Main shock and jet head temporal evolution during a sudden release of sonic very highly underexpanded gaseous jets

This study deals with the very initial transient evolution of sonic (choked) very highly underexpanded jets released through a round-shaped opening. For this purpose, we combine 3D high-fidelity numerical simulations and schlieren photography experimental techniques to investigate the main shock and the jet head propagation. We carry out a very detailed parametric study to understand the influence of the inlet diameter, initial pressure ratio, and gas combination on the main shock and the jet head propagation regimes. We reveal that during the early stages of release, the main shock propagation can be characterized into different regimes that correspond to different classical spherical blast wave theories. For the jet head evolution, we find that the initial propagation scaling laws are identical to the main shock, whereas at later time periods, the jet is self-similar and its position scales with the square root of time. For sufficiently long propagation distances, the jet head position scales linearly with time. Finally, according to our analysis results, we develop simplified models that can predict the main shock and the jet head position as a function of time during the very initial stages of the release. We then extensively validate the new models against our numerical simulations and experimental data as well as known experimental results from the literature.