Numerical investigation of three deflagration-to-detonation transition conditions related to the velocity of the spontaneous reaction wave

Abstract

In this work, the deflagration-to-detonation transition (DDT) process in a tube filled with quiescent and stoichiometric hydrogen/oxygen mixture is numerically simulated by a detailed chemical reaction model together with a high-resolution adaptive mesh refinement (AMR) mesh system. Then the flow field is analyzed in detail. It is found that for the onset of detonation in a DDT process there are three essential conditions related to the velocity of the spontaneous reaction wave DSpRW. The first condition is that on a hot spot the DSpRW should be slower than the speed of the Chapman–Jouguet (CJ) detonation wave DCJ to make sure that a spontaneous shock wave could arise originating from the spontaneous reaction wave. The spontaneous shock wave and the spontaneous reaction wave have conspicuous positive correlation to accelerate the spontaneous reaction wave to be faster than the local sound speed, which is the second DDT condition. With this condition the spontaneous reaction wave could catch up with its associated spontaneous shock wave and implement a coupling of the gasdynamics and the chemical energy release. This process is in line with Lee's SWACER idea, while throughout the process the spontaneous reaction wave propagates mainly through the Zel'dovich's reactivity gradients mechanism. Meanwhile, the gas velocity Vg is also essential to maintain the above two conditions and the resultant velocity meets the relation ∥DSpRW+Vg∥≥DCJ, which is the third condition. Distinctly this settles the wave speed gap between deflagration and detonation. More importantly, gas velocity plays an important role especially for the pressure build-up. The most important expressive differences between CJ deflagration and CJ detonation are the gas velocities of both the reactants and products as well as the pressure build-up. When these three relations successfully trigger a DDT and get a detonation wave, they still hold in the resulting detonation wave. They are delicately inherited as the inherent characters of the (detonation) wave. Formerly they are preconditioning-sustaining in the DDT process, and now they become self-sustaining in the detonation wave. Besides, the important role of the progress ratio of the induction period ε is emphasized for a spontaneous propagation.