Analytical study of ionizing blast waves in atomic hydrogen

Abstract

The ionization effect on both the evolution and internal structure of a blast wave (BW) is determined in laboratory conditions. In a first step, the Rankine–Hugoniot equations describing the structure of the shock front together with the Saha equation modeling ionization are solved analytically in a consistent way for the conditions of a cold initial atomic hydrogen gas. In a second step, a simplified approach is used by introducing an effective adiabatic index γ * that takes into account ionization arising at the shock front. Finally, γ * is used as input data in the self-similar model derived formerly by Barenblatt to describe the structure and the dynamics of the ionizing BW. For the typical laboratory conditions of blast wave experiments, ionization achieves a hydrogen gas compression up to about 11 times at the shock front of the blast wave where a thin and dense shell forms. For such a compression, the value of the effective adiabatic index is γ * ≃ 1.2 leading to a self-similar evolution of the BW where its radius R(t) varies according to R ( t ) ∝ t α * with α * ≃ 0.33. This value of α * is lower than the adiabatic expansion stage α = 2 / 5, where the total energy of the BW is conserved. Thus, ionization is found to act as a cooling effect at the shock front where a fraction of kinetic energy is absorbed to ionize the gas.