Shock Reflection Off Combined Surfaces

Abstract

A mismatch has been shown to exist between the shock wave reflection behaviour on a circular arc and that on a plane wall at the same angle of incidence [1]. For reflection off a plane wall, this change in reflection pattern from regular to Mach reflection occurs at a wall angle where the flow behind the reflection point is just sonic in a frame of reference fixed in the reflection point. This transition condition is labeled the sonic criterion [2]. Experiments confirm this (except for some minor effects due to boundary layer growth). Data for convex cylindrical surfaces has shown that the visible eruption of a Mach stem, which is taken to be evidence of the point of transition, occurs at smaller wall angles than for plane walls [3]. On the other hand, recent tests [1] using perturbations generated by shock passage over a very small step in the wall have shown that the sonic catchup occurs at wall angles not only larger than those found for the visible eruption but also larger than the angles associated with sonic catch-up for the plane wall case. Due to the relatively low resolution of the time-resolved imaging system used, the accuracy of identifying the angle of sonic catchup could be questioned in the same way as identifying the visible eruption of the Mach stem could be resolution dependent. The stem could be erupting earlier if beyond the imaging resolution and the catch up could be occurring later bringing them both closer to the plane wall case. Due to this limitation time resolved tests were then conducted on a 45. plane wall preceded by a 75mm circular arc and the change in reflection angle measured in order to confirm that the reflection was different for the same incidence angle on the two different surfaces [1], this technique not being dependent on using perturbations. The existence of a significant transition length was confirmed in the reflection pattern adjusting from the curved wall to an eventual pseudo-stationary pattern on the plane wall. The results were still limited due to imaging resolution issues so a new set of tests have been undertaken using high resolution single shot tests over a range of wall angles and a range of combined surfaces. An additional test was conducted with a circular surface on both ends of a plane wall to explore how information from each of the joints influence the reflected shock.