Three-stage isentrope for the expansion of detonation products

Abstract

Many industrial processes and certain special studies of explosions require a clear engineering understanding of the formation and decay of shock waves in the gaseous medium near the explosive charge. There have been a number of theoretical and experimental studies of the shock waves formed in air during explosions. A series of theoretical papers have furnished a solution for the problem of a strong explosion in the zone far from the surface of the explosive charge [1-5]; the conclusions and results of this work cannot be used in the near zone. Experimental work by Sadovskii [6[ revealed the basic empirical equations describing the maximum pressure at the shock front, the specific momentum, and the effective duration of the compressional phase as functions of the size of the explosive charge and the distance from it. In the energetic representation of the similarity law, the charge is described by its energy alone, which is proportional to its weight, independent of its density and shape. Measurements of the velocity and maximum pressure of the shock wave have shown [7-10] that the energetic similarity law is violated near the charge surface. According to estimates by various investigators, Sadovskii's equations are applicable only at distances greater than 10-18 charge radii, even for simple spherical charges. These investigators replace the Sadovskii equations in the zone in which they are not applicable by empirical equations for the properties of the shock wave as a function of the time or distance from the surface of a spherical charge, up to 10-12 radii. However, these equations do not relate the properties of the shock wave to those of the explosive or those of the detonation products; they incorporate only these densities and the explosives. Brode [11] carried out a numerical solution for the explosion of a spherical charge, taking into account the thermodynamic properties of air and the equation of state of the detonation products, in the form given by Johnson and Miller. A review of the literature reveals that the formation of the shock wave near an explosive charge has not been studied adequately, either theoretically or experimentally. In the present paper we report a study of the properties of the shock wave and the detonation products, beginning at the surface of the charge, and we attempt to relate the properties of the shock wave and of the detonation products with the properties of the explosive material. This problem requires a determination of the equation of state for the detonation products or the expansion isentrope and a search for the initial conditions at the charge--medium interface when the detonation wave reaches the charge surface.