Shock propagation in a low-density foam filled with fluid

Abstract

It is found that when a planar shock is imparted to a system of a foam of low mean density filled with fluid (fiber density>ambient fluid density), an undercompressed quasisteady post-shock state is established. In this state, pressure and density are lower than the values predicted by Hugoniot relations for a uniform fluid with the same average fluid-foam density. It is shown that this undercompression phenomenon is due to residual correlations of fluctuations left after the saturation of the initially rapid mixing of fiber material with the background fluid. Generalized Hugoniot relations are derived for quasiplanar shocks in nonuniform systems, with foam as an example. The behavior of fluctuations in such systems is studied. Formulas for the level of fluctuations induced by a shock as it propagates through foam and for the relaxation time of the fluctuations, are derived.

Effect of shock-generated turbulence on the Hugoniot jump conditions

“…3 of Ref. [6] asymptotically do not approach the conventional jump conditions. Even though the turbulent postshock state is not in a thermodynamic equilibrium, a shock transition to this state is well defined.…”

“…In the simulations of Ref. [6], the effective Reynolds number was, at least, an order of magnitude greater, which is why the shock profiles shown in Fig. 3 of Ref.…”

“…In this range, the function δR(γ,M 1 ) is seen to be finite and negative, indicating undercompression in agreement with the numerical findings of Refs. [6,7]. As in Ref.…”

“…[6]. Deuterium-filled CH foam was simulated in two dimensions (2D) with a periodic lattice of parallel high-density cylinders embedded in a low-density background fluid.…”

Interaction of a planar shock with an isotropic field of sound waves

“…Shock propagation in inhomogeneous media is a fundamental problem in different fields, ranging from shock tube research [1,2], astrophysics [3], aerodynamics [4,5,6,7,8,9], and laser fusion [10,11,12]. The subject is under study since more than 50 years, beginning with the first theoretical works by Ribner [4] on the interaction of planar shock waves with vorticity fields.…”