Propagation of Shock Waves of Varying Curvature

Abstract

When a shock wave having variable concave curvature propagates, it can develop a kink followed by the development of a reflected shock. A typical example is a plane incident shock encountering a surface with concave curvature, the part of the shock adjacent to the surface curves forward and subsequently develops into a Mach reflection with a Mach stem, shear layer and reflected shock. The physical mechanisms associated with the evolution of the shock profile was evaluated for shock waves with initial profiles comprising a cylindrical arc, placed in-between two straight segments, propagating in a converging channel. The temporal variation of the pressure distribution immediately behind the shock wave was studied using CFD. This revealed a pressure imbalance in the region where the curved (which was initially cylindrical) and straight shock segments meet. This imbalance occurs due to the difference in the propagation behaviour of curved and planar shock waves, and results in the development of reflected shocks on the shock front. The angle at which the channel walls converge, the initial curvature radius, and the shock Mach number, was varied between 40 and 60 degrees, 130 and 190 mm and 1.1 to 1.4, respectively. The variation with time of the pressure-gradient distribution and the maximum pressure gradient behind theshock wave was evaluated. From this, the trajectory angle of the triple points, and the rate at which the reflected shocks develop, was deduced. It was found that when shock waves with larger curvature radii propagate in channels with lower wall angles, the reflected shocks develop at a slower rate, and the triple points follow a steeper trajectory. Consequently, the likelihood of reflected shocks emerging on the shock front, within the duration of the shock propagation, is reduced. This is due to the triple points intersecting the walls, before reflected shocks can fully develop. Similarly, when the shock Mach number is higher, the trajectory angle of the triple points is greater, and they intersect the walls before the reflected shocks can emerge.

Keywords

• curved shock waves; shock diffraction; shock reflection.