Further Results on Guderley Mach Reflection and the Triple Point Paradox

Abstract

Recent numerical solutions and shock tube experiments have shown the existence of a complex reflection pattern, known as Guderley Mach reflection, which provides a resolution of the von Neumann paradox of weak shock reflection. In this pattern, there is a sequence of tiny supersonic patches, reflected shocks and expansion waves behind the triple point, with a discontinuous transition from supersonic to subsonic flow across a shock at the rear of each supersonic patch. In some experiments, however, and in some numerical computations, a distinctly different structure which has been termed Guderley reflection has been found. In this structure, there appears to be a single expansion fan at the triple point, a single supersonic patch, and a smooth transition from supersonic to subsonic flow at the rear of the patch. In this work, we present numerical solutions of the compressible Euler equations written in self-similar coordinates at a set of parameter values that were used in previous computations which found the simple single patch structure described above. Our solutions are more finely resolved than these previous solutions, and they show that Guderley Mach reflection occurs at this set of parameter values. These solutions lead one to conjecture that the two patterns are not distinct: rather, Guderley reflection is actually underresolved Guderley Mach reflection.123 722 J Sci Comput (2015) 64:721-744

Numerical study of thermochemical effects on the flowfield structure near the triple point at irregular reflection of shock waves

“…Numerical solutions also support different models, depending on the approach used in the computations. The inviscid computations [18,19,20] support the Guderley model; however, the viscous numerical [21,22] and analytical [23] solutions do not show any four-wave configurations, supporting the Sternberg model. These viscous effects caused interest to shock reflection in viscous flows at higher Mach numbers [24,25].…”

Viscous effects in Mach reflection of shock waves and passage to the inviscid limit

“…The first confirmation of this model was obtained only half a century later by solving the Euler equations numerically (Vasilev & Kraiko 1999). Further investigations (Hunter & Brio 2000;Tesdall & Hunter 2002;Hunter & Tesdall 2004;Tesdall, Sanders & Keyfitz 2007, 2008Defina, Susin & Viero 2008a;Defina, Viero & Susin 2008b;Vasilev & Olhovskiy 2009;Tesdall, Sanders & Popivanov 2015;Vasil'ev 2016) showed that, depending on problem parameters, configurations formed due to interaction of weak shock waves can have even more complicated structures and contain additional elements of small size. The experiments by Skews & Ashworth (2005) and Skews, Li & Paton (2009) performed in a large shock tube revealed the existence of a configuration similar to that predicted by Guderley and observed in the inviscid studies mentioned above.…”