Mesoscale Simulation of Mixed Equations of State with Application to Shocked Platinum-doped PMP Foams

Hydrocarbon polymers and foams are utilized in high energy-density physics (HEDP) and inertial confinement fusion (ICF) experiments as tampers, energy conversion and radiation pulse shaping layers in dynamic hohlraum Z-pinches, and ablators in ICF capsule implosions. Shocked foams frequently are found to be mixed with other materials either by intentional doping with high-Z elements or by instabilities and turbulent mixing with surrounding materials. In this paper we present one-dimensional and three-dimensional mesoscale hydrodynamic simulations of high-Z doped poly-(4-methyl-1-pentene) (PMP or TPX) foams in order to examine the validity of various equation of state (EOS) mixing rules available in two state-of-the-art simulation codes. Platinum-doped PMP foam experiments conducted at Sandia's Z facility provide data that can be used to test EOS mixing rules. We apply Sandia's ALEGRA-MHD code and the joint LLNL/SNL KULL HEDP code to model these doped foam experiments and exercise the available EOS mixing methods. One- dimensional simulations homogenize the foam with platinum dopant and show which EOS mixing methods produce results that are consistent with measured Hugoniot states. These simulations produce sharp shock fronts that are well described by traditional Hugoniot relations. Three-dimensional mesoscale simulations explicitly model the foam structure embedded with discrete platinum particles. The heterogeneous structure of the foam results in diffuse shock fronts and an unsteady post-shock state with large fluctuations about an average state. We compare shock propagation through pure foam and Pt-doped foams (50-50 mixture by weight) at equal average initial density, and examine how well the results compare to the experimentally measured Hugoniot states.