On the interaction of a planar shock with an polygon

Abstract

The interaction of a planar shock wave (M ≈ 1.2) with an SF 6 polygonal inhomogeneity surrounded by air is experimentally investigated. Six polygons including a square, two types of rectangle, two types of triangle, and a diamond are generated by the soap film technique developed in our previous work, in which thin pins are used as angular vertexes to avoid the pressure singularities caused by the surface tension. The evolutions of the shock-accelerated SF 6 polygons are captured by a high-speed schlieren system from which wave systems and the interface characteristics can be clearly identified. Both regular and irregular refraction phenomena are observed outside the volume, and more complex wave patterns, including transmitted shock, refracted shock, Mach stem and the interactions between them, are found inside the volume. Two typical irregular refraction phenomena (free precursor refraction, FPR, and free precursor von Neumann refraction, FNR) are observed and analysed, and the transition from FPR to FNR is found, providing the experimental evidence for the transition between different wave patterns numerically found in the literature. Combined with our previous work (Zhai et al., J. Fluid Mech., vol. 757, 2014, pp. 800-816), the reciprocal transitions between FPR and FNR are experimentally confirmed. The velocities and trajectories of the triple points are further measured and it is found that the motions of the triple points are self-similar or pseudo-stationary. Besides the shock dynamics phenomena, the evolutions of these shocked heavy polygonal volumes, which are quite different from the light ones, are captured and found to be closely related to their initial shapes. Specifically, for square and rectangular geometries, the different width-height ratios result in different behaviours of shock-shock interaction inside the volume, and subsequently different features for the outward jet and the interface. Quantitatively, the time-variations of the interface scales, such as the width and the normalized displacements of the edges, are obtained and compared with those from previous work. The comparison illustrates the superiority of the interface formation method and the significant effect of the initial interface shape on the interface features. Furthermore, the characteristics of the vortex core, including the velocity and vortex spacing, are experimentally measured, and the vortex velocity is compared with those from some circulation models to check the † Email address for correspondence: sanjing@ustc.edu.cn Interaction of planar shock waves with SF 6 polygons 367 validity of the models. The results in the present work enrich understanding of the shock refraction phenomenon and the database of research into Richtmyer-Meshkov instability (RMI).

Experimental investigation of cylindrical converging shock waves interacting with a polygonal heavy gas cylinder

“…In this way, the gas interface has an almost ideal two-dimensional shape with a polygonal cross-section. The effects of the thin pins and fine chamfers on the shock propagation and interface deformation have been evaluated numerically and experimentally in planar shock-polygonal interface interactions Zhai et al 2014;Luo et al 2015), which predict a good performance of the soap film method in the interface formation and the successive RM instability study.…”

“…When the initial interface is formed in the test section, the pollution of the disks by of soap liquid and the arrangement of the thin pins would contaminate the schlieren images of the evolving interface, which can be seen in studies of planar shock-polygonal interface interactions Zhai et al 2014;Luo et al 2015). Moreover, the schlieren system often obtains an integrated view of the flow field along the light path.…”

“…The type of the irregular refraction is heavily dependent on the inclined angle, defined as the angle between the boundaries of the interface and On converging shock and polygonal interface interaction the incident shock wave. For a planar shock with a fixed Mach number interacting with a polygonal interface, the inclined angle remains constant at the upstream and downstream interfaces, respectively, and thus the irregular refraction system can be identified (Zhai et al 2014;Luo et al 2015). However, for a cylindrical shock case, the inclined angle always changes as the incident shock moves along the sides of the interface, and the irregular refraction system will change as well.…”

“…In this period, rw propagates behind ts and they merge gradually (figure 10b). Because each pair of triple points originates from one apex and will converge to the focal point, the 240 T. Si, T. Long, Z. Zhai and X. Luo trajectory of each triple point at the ts front will be a curved line, which is different from the planar case (the triple point travels along almost a straight line as indicated in Luo et al 2015). As time proceeds, the focusing of ts occurs within the volume, inducing high pressure and density in the focal point.…”

“…Typically, the interfaces of different shapes between two gases include spherical bubbles formed by a soap film (Haas & Sturtevant 1987;Layes, Jourdan & Houas 2003;Ranjan et al 2005;Zhai et al 2011;Si et al 2012), circular gas cylinders (Haas & Sturtevant 1987;Hosseini & Takayama 2005;Tomkins et al 2008;Luo et al 2014b), elliptical gas cylinders On converging shock and polygonal interface interaction 227 (Zou et al 2010), single-/multi-mode interfaces generated by vibration (Jacobs & Sheeley 1995;Mariani et al 2008;Long et al 2009) or by a gas curtain (Balakumar et al 2008;Orlicz et al 2009;Balasubramanian et al 2012), rectangular blocks generated by a microfilm membrane supported by a fine wire mesh (Bates, Nikiforakis & Holder 2007), and three-dimensional interfaces with a minimum surface feature formed by the soap film technique free of supporting meshes . Recently, some polygonal interfaces have been formed in our group using thin pins to restrict the soap film and the results indicate that the soap film is a flimsy but durable material during the interface formation Zhai et al 2014;Luo et al 2015).…”