Hostname: page-component-5cf477f64f-r2nwp Total loading time: 0 Render date: 2025-04-07T21:17:17.789Z Has data issue: false hasContentIssue false
  • English
  • Français

Convergent Richtmyer–Meshkov turbulence by time-resolved planar laser-induced fluorescence measurement

Published online by Cambridge University Press:  14 March 2025

Yong Zhao ,
Juchun Ding Open the ORCID record for Juchun Ding [Opens in a new window] ,
Dong He ,
Zhangbo Zhou Open the ORCID record for Zhangbo Zhou [Opens in a new window]  and
Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window]
Yong Zhao
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Juchun Ding*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China Laoshan Laboratory, Qingdao 266237, PR China
Dong He
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Zhangbo Zhou
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Xisheng Luo*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
*
Corresponding authors: Juchun Ding, [email protected]; Xisheng Luo, [email protected]
Corresponding authors: Juchun Ding, [email protected]; Xisheng Luo, [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We report the first measurement of turbulent mixing developing from the convergent Richtmyer–Meshkov (RM) instability using time-resolved planar laser-induced fluorescence in a semi-annular convergent shock tube. A membraneless yet sharp interface with random short-wavelength perturbations, but controllable long-wavelength perturbations, is created by an automatically retractable plate, enhancing the reproducibility and reliability of RM turbulence experiments. The cylindrical air/SF$_6$ interface formed is first subjected to a convergent shock, then to its reflected shock and subsequently transits to turbulent mixing. It is found that the mixing width after reshock has a linear growth rate more than twice the rate in planar geometry. Also, the mixing width does not present power-law growth at late stages as in a planar geometry. However, the scalar spectrum and transition criterion obtained are similar to their planar counterparts. These findings indicate that the geometric constraint greatly affects the large scales of the flow, while having a weaker effect on the small scales. It is also found that the reflected shock significantly increases both scale separation and Reynolds number, explaining the rapid transition to turbulence following reshock.

JFM classification

Compressible Flows: Shock waves Instability: Nonlinear instability Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1007 , 25 March 2025 , A30
Check for updates
Copyright
© The Author(s), 2025. 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

