Skip to main content Accessibility help
×
Home

Evolution of shock-accelerated heavy gas layer

  • Yu Liang (a1) (a2), Lili Liu (a1) (a2), Zhigang Zhai (a1), Ting Si (a1) and Chih-Yung Wen (a2)...

Abstract

Richtmyer–Meshkov instability of the SF6 gas layer surrounded by air is experimentally investigated. Using the soap film technique, five kinds of gas layer with two sharp interfaces are generated such that the development of each individual interface is highlighted. The flow patterns are determined by the amplitudes and phases of two corrugated interfaces. For a layer with both interfaces planar, the interface velocity shows that the reflected rarefaction waves from the second interface accelerate the first interface motion. For a layer with the second interface corrugated but the first interface planar, the reflected rarefaction waves make the first interface develop with the same phase as the second interface. For a layer with the first interface corrugated but the second interface planar, the rippled shock seeded from the first interface makes the second interface develop with the same phase as the first interface and the layer evolves into an ‘upstream mushroom’ shape. For two interfaces corrugated with opposite (the same) phase but a larger amplitude for the first interface, the layer evolves into ‘sinuous’ shape (‘bow and arrow’ shape, which has never been observed previously). For the interface amplitude growth in the linear stage, the waves’ effects are considered in the model to give a better prediction. In the nonlinear stage, the effect of the rarefaction waves on the first interface evolution is quantitatively evaluated, and the nonlinear growth is well predicted. It is the first time in experiments to quantify the interfacial instability induced by the rarefaction waves inside the heavy gas layer.

