Prole changes in the propagation of shock waves of varying curvature

Abstract

In two distinct studies, the change in the pro le of a curved shock wave, from one continuous shock front to a con guration resembling a symmetrical pair of Mach re ections, was observed. The physical mechanisms associated with the evolution of the shock pro le was evaluated for shock waves with initial pro les comprising a cylindrical arc, placed in-between two straight segments. This was achieved through a series of Computational Fluid Dynamics (CFD) simulations and experimental tests. An understanding of this phenomenon contributes fundamental insights regarding the behaviour of curved shock waves. The propagation of these shock waves in a converging channel was modelled numerically. The temporal variation of the pressure distribution immediately behind the shock wave was examined. 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 reected shocks on the shock front. Throughout the numerical simulations, 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. This enabled the infuence of these parameters on various aspects of the evolution of the shock pro le to be determined. The variation with time of the pressure-gradient distribution and the maximum pressure gradient behind the shock 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. Shock waves with curvature radii of 145 mm and 215 mm were produced experimentally using the existing facility. Various tests were conducted for shock waves with Mach numbers ranging from 1.15 - 1.34. The schlieren images obtained from these tests were compared with the results from the corresponding CFD. There was general agreement in terms of the overall pro le change that the shock wave experienced. However, a secondary wave, which followed behind the primary shock front, was observed. Furthermore, a quantitative analysis demonstrated that the shock in the experiment was accelerating, whereas in the CFD, the shock Mach number was approximately constant. This was found to be a result of the secondary wave catching up to the primary shock front and reinforcing it. The origin of these secondary waves is the reflection of the shock wave, off the side wall of the propagation chamber, upon exiting the slit. To correct the mismatch in these results, the facility must be modi fied so that this effect is eliminated.