Balakumar, B.J., Orlicz, G.C., Tomkins, C.D. & Prestridge, K.P. 2008 Simultaneous particle-image velocimetry-planar laser-induced fluorescence measurements of Richtmyer–Meshkov instability growth in a gas curtain with and without reshock. Phys. Fluids 20 (12), 124103.CrossRefGoogle Scholar
Barnes, C.W. et al. 2002 Observation of mix in a compressible plasma in a convergent cylindrical geometry. Phys. Plasmas 9 (11), 4431–4434.CrossRefGoogle 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
Boffetta, G. & Ecke, R.E. 2012 Two-dimensional turbulence. Annu. Rev. Fluid Mech. 44 (1), 427–451.CrossRefGoogle Scholar
Carter, J., Pathikonda, G., Jiang, N., Felver, J.J., Roy, S. & Ranjan, D. 2019 Time-resolved measurements of turbulent mixing in shock-driven variable-density flows. Sci. Rep. 9 (1), 20315.CrossRefGoogle ScholarPubMed
Cook, A.W. & Dimotakis, P.E. 2001 Transition stages of Rayleigh–Taylor instability between miscible fluids. J. Fluid Mech. 443, 69–99.CrossRefGoogle Scholar
Dimotakis, P.E. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 69–98.CrossRefGoogle Scholar
Ding, J., Si, T., Chen, M., Zhai, Z., Lu, X. & Luo, X. 2017 a On the interaction of a planar shock with a three-dimensional light gas cylinder. J. Fluid Mech. 828, 289–317.CrossRefGoogle Scholar
Ding, J., Si, T., Yang, J., Lu, X., Zhai, Z. & Luo, X. 2017 b 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
Ge, J., Zhang, X.T., Li, H.F. & Tian, B.L. 2020 Late-time turbulent mixing induced by multimode Richtmyer–Meshkov instability in cylindrical geometry. Phys. Fluids 32 (12), 124116.CrossRefGoogle Scholar
Groom, M. & Thornber, B. 2021 Reynolds number dependence of turbulence induced by the Richtmyer–Meshkov instability using direct numerical simulations. J. Fluid Mech. 908, A31.CrossRefGoogle Scholar
Hosseini, S.H.R. & Takayama, K. 2005 Experimental study of Richtmyer–Meshkov instability induced by cylindrical shock waves. Phys. Fluids 17 (8), 084101.CrossRefGoogle Scholar
Jacobs, J.W. 1992 Shock-induced mixing of a light-gas cylinder. J. Fluid Mech. 234 (-1), 629–649.CrossRefGoogle Scholar
Kraichnan, R.H. 1994 Anomalous scaling of a randomly advected passive scalar. Phys. Rev. Lett. 72 (7), 1016–1019.CrossRefGoogle ScholarPubMed
Leinov, E., Malamud, G., Elbaz, Y., Levin, L.A., Ben-Dor, G., Shvarts, D. & Sadot, O. 2009 Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions. J. Fluid Mech. 626, 449–475.CrossRefGoogle Scholar
Lindl, J., Landen, O., Edwards, J., Moses, E. & Team, N. 2014 Review of the national ignition campaign 2009–2012. Phys. Plasmas 21 (2), 020501.CrossRefGoogle 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 (5), 101–104.CrossRefGoogle Scholar
Mikaelian, K.O. 1989 Turbulent mixing generated by Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Physica D 36 (3), 343–357.CrossRefGoogle Scholar
Mohaghar, M., Carter, J., Pathikonda, G. & Ranjan, D. 2019 The transition to turbulence in shock-driven mixing: effects of Mach number and initial conditions. J. Fluid Mech. 871, 595–635.CrossRefGoogle Scholar
Noble, C., Ames, A., McConnell, R., Oakley, J., Rothamer, D. & Bonazza, R. 2023 Simultaneous measurements of kinetic and scalar energy spectrum time evolution in the Richtmyer–Meshkov instability upon reshock. J. Fluid Mech. 975, A39.CrossRefGoogle Scholar
Noble, C.D., Herzog, J.M., Ames, A.M., Oakley, J., Rothamer, D.A. & Bonazza, R. 2020 High speed PLIF study of the Richtmyer–Meshkov instability upon re-shock. Physica D 410, 132519.CrossRefGoogle Scholar
Pope, S. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Rayleigh, L. 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 (2), 297–319.CrossRefGoogle Scholar
Sewell, E.G., Ferguson, K.J., Krivets, V.V. & Jacobs, J.W. 2021 Time-resolved particle image velocimetry measurements of the turbulent Richtmyer–Meshkov instability. J. Fluid Mech. 917, A41.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 (1065), 192–196.Google Scholar
Thornber, B. & Zhou, Y. 2015 Numerical simulations of the two-dimensional multimode Richtmyer–Meshkov instability. Phys. Plasmas 22 (3), 032309.CrossRefGoogle Scholar
Tritschler, V.K., Olson, B.J., Lele, S.K., Hickel, S., Hu, X.Y. & Adams, N.A. 2014 On the Richtmyer–Meshkov instability evolving from a deterministic multimode planar interface. J. Fluid Mech. 755, 429–462.CrossRefGoogle Scholar
Ukai, S., Balakrishnan, K. & Menon, S. 2011 Growth rate predictions of single- and multi-mode Richtmyer–Meshkov instability with reshock. Shock Waves 21 (6), 533–546.CrossRefGoogle Scholar
Wang, R., Song, Y., Ma, Z., Ma, D., Wang, L. & Wang, P. 2022 The transition to turbulence in rarefaction-driven Rayleigh–Taylor mixing: effects of diffuse interface. Phys. Fluids 34 (1), 015125.Google Scholar
Weber, C.R., Haehn, N.S., Oakley, J.G., Rothamer, D.A. & Bonazza, R. 2014 An experimental investigation of the turbulent mixing transition in the Richtmyer–Meshkov instability. J. Fluid Mech. 748, 457–487.CrossRefGoogle Scholar
Zhou, Y. 2001 A scaling analysis of turbulent flows driven by Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Phys. Fluids 13 (2), 538–543.CrossRefGoogle Scholar
Zhou, Y., Cabot, W.H. & Thornber, B. 2016 Asymptotic behavior of the mixed mass in Rayleigh–Taylor and Richtmyer–Meshkov instability induced flows. Phys. Plasmas 23 (5), 052712.CrossRefGoogle Scholar
Zhou, Y., Clark, T.T., Clark, D.S., Gail Glendinning, S., Aaron Skinner, M., Huntington, C.M. & Remington, B.A. 2019 Turbulent mixing and transition criteria of flows induced by hydrodynamic instabilities. Phys. Plasmas 26 (8), 080901.CrossRefGoogle Scholar
Zhou, Y., Remington, B.A., Robey, H.F., Cook, A.W., Glendinning, S.G., Dimits, A. & Eliason, D. 2003 a Progress in understanding turbulent mixing induced by Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Phys. Plasmas 10 (5), 1883–1896.CrossRefGoogle Scholar
Zhou, Y., Robey, H.F. & Buckingham, A.C. 2003 b Onset of turbulence in accelerated high-Reynolds-number flow. Phys. Rev. E 67 (5), 056305.CrossRefGoogle ScholarPubMed
Supplementary material: File

Zhao et al. supplementary material 1

Evolution of the air/SF6 interface subjected to a cylindrical convergent shock.
Download Zhao et al. supplementary material 1(File)
File 3.9 MB
Supplementary material: File

Zhao et al. supplementary material 2

Zhao et al. supplementary material
Download Zhao et al. supplementary material 2(File)
File 513.1 KB