Theory of Two-Phase Detonation-Part II: Structure

The structure of a two-phase steady detonation in a granulated solid propellant is studied, and existence conditions for a one-dimensional, steady two-phase detonation are given. Ordinary differential equations from continuum mixture theory are solved numerically to determine steady wave structure. In the limiting case where heat transfer and compaction effects are negligible, the model reduces to two ordinary differential equations that have a clear geometrical interpretation in a two-dimensional phase plane. This two-equation model predicts results that are quite similar to those of the full modeL This suggests that in the limited parameter space studied 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 can be admitted, as can weak and CJ solutions with an unshocked gas and solid. As for one-phase materials, the CJ wave speed is the speed of propagation predicted for an unsupported, one-dimensional, two-phase detonation. It is predicted that there is no admissible CJ structure with a single leading gas phase shock and unshocked solid below a critical value of initial bulk density. This result cannot be predicted from equilibrium end state analysis. Thus it is concluded that it is essential to consider reaction zone structure when assessing potential solutions.