflagration-to-detonation transition in thin tubes. This mechanism relies solely on the thermal feedback between the compression waves ahead of the flame and the temperature-sensitive laminar velocity of the flame. Within this model, the primary driver of the flame acceleration and compressive heating enhancement is the gas flow caused by the increased flame surface area. Results from the numerical integration of the reactive Navier–Stokes equations for perfect gases with a single-step chemical-kinetics model are compared with the solutions obtained when considering the flame as a steady-state discontinuity. The numerical results illustrate the flame acceleration runaway in finite time caused by a double feedback loop established in this model. The evolution of the flame acceleration towards a finite-time singularity eventually leads to the formation of a shock wave within the flame structure, triggering the onset of a detonation. Novelty and significance statement This paper presents numerical results obtained using an approach recently proposed to study the effect of flame acceleration on the one-dimensional internal structure of the flame. Unlike previous studies on flame acceleration leading to DDT based on one-dimensional models in which the flame acceleration due to the increase of its surface area is modeled by accelerating chemical kinetics, the present approach consists in the introduction of a backflow of burned gases pushing the flame tip from behind as a piston. The numerical analysis performed in this work allows considering finite reaction rates in this model obtaining results that compare favorably with those obtained when the flame is considered as a discontinuity. The results of this numerical study support previous analytical studies on the flame acceleration runaway mechanism for DDT and illustrate the acceleration process of a flame propagating over a gas flow with a markedly subsonic velocity which leads to the onset of a detonation.