Numerical calculation of the motion of a gas from a surface explosion

Abstract

The motion of a gas by the normal impact of a high-speed body at the interface between a dense half-space and a vacuum is investigated numerically. The motion of the shock wave and the shape and distribution of the parameters of the gas dispersing in the vacuum are obtained. The motion is studied during the formation of a region with high pressure at the boundary with the vacuum of a gas occupying the half-space z > 0. The assumption of cylindrical symmetry relative to the z axis enables this three-dimensional nonsteady-state problem in the general case to be solved as a two-dimensional problem. For the corresponding one-dimensional problem, the numerical solution and, for certain gases also, the analytic solutions are well known and are considered in detail in [1]. As a result of solving the two-dimensional problem, profiles of the gasdynamic quantities are obtained which are similar to the solutions in the one-dimensional case and the result of the solution by a self-similar method. The cup-shaped surface of the shock wave front with a pressure gradient on it “focusses” the dispersing gas so that its velocity component normal to the surface z = 0 is greater by an order of magnitude than the component parallel to the surface of separation of the medium, and only at individual points is their ratio close to 0.4. Therefore, the dispersing gas is formed into the shape of a “jet”, the pressure and density profiles on the axis of which have a shape similar to the one-dimensional problem of a brief shock, but in the plane z = 0 the pressure and density distributions are similar to the distributions of these quantities in the case of a powerful point explosion in an unbounded medium. The initial disturbance in the symmetrical problem being considered may be the result of either the normal impact of the body with a high velocity at the surface of the dense medium, or the consequence of the effect of a giant laser pulse, or some other process when a certain volume is formed with a high pressure at the interface between the dense medium and a vacuum, or with another low-density medium.