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. The propagation of the shock wave on either side of the interface is analyzed at first, and two regular refraction types and three irregular ones are identified. Then, according to the relative speed of the perturbation on either side, three different cases are established. Compared with the existing Catherasoo’s method, this method has improved in the following aspects: (1) the impact 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 mostly calculated based on the exact solutions of the Euler equations, except those involving post-shock subsonic rarefaction waves. This method has been employed in the interaction of a Mach number 1.17 shock with an air/SF6 interface, and gives wave structures that agree with numerical results and existing experimental data. Better agreement for the angle between the transmitted shock and the horizontal direction is obtained 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 ratio and interface inclination angles, comparisons between theoretical and numerical results have shown that our method can obtain the wave structure type 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, it is implied that the improved method in this paper is well applicable and more accurate than the existing method in identifying wave structure types, and it can also give more information about the wave structures.