The non-stationary hysteresis phenomenon in shock wave reflections

Abstract

The non-stationary transition from Mach to regular reflection followed by a reverse transition from regular to Mach reflection is investigated experimentally. A new experimental setup in which an incident shock wave reflects from a cylindrical concave surface followed by a cylindrical convex surface of the same radius is introduced. Unlike other studies that indicate problems in identifying the triple point, an in-house image processing program, which enables automatic detection of the triple point, is developed and presented. The experiments are performed in air having a specific heats ratio 1.4 at three different incident-shock-wave Mach numbers: 1.2, 1.3 and 1.4. The data are extracted from high-resolution schlieren images obtained by means of a fully automatically operated shock-tube system. Each experiment produces a single image. However, the high accuracy and repeatability of the control system together with the fast opening valve enables us to monitor the dynamic evolution of the shock reflections. Consequently, high-resolution results both in space and time are obtained. The credibility of the present analysis is demonstrated by comparing the first transition from Mach to regular reflection (MR → RR) with previous single cylindrical concave surface experiments. It is found that the second transition, back to Mach reflection (RR → MR), occurs earlier than one would expect when the shock reflects from a single cylindrical convex surface. Furthermore, the hysteresis is observed at incident-shock-wave Mach numbers smaller than those at which the dual-solution domain starts, which is the minimal value for obtaining hysteresis in steady and pseudo-steady flows. The existence of a non-stationary hysteresis phenomenon, which is different from the steady-state hysteresis phenomenon, is discovered.

High spatial and temporal resolution study of shock wave reflection over a coupled convex–concave cylindrical surface

“…This experimental set-up complements our previous study of a shock wave interaction with a concave cylindrical surface followed by a convex cylindrical surface (Geva et al 2013). …”

“…Dealing with the transient evolution of the shock wave reflection Shock wave reflection over a coupled convex-concave cylindrical surface 221 and related physical phenomena, one must employ very fast high-resolution imaging systems (Skews 2008). Over recent decades, studies in this field have dealt with a variety of problems such as: shock wave reflections from blunt objects including cylinders (Sun et al 2003;Skews & Kleine 2010;Glazer et al 2011;Kleine et al 2014), spheres (Britan et al 1995;Tanno et al 2003) and porous plates (Skews 2005); shock focusing (Johansson, Apazidis & Lesser 1999;Bond et al 2009;Skews & Kleine 2010) and the RR → MR and MR → RR transitions (Skews & Kleine 2007;Geva et al 2013;Gruber & Skews 2013). Some of these studies utilized high-speed photography with capturing rates ranging from a few thousand up to one million of frames per second (f.p.s.).…”

“…In the present study, the transition angles were found to be approximately 7 • -10 • closer to the sonic criterion than those reported in previous studies. Figure 5 should not to be confused with figure 8 in Geva et al (2013). The transition points in Geva et al (2013) show the transition angle from an entirely different process.…”

“…Figure 5 should not to be confused with figure 8 in Geva et al (2013). The transition points in Geva et al (2013) show the transition angle from an entirely different process. They show the RR → MR transition angles over the convex section when this transition occurred after the MR → RR transition took place over the preceding concave surface, i.e.…”

“…This transient problem caught the interest of many researchers due to the fact that experimental findings show significant discrepancies in the pseudo-steady predictions of the RR → MR transition position (Geva, Ram & Sadot 2013;Kleine et al 2014). In these studies, a constant-velocity moving shock wave interacted with a cylindrical convex or concave surface.…”