Some Features of the Curvature of a Two-Dimensional Detonation Shock Front at a Simple Refraction Locus

We present a theoretical study of the interaction of a constant-velocity two-dimensional detonation wave with its surrounding medium. For the case of pure refraction, we obtain exact expressions for the interface curvatures of the shock fronts in both the explosive (X) and its confinement (C) in terms of the detonation velocity D, the material properties of X and C and, if the flow is cylindrically symmetric, the radius of the explosive charge. These relations are obtained from the constraints imposed on the flow derivatives of the pressure P and the flow turning angle 0 by the conservation laws, the boundary conditions at the curved shock fronts and the contact conditions matching P and 0 along the interface. This model is used in our numerical analysis of a polytropic explosive with a pressure-dependent decomposition rate and a polytropic confinement. We find that, for a given D, the explosive's interface curvature C, decreases as the confinement's density increases. Detonation wave front dynamic in condensed explosives is currently studied by using evolution equations which relate the geometrical and kinematical properties of the wave surface. There are essentially two approaches. In the first one [I] the detonation is considered as a generalized CJ wave, specifically a curved partially reactive sonic hydrodynamic discontinuity. Under the assumption that the spatial and time flow derivatives are finite at the reactive side of this discontinuity, the analysis yields an hyperbolic evolutio