High Resolution Experimental Investigation of the Reflection Over a Convex-Concave Cylindrical Model

Abstract

The reflection pattern over a convex cylindrical surface followed by a concave cylindrical surface is studied using a high spatial resolution and high temporal resolution experimental setup. This fully automated setup enabled the repetition of experiments many times while retaining extremely high repeatability. For the investigated moderate shock strengths (1.2–1.4), the repeatability was less than 0.01 in the incident shock wave Mach number. Each experiment produced a single schlieren image with a pixel size of 0.03 mm. Thus, it was possible to distinguish minuscule flow features of size 0.06 mm. All the images were later combined into a detailed description of a single reflection process. The process was analyzed using an automatic image processing procedure that located the triple point in each image. The tested model enabled studying both the evolution of the RR → MR transition over the convex segment and the evolution of a complicated shock pattern reflection over the concave part. It was found that the RR → MR nonstationary transition is closer to the pseudo-steady criterion in comparison to previous experimental studies. Yet, based on error estimation analysis and in contrast to Kleine et al. (J Fluid Mech 740:47–60, 2014) the pseudo-steady criterion will remain 3o–8o higher than the dynamic transitions investigated. Over the concave segment, we observed the evolution of a newly three-shock configuration established on the Mach stem of the original reflection (MRMR). This double Mach configuration explains the enhancement in the pressure when using blunt entry reflectors. The transition of the newly formed MR to regular reflection (MRRR) was also investigated. The reflection process over the concave segment depends on the first reflection process. Since the later dictates a specific relative angle between the incident shock wave and the original Mach stem. This angle can be later used to adjust the MRMR → MRRR transition angles. Even though this three-shock configuration originated from the Mach stem, it was found that the adjusted transition angles were close to the MR → RR transition angles reported in the literature.