| The structure of a two-phase steady detonation in a granulated solid propellant has been studied, and existence conditions for a one-dimensional, steady two-phase detonation have been predicted. Ordinary differential equations from continuum mixture theory have been solved numerically to determine steady wave structure. In the limiting case where there is no chemical reaction and no gas phase effects, the model describes inert compaction waves. The equations predict detonation structure when reaction and gas phase effects are included. In the limiting case where heat transfer and compaction effects are negligible, the model reduces to two ordinary differential equations which have a clear geometrical interpretation in a two-dimensional phase plane. The two-equation model predicts results which are quite similar to those of the full model which suggests that heat transfer and compaction are not important mechanisms in determining the detonation structure. It is found that strong and Chapman-Jouguet (CJ) detonation solutions with a leading gas phase shock and unshocked solid are admitted as are weak and CJ solutions with an unshocked gas and solid. The initial conditions determine which of these solutions is obtained. As for one-phase materials, the CJ wave speed is the speed of propagation predicted for an unsupported, one-dimensional, two-phase detonation. The model predicts that there is no physically admissible CJ structure below a critical value of initial bulk density. This result is not predicted from equilibrium end state analysis, and based on this result, it is concluded that it is essential to consider reaction zone structure. |
