Modeling of the spherical explosion attenuation process using aqueous foam

The two-phase model of dry aqueous foam dynamic behavior under the strong shock wave influence is presented under assumption that the foam structure under shock loading is destroyed into a suspension of monodispersed microdrops with the formation of a gas-droplet mixture. The system of equations for the model of aqueous foam includes the laws of conservation of mass, momentum and energy for each phase in accordance with the single- pressure, two-speed, two-temperature approximations in a three-dimensional formulation, taking into account the Schiller-Naumann interfacial drag force and the Ranz-Marshall interfacial contact heat transfer. The thermodynamic properties of air and water forming a gas-droplet mixture are described by the Peng-Robinson and Mie-Grueneisen equations of state. The presence of non-uniform process in height of aqueous foam syneresis, which is due to gravitational forces, is taken into account by setting the distribution of the liquid volume fraction in the foam. An additional consideration of the syneresis process during calculating the intensity of interphase drag forces according to the Schiller-Naumann model was controlled by introducing the parameter depending on the spatial distribution of the initial liquid volume fraction of the foam. The spherical explosion is modeled in the form of the shock wave pulse whose energy coincided with the charge energy of the HE used in the experiments. The problem numerical solution is implemented using the OpenFOAM free software package based on the two-step PIMPLE computational algorithm. The numerical solution of the problem, obtained on the basis of the proposed gas-droplet mixture model, is in satisfactory agreement with the experimental data on a spherical explosion in aqueous foam. The analysis of the spherical shock wave dynamics while its propagation through aqueous foam is given. The causes of the significant decrease in the amplitude and velocity shock waves propagation in the medium under study are investigated.