Rankine–Hugoniot relations for shocks in heterogeneous mixtures

Abstract

The conservation of mass, momentum and energy are not sufficient to close a system of jump relations for shocks propagating in a heterogeneous mixture of compressible fluids. We propose here a closed set of relations corresponding to a two-stage structure of shock fronts. At the first stage, microkinetic energy due to the relative motion of mixture components is produced at the shock front. At the second stage, this microkinetic energy disappears inducing strong variations in the thermodynamical states that reach mechanical equilibrium. The microkinetic energy produced at the shock front is estimated by using an idea developed earlier for turbulent shocks in compressible fluids. The relaxation zone between the shocked state and the equilibrium state is integrated over a thermodynamic path a justification of which is provided. Comparisons with experiments on shock propagation in a mixture of condensed materials confirm the proposed theory.