Numerical studies of shock–vortex interaction over a wedge during shock-wave diffraction—A new approach

Abstract

In this study, shock wave diffraction has been investigated through a numerical simulation of a moving normal shock incident on a sharp-edged wedge. Schardin's problem is revisited using some existing and new mathematical tools. Two-dimensional compressible Navier–Stokes equation is solved using a higher-order version of the rhoCentralFoam solver in the OpenFOAM platform. Overall flow structures are captured with high efficacy. The divergence of the Lamb vector is used to probe the interaction between vorticity bearing and fluid straining motion, which increases dramatically inside the primary vortex after collision with the reflected Mach stem and increases the turbulent kinetic energy (TKE). In the separated shear layer that emerges from the wedge tip, there is a reduction of TKE after the collision between the lambda shock and accelerated shock. The vorticity pumping into the mean flow by the baroclinic torque is dominant in the separated shear layer before the above collision, whereas after collision it is only dominant inside the primary vortex. A new vector M is introduced here, which is the cross product of the vorticity vector and the pressure gradient vector. The divergence of M shows the interaction between the pressure gradient and the vorticity gradient. This interaction affects the separation bubble formed over the base wall of the wedge due to the shock-wave/boundary layer interaction induced by the lambda shock. Dynamic mode decomposition shows a dominant mode at a frequency of 125.7 Hz, which is due to low-frequency shock oscillation.