Comparative analysis of flow behind a normal shock wave reflected off a wavy end-wall at different Mach numbers and wave amplitudes

Abstract

The interaction between an incident shock wave and a wavy end-wall in a three-dimensional geometry is numerically simulated by using a high-order finite-difference solver with a ghost-cell immersed boundary method. The aim is to discover the differences of the unsteady propagation characteristics of triple bifurcation points and transverse waves at different incident shock Mach numbers (M 1 ) and wavy wall amplitudes (A ww ). For a benchmark case with M 1 = 1.5 and A ww = 1 mm, the simulated results are in a good agreement with other studies, indicating the reliability of the current simulation technique. The numerical results at M 1 = 1.5, 1.9, 2.5, and 3.5 show that the Mach numbers of the transverse shock waves issued from the triple bifurcation points decrease with time according to a power function. It indicates that the deformation of the shock wave attenuates with time and its flat shape is gradually recovered. The stronger the incident shock wave is, the faster the deformation decays. In the central region, a petal-like vortex structure is observed near the wavy wall and its advancing speed with periodic fluctuation correlates with the cycle of the transverse motion of the triple bifurcation point. With the increase of M 1 , the petal-like vortex gradually grows up in size, and a faster rate can be observed in the normal direction. By comparing the propagation characteristics of transverse waves at different wavy wall amplitudes, it is discovered that the cellular pattern becomes more diverse as the wall amplitude increases. This is due to the multiple collisions of the transverse waves on the wavy wall, which leads to the multi-modal waves system in the shocked gas.