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Research Papers: Fundamental Issues and Canonical Flows

# Planar Shock Focusing Through Perfect Gas Lens: First Experimental Demonstration

[+] Author and Article Information
Laurent Biamino, Christian Mariani, Lazhar Houas

Aix-Marseille Université,
CNRS, IUSTI UMR 7343,
5 rue Enrico Fermi,
Marseille 13013, France

Georges Jourdan

Aix-Marseille Université,
CNRS, IUSTI UMR 7343,
5 rue Enrico Fermi,
Marseille 13013, France
e-mail: Georges.Jourdan@polytech.univ-mrs.fr

Marc Vandenboomgaerde, Denis Souffland

CEA, DAM, DIF,
F-91297 Arpajon, France

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 29, 2013; final manuscript received January 9, 2014; published online July 9, 2014. Assoc. Editor: Robin Williams.

J. Fluids Eng 136(9), 091204 (Jul 09, 2014) (6 pages) Paper No: FE-13-1061; doi: 10.1115/1.4026562 History: Received January 29, 2013; Revised January 09, 2014

## 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.

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## References

Richtmyer, R., 1960, “Taylor Instability in Shock Acceleration of Compressible Fluids,” Commun. Pure Appl. Math., 13(2), pp. 297–319.
Meshkov, E., 1969, “Interface of Two Gases Accelerated by a Shock Wave,” Fluid Dyn., 4(5), pp. 101–104.
Dimotakis, P., and Samtaney, R., 2006, “Planar Shock Cylindrical Focusing by a Perfect-Gas Lens,” Phys. Fluid., 18(3), p. 031705.
Vandenboomgaerde, M., and Aymard, C., 2011, “Analytical Theory for Planar Shock Focusing Through Perfect Gas Lens and Shock Tube Experiment Designs,” Phys. Fluid., 23(1), p. 016101.
Jourdan, G., Houas, L., Schwaederlé, L., Layes, G., Carrey, R., and Diaz, F., 2004, “A New Variable Inclination Shock Tube for Multiple Investigations,” Shock Waves, 13(6), pp. 501–504.

## Figures

Fig. 1

Sketch of the circular transmitted shock wave for the fast-slow configuration. The dash-dotted line and curve represent the incident shock wave and the interface C at t = 0, respectively. The hatched curves represent the transmitted shock wave (taken from Ref. [4]).

Fig. 2

Details of the convergent section that is mounted on the tube end and locations of the pressure gauges

Fig. 3

Schematic description of the convergent section assembled at the tube exit

Fig. 4

Photography of the convergent section assembled at the tube exit

Fig. 5

Stereolithographed grid (left) on which was deposited a nitrocellulose membrane (right) mounted in the convergent section

Fig. 6

Sequence of schlieren photographs showing the refraction of a planar shock wave (Mis = 1.15 in air) through an air/air elliptic interface. The planar shock wave propagates from left to right (T80#823), and the acquisition frequency of 40,000 frames per second for a spatial resolution of 460×201 pixels was retained.

Fig. 7

Sequence of schlieren photographs showing the refraction of a planar shock wave (Mis = 1.15 in air) through an air/SF6 elliptic interface. The planar shock wave propagates from left to right (T80#823), and the acquisition frequency of 54,000 frames per second for a spatial resolution of 312×182 pixels was retained.

Fig. 10

Reconstructed trajectory of the cylindrical shock in the convergent section, resulting from the refraction of a planar shock wave in air (Mis = 1.15) through the elliptic air/SF6 interface (T80#828)

Fig. 9

Pressure histories recorded in the convergent section from stations Cc1 to Cc5, resulting from the refraction of a planar shock wave in air (Mis = 1.15) through the elliptic air/SF6 interface (T80#828)

Fig. 8

Pressure histories recorded in the driven section at stations C8 and C7, resulting from the refraction of a planar shock wave in air (Mis = 1.15) through the elliptic air/SF6 interface (T80#828)

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