Two-dimensional optimal jetless solutions for hypervelocity impact and shock waves interaction

Abstract

Two problems with similar hydrodynamic flows are considered. The first one is the problem of the hypervelocity impact of axisymmetric bodies with cavities on colliding surfaces. The second one is also axisymmetric case of interaction of shock wave (SW) propagating along axis and incident under some angle on the boundary of contact with a substance of higher impedance. In this case the incident SW is always oblique in coordinates of contact boundary. Let denote by T the intersection point of the free boundaries of the bodies in the first case, i.e., the point where begins the boundary of contact of two bodies. In the second case, T is the point at which the front of the incident SW reaches the boundary of contact of two media. In both cases, we have a similar hydrodynamic flows in the region behind the point T bounded by SW and the given flow parameters before SW. Managing movement of T by different ways one may get different solutions. Under optimal solution we mean here movement of T is such way that speed of T in coordinates of the correspondent substance is equal to the speed of the SW in the substance behind T during all time of movement in direction to axis of symmetry. For the problems, an assumption is reasonable that these optimal solutions inside a small area with a given finite space size reach the maximum pressure and temperature of the substance at the maximum compression for the given velocities and materials.