Asymptotic scaling laws for spherical and cylindrical finite-source blast waves

In this study we consider the spherical and cylindrical blast waves generated by the sudden release of a sphere or cylinder of compressed gas. The model problems are useful to understand explosion flow physics, such as the instability at the gas contact discontinuity and the interaction between the shock wave and the gas contact. The explosion flows here are dictated by the initial pressure and sound-speed ratios between the compressed gas and the ambience, which can vary over a wide range in practical applications. Therefore, it is of interest to investigate the scaling laws for the spherical symmetric or axisymmetric explosion flows. Numerical simulations for a wide range of initial pressure and sound-speed ratios are performed. A long-term length scale that incorporates the initial charge radius and the initial pressure ratio is introduced, which is shown to collapse the trajectories of the main shock, the gas contact, and the secondary shock for a wide range of parameters. The results indicate that an asymptotic similarity solution exists for both the far and near fields in the long term.