Stabilization of detonation waves in a supersonic flow

A supersonic flow in a channel of variable cross-section is studied in a quasi-one-dimensional approximation in the framework of a model of infinitely thin detonation waves. An analytical method is developed to analyze the conditions for the existence of steady flow behind a detonation wave using special coordinates. On the basis of numerical experiments, it is shown that the detonation wave can be stabilized. A stability analysis of the steady state is performed with respect to small heat release disturbances. This analysis allows one to make a selection of the emergent flow pattern.