One-dimensional linear stability of curved detonations

Abstract

In this paper, a one–dimensional stability analysis of weakly curved, quasi–steady detonation waves is performed using a numerical shooting method, for an idealized detonation with a single irreversible reaction. Neutral stability boundaries are determined and shown in an activation temperature–curvature diagram, and the dependence of the complex growth rates on curvature is investigated for several cases. It is shown that increasing curvature destabilizes detonation waves, and hence curved detonations can be unstable even when the planar front is stable. Even a small increase in curvature can significantly destabilize the wave. It is also shown that curved detonations are always unstable sufficiently near the critical curvature above which there are no underlying quasi–steady solutions.