Planar Shock Focusing Through Perfect Gas Lens: First Experimental Demonstration

Abstract

When a shock wave crosses an interface between two materials, this interface becomes unstable and the Richtmyer–Meshkov instability develops. Such instability has been extensively studied in the planar case, and numerous results were presented during the previous workshops. But the Richtmyer–Meshkov (Richtmyer, 1960, “Taylor Instability in Shock Acceleration of Compressible Fluids,” Commun. Pure Appl. Math., 13(2), pp. 297–319; Meshkov, 1969, “Interface of Two Gases Accelerated by a Shock Wave,” Fluid Dyn., 4(5), pp. 101–104) instability also occurs in a spherical case where the convergence effects must be taken into account. As far as we know, no conventional (straight section) shock tube facility has been used to experimentally study the Richtmyer–Meshkov instability in spherical geometry. The idea originally proposed by Dimotakis and Samtaney (2006, “Planar Shock Cylindrical Focusing by a Perfect-Gas Lens,” Phys. Fluid., 18(3), pp. 031705–031708) and later generalized by Vandenboomgaerde and Aymard (2011, “Analytical Theory for Planar Shock Focusing Through Perfect Gas Lens and Shock Tube Experiment Designs,” Phys. Fluid., 23(1), pp. 016101–016113) was to retain the flexibility of a conventional shock tube to convert a planar shock wave into a cylindrical one through a perfect gas lens. This can be done when a planar shock wave passes through a shaped interface between two gases. By coupling the shape with the impedance mismatch at the interface, it is possible to generate a circular transmitted shock wave. In order to experimentally check the feasibility of this approach, we have implemented the gas lens technique on a conventional shock tube with the help of a convergent test section, an elliptic stereolithographed grid, and a nitrocellulose membrane. First experimental sequences of schlieren images have been obtained for an incident shock wave Mach number equal to 1.15 and an air/SF6-shaped interface. Experimental results indicate that the shock that moves in the converging part has a circular shape. Moreover, pressure histories that were recorded during the experiments show pressure increase behind the accelerating converging shock wave.