Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T14:15:03.671Z Has data issue: false hasContentIssue false
  • English
  • Français

Convergent Richtmyer–Meshkov instability of heavy gas layer with perturbed inner surface

Published online by Cambridge University Press:  03 September 2020

Rui Sun ,
Juchun Ding Open the ORCID record for Juchun Ding [Opens in a new window] ,
Zhigang Zhai Open the ORCID record for Zhigang Zhai [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]
Rui Sun
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Juchun Ding*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Zhigang Zhai
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Ting Si
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Xisheng Luo
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The convergent Richtmyer–Meshkov instability (RMI) of an $\textrm {SF}_6$ layer with a uniform outer surface and a sinusoidal inner surface surrounded by air (generated by a novel soap film technique) is studied in a semiannular convergent shock tube using high-speed schlieren photography. The outer interface initially suffers only a slight deformation over a long period of time, but distorts quickly at late stages when the inner interface is close to it and produces strong coupling effects. The development of the inner interface can be divided into three stages. At stage I, the interface amplitude first drops suddenly to a lower value due to shock compression, then decreases gradually to zero (phase reversal) and later increases sustainedly in the negative direction. After the reshock (stage II), the perturbation amplitude exhibits long-term quasi-linear growth with time. The quasi-linear growth rate depends weakly on the pre-reshock amplitude and wavelength, but strongly on the pre-reshock growth rate. An empirical model for the growth of convergent RMI under reshock is proposed, which reasonably predicts the present results and those in the literature. At stage III, the perturbation growth is promoted by the Rayleigh–Taylor instability caused by a rarefaction wave reflected from the outer interface. It is found that both the Rayleigh–Taylor effect and the interface coupling depend heavily on the layer thickness. Therefore, controlling the layer thickness is an effective way to modulate the late-stage instability growth, which may be useful for the target design.

