Converging detonation waves in a dusty gas

The problem of converging detonation waves propagating through a dusty gas and releasing a constant amount of energy per unit mass is studied. The dusty gas is assumed to be a mixture of small solid particles and a perfect gas. The solid particles are distributed continuously in the perfect gas. An expression for the similarity exponent is determined for the detonation wave travelling in the Chapman-Jouguet regime. Also, the variation of the flow variables just behind the detonation front with the radius of the front are obtained. It is found that the presence of dust particles in the medium has a significant effect on the similarity exponent and the flow variables.