Copyright

Corresponding author

Email address for correspondence: sanjing@ustc.edu.cn

References

Hide All
Arnett, W. D., Bahcall, J. N., Kirshner, R. P. & Woosley, S. E. 1989 Supernova 1987A. Annu. Rev. Astron. Astrophys. 27 (1), 629700.
Bai, J. S., Zou, L. Y., Wang, T., Liu, K., Huang, W. B., Liu, J. H., Li, P., Tan, D. W. & Liu, C. L. 2010 Experimental and numerical study of shock-accelerated elliptic heavy gas cylinders. Phys. Rev. E 82 (5), 056318.
Bai, X., Deng, X. L. & Jiang, L. 2018 A comparative study of the single-mode Richtmyer–Meshkov instability. Shock Waves 28 (4), 795813.
Balakumar, B. J., Orlicz, G. C., Ristorcelli, J. R., Balasubramanian, S., Prestridge, K. P. & Tomkins, C. D. 2012 Turbulent mixing in a Richtmyer–Meshkov fluid layer after reshock: velocity and density statistics. J. Fluid Mech. 696, 6793.
Bates, J. W. 2004 Initial value problem solution for isolated rippled shock fronts in arbitrary fluid media. Phys. Rev. E 69 (5), 056313.
Bell, G. I.1951 Taylor instability on cylinders and spheres in the small amplitude approximation. Report No. LA-1321, LANL 1321.
Brouillette, M. 2002 The Richtmyer–Meshkov instability. Annu. Rev. Fluid Mech. 34 (1), 445468.
Budzinski, J. M., Benjamin, R. F. & Jacobs, J. W. 1994 Influence of initial conditions on the flow patters of a shock-accelerated thin fluid layer. Phys. Fluids 6 (11), 35103512.
Buttler, W. T., Oró, D. M., Preston, D. L., Mikaelian, K. O., Cherne, F. J., Hixson, R. S., Mariam, F. G., Morris, C., Stone, J. B., Terrones, G. et al. 2012 Unstable Richtmyer–Meshkov growth of solid and liquid metals in vacuum. J. Fluid Mech. 703, 6084.
Collins, B. D. & Jacobs, J. W. 2002 PLIF flow visualization and measurements of the Richtmyer–Meshkov instability of an air/SF6 interface. J. Fluid Mech. 464, 113136.
Dell, Z., Stellingwerf, R. F. & Abarzhi, S. I. 2015 Effect of initial perturbation amplitude on Richtmyer–Meshkov flows induced by strong shocks. Phys. Plasmas 22 (9), 092711.
Ding, J., Li, J., Sun, R., Zhai, Z. & Luo, X. 2019 Convergent Richtmyer–Meshkov instability of a heavy gas layer with perturbed outer interface. J. Fluid Mech. 878, 277291.
Ding, J., Si, T., Chen, M., Zhai, Z., Lu, X. & Luo, X. 2017 On the interaction of a planar shock with a three-dimensional light gas cylinder. J. Fluid Mech. 828, 289317.
de Frahan, M. T. H., Movahed, P. & Johnsen, E. 2015 Numerical simulations of a shock interacting with successive interfaces using the discontinuous Galerkin method: the multilayered Richtmyer–Meshkov and Rayleigh–Taylor instabilities. Shock Waves 25 (4), 329345.
Hahn, M., Drikakis, D., Youngs, D. L. & Williams, R. J. R. 2011 Richtmyer–Meshkov turbulent mixing arising from an inclined material interface with realistic surface perturbations and reshocked flow. Phys. Fluids 23 (4), 046101.
Holmes, R. L., Dimonte, G., Fryxell, B., Gittings, M. L., Grove, J. W., Schneider, M., Sharp, D. H., Velikovich, A. L., Weaver, R. P. & Zhang, Q. 1999 Richtmyer–Meshkov instability growth: experiment, simulation and theory. J. Fluid Mech. 389, 5579.
Ishizaki, R., Nishihara, K., Sakagami, H. & Ueshima, Y. 1996 Instability of a contact surface driven by a nonuniform shock wave. Phys. Rev. E 53 (6), R5592.
Ishizaki, R., Nishihara, K., Wouchuk, J. G., Shigemori, K., Nakai, M., Miyanaga, N., Azechi, H. & Mima, K. 1999 Rippled shock propagation and hydrodynamic perturbation growth in laser implosion. J Mater. Process Tech. 85 (1), 3438.
Jacobs, J. W., Jenkins, D. G., Klein, D. L. & Benjamin, R. F. 1995 Nonlinear growth of the shock-accelerated instability of a thin fluid layer. J. Fluid Mech. 295, 2342.
Jacobs, J. W., Klein, D. L., Jenkins, D. G. & Benjamin, R. F. 1993 Instability growth patterns of a shock-accelerated thin fluid layer. Phys. Rev. Lett. 70 (5), 583586.
Jourdan, G. & Houas, L. 2005 High-amplitude single-mode perturbation evolution at the Richtmyer–Meshkov instability. Phys. Rev. Lett. 95 (20), 204502.
Liang, Y., Ding, J., Zhai, Z., Si, T. & Luo, X. 2017 Interaction of cylindrically converging diffracted shock with uniform interface. Phys. Fluids 29 (8), 086101.
Liang, Y., Zhai, Z., Ding, J. & Luo, X. 2019 Richtmyer–Meshkov instability on a quasi-single-mode interface. J. Fluid Mech. 872, 729751.
Liao, S., Zhang, W., Chen, H., Zou, L., Liu, J. & Zheng, X. 2019 Atwood number effects on the instability of a uniform interface driven by a perturbed shock wave. Phys. Rev. E 99 (1), 013103.
Lindl, J. D., Amendt, P., Berger, R. L., Glendinning, S. G., Glenzer, S. H., Haan, S. W., Kauffman, R. L., Landen, O. L. & Suter, L. J. 2004 The physics basis for ignition using indirect-drive targets on the National Ignition Facility. Phys. Plasmas 11 (2), 339491.
Liu, L., Liang, Y., Ding, J., Liu, N. & Luo, X. 2018a An elaborate experiment on the single-mode Richtmyer–Meshkov instability. J. Fluid Mech. 853, R2.
Liu, W., Li, X., Yu, C., Fu, Y., Wang, P., Wang, L. & Ye, W. 2018b Theoretical study on finite-thickness effect on harmonics in Richtmyer–Meshkov instability for arbitrary atwood numbers. Phys. Plasmas 25 (12), 122103.
Luo, X., Dong, P., Si, T. & Zhai, Z. 2016 The Richtmyer–Meshkov instability of a ‘V’ shaped air/SF6 interface. J. Fluid Mech. 802, 186202.
Luo, X., Liang, Y., Si, T. & Zhai, Z. 2019 Effects of non-periodic portions of interface on Richtmyer–Meshkov instability. J. Fluid Mech. 861, 309327.
Luo, X., Wang, M., Si, T. & Zhai, Z. 2015 On the interaction of a planar shock with an SF6 polygon. J. Fluid Mech. 773, 366394.
