Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-17T17:08:33.049Z Has data issue: false hasContentIssue false
  • English
  • Français

On shock-induced evolution of a gas layer with two fast/slow interfaces

Published online by Cambridge University Press:  24 March 2022

Yu Liang Open the ORCID record for Yu Liang [Opens in a new window]  and
Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window]
Yu Liang
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China NYUAD Research Institute, New York University Abu Dhabi, Abu Dhabi 129188, UAE
Xisheng Luo*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The shock-induced evolution of a gas layer with two fast/slow interfaces is investigated theoretically and experimentally. Specifically, the gas layer is located between a lighter gas and a heavier gas, forming a light/medium/heavy (LMH) configuration. Linear stability analysis is utilised to derive a new analytical model to quantify the Richtmyer–Meshkov instability (RMI) on the two interfaces of such an A/B/C-type fluid layer. Three quasi-one-dimensional (1-D) LMH fluid layers with different initial layer thicknesses are generated to study the wave patterns and interface motions. A general 1-D theory is established to describe the motions of the shock/rarefaction waves reverberating inside the fluid layer and the displacements of the two interfaces. Six quasi-2-D LMH fluid layers with diverse initial layer-thickness and amplitude combinations are created to explore the hydrodynamic instabilities of the two interfaces. It is found that the interface coupling significantly influences the interface evolution, even resulting in an abnormal phase reversal of a shocked fast/slow interface if the two interfaces are anti-phase and the initial layer is very thin. The specific conditions for the abnormal phase reversal and the instability freeze out are deduced. Moreover, the additional RMI (or Rayleigh–Taylor stabilisation) imposed by the shock (or rarefaction waves) reverberating inside an LMH fluid layer on the first (or second) interface is quantified. It is proved that the reverberating waves inside an LMH fluid layer stabilise the two interfaces. Finally, a nonlinear model is obtained by incorporating the nonlinearity effect into the linear model, which well describes the perturbation growths of the two interfaces in a later regime.

JFM classification

Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 939 , 25 May 2022 , A16
Check for updates
Copyright
© The Author(s), 2022. 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

