Theoretical determination of the critical conditions for the direct initiation of detonations in hydrogen-oxygen mixtures

Abstract

The problem of the direct initiation of detonations by an energy source has been studied using both a one-step reaction model and a detailed chemistry for hydrogen-oxygen mixtures. The nonlinear curvature effect defines a minimum radius R c below which there is no generalised Chapman-Jourguet (CJ) detonation. Consequently, the detonation front with a radius smaller than R c cannot propagate in a self-sustained manner. For hydrogen-oxygen spherical detonations, this critical radius is about 500 times larger than the thickness of the planar CJ detonation front, in good agreement with our theoretical results based on a one-step reaction model. The so-determined critical conditions are applied on the direct initiation of a curved detonation. It has been found that the criterion based on the nonlinear curvature effect works well for the initiation of spherical or cylindrical detonations. The predicted critical radius and the critical energy are in good agreement with both numerical and experimental results. The influence of the one-dimensional intrinsic instability of the detonation front upon the direct initiation has also been examined via direct numerical simulations. For a sufficiently large activation energy, the strong instability appears in the propagation of the plane detonation front, a quasi-steady regime may be observed during the direct initiation for the initiation energy near the critical value. For very large activation energy, the planar detonation cannot propagate via auto-ignition mechanism, the detonation wave cannot be initiated even in the planar case.