Luo, X., Zhang, F., Ding, J., Si, T., Yang, J., Zhai, Z. & Wen, C. Y. 2018 Long-term effect of Rayleigh–Taylor stabilization on converging Richtmyer–Meshkov instability. J. Fluid Mech. 849, 231244.
Mariani, C., Vandenboomgaerde, M., Jourdan, G., Souffland, D. & Houas, L. 2008 Investigation of the Richtmyer–Meshkov instability with stereolithographed interfaces. Phys. Rev. Lett. 100 (25), 254503.
Meshkov, E. E. 1969 Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 4 (5), 101104.
Meyer, K. A. & Blewett, P. J. 1972 Numerical investigation of the stability of a shock-accelerated interface between two fluids. Phys. Fluids 15 (5), 753759.
Mikaelian, K. O. 1985 Richtmyer–Meshkov instabilities in stratified fluids. Phys. Rev. A 31 (1), 410419.
Mikaelian, K. O. 1990 Rayleigh–Taylor and Richtmyer–Meshkov instabilities in multilayer fluids with surface tension. Phys. Rev. A 42 (12), 7211.
Mikaelian, K. O. 1995 Rayleigh–Taylor and Richtmyer–Meshkov instabilities in finite-thickness fluid layers. Phys. Fluids 7 (4), 888890.
Mikaelian, K. O. 1996 Numerical simulations of Richtmyer–Meshkov instabilities in finite-thickness fluid layers. Phys. Fluids 8 (5), 12691292.
Morgan, R. V., Likhachev, O. A. & Jacobs, J. W. 2016 Rarefaction-driven Rayleigh–Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory. J. Fluid Mech. 791, 3460.
Niederhaus, C. E. & Jacobs, J. W. 2003 Experimental study of the Richtmyer–Meshkov instability of incompressible fluids. J. Fluid Mech. 485, 243277.
Orlicz, G. C., Balakumar, B. J., Tomkins, C. D. & Prestridge, K. P. 2009 A Mach number study of the Richtmyer–Meshkov instability in a varicose, heavy-gas curtain. Phys. Fluids 21 (6), 064102.
Ott, E. 1972 Nonlinear evolution of the Rayleigh–Taylor instability of a thin layer. Phys. Rev. Lett. 29 (21), 1429.
Plesset, M. S. 1954 On the stability of fluid flows with spherical symmetry. J. Appl. Phys. 25 (1), 9698.
Prestridge, K. 2018 Experimental adventures in variable-density mixing. Phys. Rev. Fluids 3 (11), 110501.
Prestridge, K., Vorobieff, P., Rightley, P. M. & Benjamin, R. F. 2000 Validation of an instability growth model using Particle Image Velocimtery measurement. Phys. Rev. Lett. 84 (19), 43534356.
Ranjan, D., Oakley, J. & Bonazza, R. 2011 Shock-bubble interactions. Annu. Rev. Fluid Mech. 43, 117140.
Rayleigh, Lord 1883 Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc. 14, 170177.
Richtmyer, R. D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 13 (2), 297319.
Rightley, P. M., Vorobieff, P., Martin, R. & Benjamin, R. F. 1999 Experimental observations of the mixing transition in a shock-accelerated gas curtain. Phys. Fluids 11 (1), 186200.
Rikanati, A., Oron, D., Sadot, O. & Shvarts, D. 2003 High initial amplitude and high Mach number effects on the evolution of the single-mode Richtmyer–Meshkov instability. Phys. Rev. E 67, 026307.
Sadot, O., Erez, L., Alon, U., Oron, D., Levin, L. A., Erez, G., Ben-Dor, G. & Shvarts, D. 1998 Study of nonlinear evolution of single-mode and two-bubble interaction under Richtmyer–Meshkov instability. Phys. Rev. Lett. 80 (8), 16541657.
Shimoda, J., Inoue, T., Ohira, Y., Yamazaki, R., Bamba, A. & Vink, J. 2015 On cosmic-ray production efficiency at Supernova remnant shocks propagating into realistic diffuse interstellar medium. Astrophys. J. 803 (2), 98103.
Taylor, G. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proc. R. Soc. Lond. A 201 (1065), 192196.
Tomkins, C., Kumar, S., Orlicz, G. & Prestridge, K. 2008 An experimental investigation of mixing mechanisms in shock-accelerated flow. J. Fluid Mech. 611, 131150.
Tomkins, C. D., Balakumar, B. J., Orlicz, G., Prestridge, K. P. & Ristorcelli, J. R. 2013 Evolution of the density self-correlation in developing Richtmyer–Meshkov turbulence. J. Fluid Mech. 735, 288306.
Vandenboomgaerde, M., Rouzier, P., Souffland, D., Biamino, L., Jourdan, G., Houas, L. & Mariani, C. 2018 Nonlinear growth of the converging Richtmyer–Meshkov instability in a conventional shock tube. Phys. Rev. Fluids 3 (1), 014001.
Zhai, Z., Liang, Y., Liu, L., Ding, J., Luo, X. & Zou, L. 2018a Interaction of rippled shock wave with flat fast–slow interface. Phys. Fluids 30 (4), 046104.
Zhai, Z., Zou, L., Wu, Q. & Luo, X. 2018b Review of experimental Richtmyer–Meshkov instability in shock tube: from simple to complex. Proc. Inst. Mech. Engrs, Part C 232 (16), 28302849.
Zhang, Q., Deng, S. & Guo, W. 2018 Quantitative theory for the growth rate and amplitude of the compressible Richtmyer–Meshkov instability at all density ratios. Phys. Rev. Lett. 121 (17), 174502.
Zhang, Q. & Guo, W. 2016 Universality of finger growth in two-dimensional Rayleigh–Taylor and Richtmyer–Meshkov instabilities with all density ratios. J. Fluid Mech. 786, 4761.
Zhou, Y. 2017a Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I. Phys. Rep. 720–722, 1136.
Zhou, Y. 2017b Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II. Phys. Rep. 723–725, 1160.
Zou, L., Liu, J., Liao, S., Zheng, X., Zhai, Z. & Luo, X. 2017 Richtmyer–Meshkov instability of a flat interface subjected to a rippled shock wave. Phys. Rev. E 95 (1), 013107.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Evolution of shock-accelerated heavy gas layer

  • Yu Liang (a1) (a2), Lili Liu (a1) (a2), Zhigang Zhai (a1), Ting Si (a1) and Chih-Yung Wen (a2)...

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed