Interaction of Multiple Cylindrical Expanding Shock Waves

Abstract

The study of shock-shock interaction has interested researchers since the days of Ernst Mach. The nonlinearity of the shocks yields a complex interaction featuring a Mach stem. This phenomenon is very similar to the reflection patterns of a planar shock wave over an inclined wedge. As the shocks expand, the two-shock system is no longer able to turn the flow as much as needed, and a Mach stem is generated. As the shocks continue to expand, so too does the Mach stem. The expansion of a shock wave has been studied analytically by Lin (J Appl Phys 25:54–57, 1950) and Taylor (Proc R Soc Ser A Math Phys Sci 201:159–174, 1954) for two and three dimensions, respectively. In these cases, however, there is only a single blast. For shock-shock interaction, von Neumann’s (Oblique Reflection of Shocks. Bureau of Ordinance, Washington, DC, 1943) work using a planar shock wave over a wedge, while similar, does not consider the decaying properties behind an expanding shock wave. This study will focus on two separate numerical methods; geometrical shock dynamics (GSD) and Euler simulations. Each of them was used to study a two-dimensional shock interaction case with two cylindrically expanding shock waves. The results from the GSD and Euler simulations were then compared to analogous experimental work conducted by Higashino et al. (Shock Waves 1:275, 1991). Good agreement is seen between the three cases apart from early times in the case of GSD.