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On divergent Richtmyer–Meshkov instability of a light/heavy interface

Published online by Cambridge University Press:  02 September 2020

Ming Li ,
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] ,
Naian Liu ,
Shenghong Huang  and
Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window]
Ming Li
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
Naian Liu
Affiliation:
State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei230026, PR China
Shenghong Huang
Affiliation:
CAS Key Laboratory of Mechanical Behavior and Design of Materials, 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 State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei230026, PR China
*
†Email addresses for correspondence: djc@ustc.edu.cn, xluo@ustc.edu.cn
†Email addresses for correspondence: djc@ustc.edu.cn, xluo@ustc.edu.cn
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Abstract

We report the first experiments on divergent shock-driven Richtmyer–Meshkov instability (RMI) at well-controlled single-mode interfaces. These experiments are performed in a novel divergent shock tube designed by shock dynamics theory. Generally, the perturbation growth can be divided into three successive stages: linear growth, quick reduction in growth rate and instability freeze-out. It is observed that the growth rate at each stage is far lower than its counterpart in planar or convergent geometry due to geometric divergence. We also found that nonlinearity is much weaker than that in planar or convergent RMI, and has a negligible influence on the overall amplitude growth even at late stages when it has become strong. This weak nonlinear effect is because the growth of the third harmonic counteracts its feedback to the fundamental mode. As a consequence, the linear theory of Bell (report no. LA-1321) accounting for geometric divergence and Rayleigh–Taylor (RT) stabilization caused by flow deceleration can reasonably predict the present results from early to late stages. The instability freeze-out at late times is ascribed to the negative growth induced by geometric divergence and RT stabilization, and is also well reproduced by the linear theory.

JFM classification

Mixing: Turbulent mixing Compressible Flows: Shock waves Turbulent Flows: Compressible turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 901 , 25 October 2020 , A38
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Arnett, W. D., Bahcall, J. N., Kirshner, R. P. & Woosley, S. E. 1989 Supernova 1987A. Annu. Rev. Astron. Astrophys. 27, 629–700.CrossRefGoogle Scholar
Bell, G. I. 1951 Taylor instability on cylinders and spheres in the small amplitude approximation. Report No. LA-1321. LANL.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
Chandra, N., Ganpule, S., Kleinschmit, N. N., Feng, R., Holmberg, A. D., Sundaramurthy, A., Selvan, V. & Alai, A. 2012 Evolution of blast wave profiles in simulated air blasts: experiment and computational modeling. Shock Waves 22, 403–415.CrossRefGoogle Scholar
Chester, W. 1954 The quasi-cylindrical shock tube. Philos. Mag. 45, 1293–1301.CrossRefGoogle Scholar
Chisnell, R. F. 1957 The motion of a shock wave in a channel, with applications to cylindrical and spherical shock waves. J. Fluid Mech. 2, 286–298.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., Si, T., Yang, J., Lu, X., Zhai, Z. & Luo, X. 2017 Measurement of a Richtmyer–Meshkov instability at an air-SF$_6$ interface in a semiannular shock tube. Phys. Rev. Lett. 119 (1), 014501.CrossRefGoogle Scholar
Hosseini, S. H. R., Ogawa, T. & Takayama, K. 2000 Holographic interferometric visualization of the Richtmyer-Meshkov instability induced by cylindrical shock waves. J. Vis. 2 (3–4), 371–380.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
Kuranz, C. C., Park, H. S., Huntington, C. M., Miles, A. R., Remington, B. A., Plewa, T., Trantham, M. R., Robey, H. F., Shvarts, D., Shimony, A., et al. 2018 How high energy fluxes may affect Rayleigh–Taylor instability growth in young supernova remnants. Nat. Commun. 9, 1564.CrossRefGoogle ScholarPubMed
Lei, F., Ding, J., Si, T., Zhai, Z. & Luo, X. 2017 Experimental study on a sinusoidal air/SF$_6$ interface accelerated by a cylindrically converging shock. J. Fluid Mech. 826, 819–829.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
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., Li, M., Ding, J., Zhai, Z. & Si, T. 2019 Nonlinear behaviour of convergent Richtmyer–Meshkov instability. J. Fluid Mech. 877, 130–141.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
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. London Math. Soc. 14, 170–177.Google Scholar
Reshotko, E. 1976 Boundary-layer stability and transition. Annu. Rev. Fluid Mech. 8, 311–349.CrossRefGoogle Scholar
Richtmyer, R. D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Math. 13, 297–319.CrossRefGoogle Scholar
Saric, W. S., Reed, H. L. & Kerschen, E. J. 2002 Boundary-layer receptivity to freestream disturbances. Annu. Rev. Fluid Mech. 34, 291–319.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
Stewart, J. B. & Pecora, C. 2015 Explosively driven air blast in a conical shock tube. Rev. Sci. Instrum. 86, 035108.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. & Aymard, C. 2011 Analytical theory for planar shock focusing through perfect gas lens and shock tube experiment designs. Phys. Fluids 23 (1), 016101.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
Wang, L. F., Wu, J. F., Guo, H. Y., Ye, W. H., Liu, J., Zhang, W. Y. & He, X. T. 2015 Weakly nonlinear Bell–Plesset effects for a uniformly converging cylinder. Phys. Plasmas 22, 082702.Google Scholar
Whitham, G. B. 1958 On the propagation of shock waves through regions of non-uniform area or flow. J. Fluid Mech. 4, 337–360.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., 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
Zhan, D., Li, Z., Yang, J., Zhu, Y. & Yang, J. 2018 Note: a contraction channel design for planar shock wave enhancement. Rev. Sci. Instrum. 89, 056104.CrossRefGoogle ScholarPubMed
Zhou, Y. 2017 Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I. Phys. Rep. 720–722, 1–136.Google Scholar