The formation of a secondary shock wave behind a shock wave diffracting at a convex corner

Abstract

This paper deals with the formation of a secondary shock wave behind the shock wave diffracting at a two-dimensional convex corner for incident shock Mach numbers ranging from 1.03 to 1.74 in air. Experiments were carried out using a 60 mm $\times$ 150 mm shock tube equipped with holographic interferometry. The threshold incident shock wave Mach number ( $M_s$ ) at which a secondary shock wave appeared was found to be $M_s$ = 1.32 at an 81° corner and $M_s$ = 1.33 at a 120° corner. These secondary shock waves are formed due to the existence of a locally supersonic flow behind the diffracting shock wave. Behind the diffracting shock wave, the subsonic flow is accelerated and eventually becomes locally supersonic. A simple unsteady flow analysis revealed that for gases with specific heats ratio $\gamma = 1.4$ the threshold shock wave Mach number was $M_s$ = 1.346. When the value of $M_s$ is less than this, the vortex is formed at the corner without any discontinuous waves accompanying above the slip line. The viscosity was found to be less effective on the threshold of the secondary shock wave, although it attenuated the pressure jump at the secondary shock wave. This is well understood by the consideration of the effect of the wall friction in one-dimensional duct flows. In order to interpret the experimental results a numerical simulation using a shock adaptive unstructured grid Eulerian solver was also carried out.