On theoretical calculation method for two-dimensional planar shock wave refractions

Abstract

A theoretical calculation method for wave structures in the flow resulting from the interaction between the two-dimensional planar shock and the material interface is developed. First, the propagation of the shock wave on either side of the interface is analyzed, and two regular refraction types and three irregular ones are identified. Then, according to the relative speed of the perturbations on either side, three different interaction cases are established. Compared with the existing Catherasoo’s method, this method is improved in the following aspects: 1) the influence of the perturbation in the post-shock flow field on the interaction is taken into account, including its type and whether it can catch up and interact with the shock front; 2) the interactions between different waves are calculated mostly based on the exact solutions of the Euler equations, except those involving post-shock subsonic rarefaction waves. This method has been used to investigate the interaction of a Mach number 1.17 shock with an air/SF₆ interface, and give wave structures that accord with numerical results and existing experimental data. The angle between the transmitted shock and the horizontal direction is obtained to be in better agreement with experimental data than Catherasoo’s result, and more parameters are obtained, such as the reflected wave and the interface deflection angle. For cases involving a Mach number 2.00 shock with different material density ratios and interface inclination angles, comparisons between theoretical and numerical results show that our method can obtain the type of wave structure more accurately than Catherasoo’s method, and identify a refraction type in which the post-shock strong perturbation catches up with the shock front and a three-wave structure is formed, whereas Catherasoo’s method cannot handle this case. Thus, the results show that the improved method in this work has better applicability and higher accuracy than the existing method in identifying the type of wave structure, and can also provide more information about the wave structures.