JFM classification

Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 902 , 10 November 2020 , A3
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Apazidis, N., Lesser, M. B., Tillmark, N. & Johansson, B. 2002 An experimental and theoretical study of converging polygonal shock waves. Shock Waves 12, 39–58.CrossRefGoogle Scholar
Bell, G. I. 1951 Taylor instability on cylinders and spheres in the small amplitude approximation. Report No. LA-1321, LANL 1321.Google Scholar
Biamino, L., Jourdan, G., Mariani, C., Houas, L., Vandenboomgaerde, M. & Souffland, D. 2015 On the possibility of studying the converging Richtmyer–Meshkov instability in a conventional shock tube. Exp. Fluids 56 (2), 1–5.CrossRefGoogle Scholar
Brouillette, M. 2002 The Richtmyer–Meshkov instability. Annu. Rev. Fluid Mech. 34, 445–468.CrossRefGoogle Scholar
Charakhch'an, A. A. 2000 Richtmyer–Meshkov instability of an interface between two media due to passage of two successive shocks. J. Appl. Mech. Tech. Phys. 41, 23–31.CrossRefGoogle Scholar
Dimotakis, P. E. & Samtaney, R. 2006 Planar shock cylindrical focusing by a perfect-gas lens. Phys. Fluids 18, 031705.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-$\textrm {SF}_6$ interface in a semiannular shock tube. Phys. Rev. Lett. 119 (1), 014501.CrossRefGoogle Scholar
Fincke, J. R., Lanier, N. E., Batha, S. H., Hueckstaedt, R. M., Magelssen, G. R., Rothman, S. D., Parker, K. W. & Horsfield, C. J. 2004 Postponement of saturation of the Richtmyer–Meshkov instability in a convergent geometry. Phys. Rev. Lett. 93, 115003.CrossRefGoogle Scholar
Guderley, G. 1942 Starke kugelige und zylinderische Verdichtungsstöße in der Nähe des Kugelmittelpunktes bzw. der Zylinderasche. Luftfahrtforschung 19, 302–312.Google Scholar
Hosseini, S. H. R., Ondera, O. & Takayama, K. 2000 Characteristics of an annular vertical diaphragmless shock tube. Shock Waves 10, 151–158.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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, 23–42.CrossRefGoogle Scholar
Leinov, E., Malamud, G., Elbaz, Y., Levin, L. A., Ben-Dor, G., Shvarts, D. and Sadot, O. 2009 Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions. J. Fluid Mech. 626, 449–475.CrossRefGoogle Scholar
Li, J., Ding, J., Si, T. & Luo, X. 2020 Convergent Richtmyer–Meshkov instability of light gas layer with perturbed outer surface. J. Fluid Mech. 884, R2.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Liang, Y., Liu, L., Zhai, Z., Si, T. & Wen, C. 2020 Evolution of shock-accelerated heavy gas layer. J. Fluid Mech. 886, A7.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, L., Liang, Y., Ding, J., Liu, N. & Luo, X. 2018 An elaborate experiment on the single-mode Richtmyer–Meshkov instability. J. Fluid Mech. 853, R2.CrossRefGoogle Scholar
Lombardini, M., Pullin, D. I. & Meiron, D. I. 2014 Turbulent mixing driven by spherical implosions. Part 2. Turbulence statistics. J. Fluid Mech. 748, 113–142.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., Wang, X. & Si, T. 2013 The Richtmyer–Meshkov instability of a three-dimensional air/$\textrm {SF}_6$ interface with a minimum-surface feature. J. Fluid Mech. 722, R2.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. 1989 Turbulent mixing generated by Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Physica D 36, 343–357.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. 2018 Design considerations for indirectly driven double shell capsules. Phys. Plasmas 25, 092706.CrossRefGoogle Scholar
Perry, R. W. & Kantrowitz, A. 1951 The production and stability of converging shock waves. J. Appl. Phys. 22, 878–886.CrossRefGoogle Scholar
Peterson, J. R., Johnson, B. M. & Haan, S. W. 2018 Instability growth seeded by DT density perturbations in ICF capsules. Phys. Plasmas 25, 092705.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
Si, T., Long, T., Zhai, Z. & Luo, X. 2015 Experimental investigation of cylindrical converging shock waves interacting with a polygonal heavy gas cylinder. J. Fluid Mech. 784, 225–251.CrossRefGoogle Scholar
Si, T., Zhai, Z. & Luo, X. 2014 Experimental study of Richtmyer–Meshkov instability in a cylindrical converging shock tube. Laser Part. Beams 32, 343–351.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
Ukai, S., Balakrishnan, K. & Menon, S. 2011 Growth rate predictions of single- and multi-mode Richtmyer–Meshkov instability with reshock. Shock Waves 21, 533–546.CrossRefGoogle 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
Yang, J., Kubota, T. & Zukoski, E. E. 1993 Application of shock-induced mixing to supersonic combustion. AIAA J. 31, 854–862.CrossRefGoogle Scholar
Zhai, Z., Li, W., Si, T., Luo, X., Yang, J. & Lu, X. 2017 Refraction of cylindrical converging shock wave at an air/helium gaseous interface. Phys. Fluids 29, 016102.CrossRefGoogle Scholar
Zhai, Z., Liang, Y., Liu, L., Ding, J., Luo, X. & Zou, L. 2018 a Interaction of rippled shock wave with flat fast-slow interface. Phys. Fluids 30 (4), 046104.CrossRefGoogle Scholar
Zhai, Z., Liu, C., Qin, F., Yang, J. & Luo, X. 2010 Generation of cylindrical converging shock waves based on shock dynamics theory. Phys. Fluids 22, 041701.CrossRefGoogle Scholar
Zhai, Z., Zou, L., Wu, Q. & Luo, X. 2018 b Review of experimental Richtmyer–Meshkov instability in shock tube: from simple to complex. Proc. Inst. Mech. Engrs 232 (16), 2830–2849.Google Scholar
Zhou, Y. 2017 a Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I. Phys. Rep. 720–722, 1–136.Google Scholar
Zhou, Y. 2017 b Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II. Phys. Rep. 723–725, 1–160.Google Scholar
Zou, L., Al-Marouf, M., Cheng, W., Samtaney, R., Ding, J. & Luo, X. 2019 Richtmyer–Meshkov instability of an unperturbed interface subjected to a diffracted convergent shock. J. Fluid Mech. 879, 448–467.CrossRefGoogle Scholar