Detailed features of one-dimensional detonations

Abstract

The oscillation mechanism and reignition process of one-dimensional unsteady detonations are numerically studied using a one-step chemical reaction model governed by Arrhenius kinetics. A series of simulations, without perturbations from the outflow boundary to the detonation front, are carried out while the degree of overdrive, f, is varied between 1.10 and 1.74 (f=D2/DCJ2; where D is detonation velocity). Shock pressure histories and x–t diagrams are utilized in order to attain precise understanding of the one-dimensional unsteady detonations. At higher degrees of overdrive, f=1.40–1.74, shock pressure histories agree with those of previous studies. The oscillation mechanism is the same as that of the large-disturbance regime of unsteady shock-induced combustion around a projectile. At lower degrees of overdrive, f<1.30, grid resolution affects the eventual results, because half reaction time in the shock pressure exhibits considerable variation. Four typical kinds of oscillation pattern are discussed and are explained by their x–t diagrams and shock pressure histories. Each oscillation mechanism is essentially the same as that of the large-disturbance regime. The reignition process in the failed regime was numerically investigated at f=1.01–1.25. The reignition points tend to converge on a specified point in study of grid refinement, although the oscillation of the shock pressure histories becomes chaotic, suggesting the existence of a unique solution for reignition. All the simulation results for f=1.01–1.20 show the failed regime after initial disturbance at the early stage. The failed regime is compared with the solution of the Riemann problem, and analysis consisting of a Rayleigh line for weak leading shock and a partially burnt Hugoniot curve is adopted. Analysis suggests the concept of partial chemical heat release, indicating the possibility of discontinuous change in conditions, and, indeed, simulation indicates occurrence of explosion. The explosion time derived from the analysis agrees well with the results of simulation.