Richtmyer-Meshkov Instability in a Cylindrical Geometry Using a Conventional Shock Tube

Abstract

During the past 20 years, there was considerable amount of analytical, computational, and experimental works dealing with the planar version of the problem of the Richtmyer-Meshkov instability (RMI). However, this problem is often spherical, and so far there have been only few experimental studies in such configuration, except the cases of both shock-accelerated cylinders [1] and spheres [2] which can be categorized under this label. In convergent geometry, the RMI differs from the planar case due to both the geometrical effects on the instability and a different mono-dimensional (1D) motion of the interface itself. Thus, to better understand the dynamics of this instability in convergent geometry and validate models in such configuration, new experimental data are needed. Holder et al. [3] reported laboratory experiments with a convergent shock tube, using a detonable gas mixture to produce a cylindrically convergent shock. Recently, Zhai et al. [4], Apazidis et al. [5], and Biamino et al. [6] have experimentally proven the possibility of generating a converging cylindrical shock wave using a conventional shock tube. Zhai et al. proposed to design a shock tube having a curved wall test section. This specific wall converts a planar shock wave into a cylindrical one. Apazidis et al. have developed a device where the shock wave propagates inside an annular chamber and focuses after its reflection on the end-wall. Biamino et al. have used and implemented the gas lens theory revisited by Vandenboomgaerde and Aymard [7]. This theory was originally proposed by Dimotakis and Samtaney [8]. This work was the first experimental demonstration of the gas lens technique applied to the T80 conventional shock tube of IUSTI. It was shown that a planar incident shock wave propagating in air (M _is = 1.15) which refracts through a specific elliptical air/SF₆ interface generates a cylindrical transmitted shock wave in a two-dimensional wedge geometry with a 30° half apex angle. We were able to diagnose the morphing and the focusing of the shock wave. This study constituted the first step toward canonical experiments on the converging RMI in shock tube environment, for which a second interface had to be implemented. Thus, a new two-dimensional wedge test section (15° half apex angle) was designed to accommodate two interfaces: a first air/SF₆ interface of elliptical shape to convert the incident planar shock wave into a cylindrical converging one and a second sinusoidal SF₆/air interface to study the converging RMI (see Fig. 1). In the present work, the details of this new experimental apparatus were implemented on the T80 shock tube, and the first results are reported. In particular, the evolution process of interfacial structures induced by RMI is shown.