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The features of one-dimensional unsteady detonations are studied numerically using a hydrogen-air detailed chemical reaction model. A series of simulations are carried out while degree of overdrive, initial pressure, initial temperature, and equivalence ratio are varied. The oscillation modes and mechanisms of the one-dimensional detonations are discussed with reference to shock pressure histories and x-t diagrams of density distributions. As the degree of overdrive is reduced with a stoichiometric mixture of hydrogen-air at P0=0.421 atm and T0=293 K, a steady state appears, along with a high-frequency mode and a low-frequency mode. The oscillation mechanism of the high-frequency mode is the same as that of the regular regime of unsteady shock-induced combustion observed around a spherical projectile flying at hypersonic velocity in detonable gases. The degree of overdrive threshold between the steady and unsteady region increases monotonically with initial pressure and decreases monotonically with initial temperature. When the equivalence ratio is changed, the threshold has a minimum value around [lowercase_phi_synonym]=1. We focus attention on a nondimensional effective activation energy, which is generally used for linear stability analysis. The oscillation mode depends highly on the nondimensional effective activation energy. The oscillation of the detonation front appears as the nondimensional effective activation energy goes past a threshold value of 5.2. Furthermore, we investigate the failed regime and possible reignition in this regime. In the failed regime, a detonation wave breaks up into a leading shock, a contact discontinuity, and a rarefaction wave. When the shock is weak, reignition time becomes very long. Therefore, the reignition after the failed regime is difficult to reproduce in the restricted computational domain. The reignition process in the failed regime is investigated by means of analysis consisting of integration along the point of intersection between a Rayleigh line for weak leading shock and a partially burnt Hugoniot curve. The reignition time increases dramatically with decreasing temperature behind the shock wave, when the gas condition goes past the second explosion limit. The second explosion limit is one of the characteristics of the hydrogen-air detailed chemical reaction model and does not exist in the one-step chemical reaction model. Lastly, the reignition time obtained by the analysis is compared with that obtained by the simulation results. The simulation results agree well with the analytical results. [ABSTRACT FROM AUTHOR]

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/D²[sub CJ]; 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... [ABSTRACT FROM AUTHOR]