Physical interpretation of mathematically invarient k(r,p) type equations ofstate for hydrodynamically driven flow

摘要

In order to apply the power of a full group analysis to the problem of anexpanding shock in planar, cylindrical, and spherical geometries, the expression for the shock front position R (t) has been modified to allow the wave to propagate through a general non-uniform medium. This representation incorporates the group parameter ratios as meaningful physical quantities and reduces to the classical Sedov-Taylor solution for a uniform media. Expected profiles for the density, particle velocity, and pressure behind a spherically diverging shock wave are then calculated using the Tait equation of state for a moderate (i.e., 20 t TNT equivalent) blast load propagating through NaC1. The changes in flow variables are plotted for Mach < 1.5. Finally, effects due to variations in the material uniformity are shown as changes in the first derivative of the bulk modulus (i.e., Ko').