Invariant Functional Forms For K P P Type Equations Of State For Hydrodynamically Driven Flow

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Physical Interpretation of Mathematically Invariant K(r, P) Type Equations of State for Hydrodynamically Driven Flow

In order to apply the power of a full group analysis to the problem of an expanding 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 NaCl. 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').