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Convergent Richtmyer–Meshkov instability of light gas layer with perturbed outer surface

Published online by Cambridge University Press:  17 December 2019

Jianming Li ,
Juchun Ding Open the ORCID record for Juchun Ding [Opens in a new window] ,
Ting Si Open the ORCID record for Ting Si [Opens in a new window]  and
Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window]
Jianming Li
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics,University of Science and Technology of China, Hefei230026, China
Juchun Ding*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics,University of Science and Technology of China, Hefei230026, China
Ting Si
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics,University of Science and Technology of China, Hefei230026, China
Xisheng Luo
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics,University of Science and Technology of China, Hefei230026, China
*
†Email address for correspondence: [email protected]
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Abstract

The Richtmyer–Meshkov instability of a helium layer surrounded by air is studied in a semi-annular convergent shock tube by high-speed schlieren photography. The gas layer is generated by an improved soap film technique such that its boundary shapes and thickness are precisely controlled. It is observed that the inner interface of the shocked light gas layer remains nearly undisturbed during the experimental time, even after the reshock, which is distinct from its counterpart in the heavy gas layer. This can be ascribed to the faster decay of the perturbation amplitude of the transmitted shock in the helium layer and Rayleigh–Taylor stabilization on the inner surface (light/heavy) during flow deceleration. The outer interface first experiences ‘accelerated’ phase inversion owing to geometric convergence, and later suffers a continuous deformation. Compared with a sole heavy/light interface, the wave influence (interface coupling) inhibits (promotes) growth of instability of the outer interface.

JFM classification

Compressible Flows: Shock waves
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 884 , 10 February 2020 , R2
Copyright
© 2019 Cambridge University Press

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References

Bates, J. W. 2004 Initial-value-problem solution for isolated rippled shock fronts in arbitrary fluid media. Phys. Rev. E 69, 056313.Google ScholarPubMed
Bell, G. I.1951 Taylor instability on cylinders and spheres in the small amplitude approximation. Rep. No. LA-1321, LANL 1321.Google Scholar
Brouillette, M. 2002 The Richtmyer–Meshkov instability. Annu. Rev. Fluid Mech. 34, 445–468.CrossRefGoogle Scholar
Ding, J., Li, J., Rui, S., Zhai, Z. & Luo, X. 2019 Convergent Richtmyer–Meshkov instability of heavy gas layer with perturbed outer interface. J. Fluid Mech. 878, 277–291.CrossRefGoogle Scholar
Ding, J., Si, T., Yang, J., Lu, X., Zhai, Z. & Luo, X. 2017 Measurement of a Richtmyer–Meshkov instability at an air–SF6 interface in a semiannular shock tube. Phys. Rev. Lett. 119 (1), 014501.CrossRefGoogle Scholar
Hosseini, S. H. R. & Takayama, K. 2005 Experimental study of Richtmyer–Meshkov instability induced by cylindrical shock waves. Phys. Fluids 17, 084101.CrossRefGoogle Scholar
Lindl, J., Landen, O., Edwards, J., Moses, E. & Team, N. 2014 Review of the National Ignition Campaign 2009–2012. Phys. Plasmas 21, 020501.CrossRefGoogle Scholar
Liu, W. H., Yu, C. P., Ye, W. H., Wang, L. F. & He, X. T. 2014 Nonlinear theory of classical cylindrical Richtmyer–Meshkov instability for arbitrary Atwood numbers. Phys. Plasmas 21, 062119.Google Scholar
Lombardini, M., Pullin, D. I. & Meiron, D. I. 2014 Turbulent mixing driven by spherical implosions. Part 1. Flow description and mixing-layer growth. J. Fluid Mech. 748, 85–112.CrossRefGoogle Scholar
Luo, X., Ding, J., Wang, M., Zhai, Z. & Si, T. 2015 A semi-annular shock tube for studying cylindrically converging Richtmyer–Meshkov instability. Phys. Fluids 27 (9), 091702.CrossRefGoogle Scholar
Luo, X., Zhang, F., Ding, J., Si, T., Yang, J., Zhai, Z. & Wen, C. 2018 Long-term effect of Rayleigh–Taylor stabilization on converging Richtmyer–Meshkov instability. J. Fluid Mech. 849, 231–244.CrossRefGoogle Scholar
Meshkov, E. E. 1969 Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 4, 101–104.CrossRefGoogle Scholar
Mikaelian, K. O. 1995 Rayleigh–Taylor and Richtmyer–Meshkov instabilities in finite-thickness fluid layers. Phys. Fluids 7 (4), 888–890.CrossRefGoogle Scholar
Montgomery, D. S., Daughton, W. S., Albright, B. J., Simakov, A. N., Wilson, D. C., Dodd, E. S., Kirkpatrick, R. C., Watt, R. G., Gunderson, M. A., Loomis, E. N. et al. 2018 Design considerations for indirectly driven double shell capsules. Phys. Plasmas 25, 092706.CrossRefGoogle Scholar
Plesset, M. S. 1954 On the stability of fluid flows with spherical symmetry. J. Appl. Phys. 25, 96–98.CrossRefGoogle Scholar
Ranjan, D., Oakley, J. & Bonazza, R. 2011 Shock–bubble interactions. Annu. Rev. Fluid Mech. 43, 117–140.CrossRefGoogle Scholar
Rayleigh, Lord 1883 Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc. 14, 170–177.Google Scholar
Richtmyer, R. D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 13, 297–319.CrossRefGoogle Scholar
Schwendeman, D. W. & Whitham, G. B. 1987 On converging shock waves. Proc. R. Soc. Lond. A 413, 297311.CrossRefGoogle Scholar
Taylor, G. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proc. R. Soc. Lond. A 201, 192–196.Google Scholar
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, 014001.CrossRefGoogle Scholar
Wang, L. F., Wu, J. F., Ye, W. H., Zhang, W. Y. & He, X. T. 2013 Weakly nonlinear incompressible Rayleigh–Taylor instability growth at cylindrically convergent interfaces. Phys. Plasmas 20, 042708.Google Scholar
Yang, J., Kubota, T. & Zukoski, E. E. 1993 Application of shock-induced mixing to supersonic combustion. AIAA J. 31, 854–862.CrossRefGoogle Scholar