Aglitskiy, Y., et al. 2006 Perturbation evolution started by Richtmyer–Meshkov instability in planar laser targets. Phys. Plasmas 13 (8), 080703.CrossRefGoogle Scholar
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, 67–93.CrossRefGoogle Scholar
Balakumar, B.J., Orlicz, G.C., Tomkins, C.D. & Prestridge, K. 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, 124103.CrossRefGoogle Scholar
Brouillette, M. 2002 The Richtmyer–Meshkov instability. Annu. Rev. Fluid Mech. 34, 445–468.CrossRefGoogle Scholar
Budzinski, J.M., Benjamin, R.F. & Jacobs, J.W. 1994 Influence of initial conditions on the flow patterns of a shock-accelerated thin fluid layer. Phys. Fluids 6, 3510–3512.CrossRefGoogle Scholar
Dimonte, G. & Ramaprabhu, P. 2010 Simulations and model of the nonlinear Richtmyer–Meshkov instability. Phys. Fluids 22, 014104.CrossRefGoogle Scholar
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, 277–291.CrossRefGoogle Scholar
Drake, R.P. 2018 High-Energy-Density Physics: Foundation of Inertial Fusion and Experimental Astrophysics. Springer.CrossRefGoogle Scholar
Fraley, G. 1986 Rayleigh–Taylor stability for a normal shock wave-density discontinuity interaction. Phys. Fluids 29, 376–386.CrossRefGoogle Scholar
Goncharov, V.N. 2002 Analytical model of nonlinear, single-mode, classical Rayleigh–Taylor instability at arbitrary Atwood numbers. Phys. Rev. Lett. 88, 134502.CrossRefGoogle ScholarPubMed
Haines, B.M., et al. 2021 Constraining computational modeling of indirect drive double shell capsule implosions using experiments. Phys. Plasmas 28 (3), 032709.CrossRefGoogle Scholar
Hecht, J., Alon, U. & Shvarts, D. 1994 Potential flow models of Rayleigh–Taylor and Richtmyer–Meshkov bubble fronts. Phys. Fluids 6, 4019–4030.CrossRefGoogle Scholar
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
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, 583–586.CrossRefGoogle ScholarPubMed
Jacobs, J.W. & Sheeley, J.M. 1996 Experimental study of incompressible Richtmyer–Meshkov instability. Phys. Fluids 8, 405–415.CrossRefGoogle Scholar
Kuranz, C.C., et al. 2018 How high energy fluxes may affect Rayleigh–Taylor instability growth in young supernova remnants. Nat. Commun. 9, 1564.CrossRefGoogle ScholarPubMed
Li, C. & Book, D.L. 1991 Instability generated by acceleration due to rarefaction waves. Phys. Rev. A 43 (6), 3153.CrossRefGoogle ScholarPubMed
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
Li, C., Kailasanath, K. & Book, D.L. 1991 Mixing enhancement by expansion waves in supersonic flows of different densities. Phys. Fluids A 3 (5), 1369–1373.CrossRefGoogle Scholar
Liang, Y., Liu, L., Zhai, Z., Ding, J., Si, T. & Luo, X. 2021 Richtmyer–Meshkov instability on two-dimensional multi-mode interfaces. J. Fluid Mech. 928, A37.CrossRefGoogle Scholar
Liang, Y., Liu, L., Zhai, Z., Si, T. & Wen, C.-Y. 2020 a Evolution of shock-accelerated heavy gas layer. J. Fluid Mech. 886, A7.CrossRefGoogle Scholar
Liang, Y. & Luo, X. 2021 a On shock-induced heavy-fluid-layer evolution. J. Fluid Mech. 920, A13.CrossRefGoogle Scholar
Liang, Y. & Luo, X. 2021 b Shock-induced dual-layer evolution. J. Fluid Mech. 929, R3.CrossRefGoogle Scholar
Liang, Y. & Luo, X. 2022 On shock-induced light-fluid-layer evolution. J. Fluid Mech. 933, A10.CrossRefGoogle Scholar
Liang, Y., Zhai, Z., Ding, J. & Luo, X. 2019 Richtmyer–Meshkov instability on a quasi-single-mode interface. J. Fluid Mech. 872, 729–751.CrossRefGoogle Scholar
Liang, Y., Zhai, Z., Luo, X. & Wen, C. 2020 b Interfacial instability at a heavy/light interface induced by rarefaction waves. J. Fluid Mech. 885, A42.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., Liang, Y., Si, T. & Zhai, Z. 2019 Effects of non-periodic portions of interface on Richtmyer–Meshkov instability. J. Fluid Mech. 861, 309–327.CrossRefGoogle Scholar
Luo, X., Liu, L., Liang, Y., Ding, J. & Wen, C.Y. 2020 Richtmyer–Meshkov instability on a dual-mode interface. J. Fluid Mech. 905, A5.CrossRefGoogle Scholar
Mansoor, M.M., Dalton, S.M., Martinez, A.A., Desjardins, T., Charonko, J.J. & Prestridge, K.P. 2020 The effect of initial conditions on mixing transition of the Richtmyer–Meshkov instability. J. Fluid Mech. 904, A3.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
Meyer, K.A. & Blewett, P.J. 1972 Numerical investigation of the stability of a shock-accelerated interface between two fluids. Phys. Fluids 15, 753–759.CrossRefGoogle Scholar
Mikaelian, K.O. 1985 Richtmyer–Meshkov instabilities in stratified fluids. Phys. Rev. A 31, 410–419.CrossRefGoogle ScholarPubMed
Mikaelian, K.O. 1995 Rayleigh–Taylor and Richtmyer–Meshkov instabilities in finite-thickness fluid layers. Phys. Fluids 7 (4), 888–890.CrossRefGoogle Scholar
Mikaelian, K.O. 1996 Numerical simulations of Richtmyer–Meshkov instabilities in finite-thickness fluid layers. Phys. Fluids 8 (5), 1269–1292.CrossRefGoogle Scholar
Mikaelian, K.O. 1998 Analytic approach to nonlinear Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Phys. Rev. Lett. 80, 508–511.CrossRefGoogle Scholar
Mikaelian, K.O. 2003 Explicit expressions for the evolution of single-mode Rayleigh–Taylor and Richtmyer–Meshkov instabilities at arbitrary Atwood numbers. Phys. Rev. E 67, 026319.CrossRefGoogle ScholarPubMed
Montgomery, D.S., et al. 2018 Design considerations for indirectly driven double shell capsules. Phys. Plasmas 25 (9), 092706.CrossRefGoogle Scholar
Morgan, R.V., Cabot, W.H., Greenough, J.A. & Jacobs, J.W. 2018 Rarefaction-driven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime. J. Fluid Mech. 838, 320–355.CrossRefGoogle Scholar
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, 34–60.CrossRefGoogle Scholar
Nishihara, K., Wouchuk, J.G., Matsuoka, C., Ishizaki, R. & Zhakhovsky, V.V. 2010 Richtmyer–Meshkov instability: theory of linear and nonlinear evolution. Phil. Trans. R. Soc. A 368, 1769–1807.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Orlicz, G.C., Balasubramanian, S. & Prestridge, K.P. 2013 Incident shock Mach number effects on Richtmyer–Meshkov mixing in a heavy gas layer. Phys. Fluids 25 (11), 114101.CrossRefGoogle Scholar
Peng, N., Yang, Y., Wu, J. & Xiao, Z. 2021 Mechanism and modelling of the secondary baroclinic vorticity in the Richtmyer–Meshkov instability. J. Fluid Mech. 911, A56.CrossRefGoogle Scholar
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, 4353–4356.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
Rightley, P.M., Vorobieff, P. & Benjamin, R.F. 1997 Evolution of a shock-accelerated thin fluid layer. Phys. Fluids 9 (6), 1770–1782.CrossRefGoogle Scholar
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, 1654–1657.CrossRefGoogle Scholar
Sohn, S.I. 2003 Simple potential-flow model of Rayleigh–Taylor and Richtmyer–Meshkov instabilities for all density ratios. Phys. Rev. E 67, 026301.CrossRefGoogle ScholarPubMed
Sun, R., Ding, J., Zhai, Z., Si, T. & Luo, X. 2020 Convergent Richtmyer–Meshkov instability of heavy gas layer with perturbed inner surface. J. Fluid Mech. 902, A3.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
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, 288–306.CrossRefGoogle Scholar
Tomkins, C., Kumar, S., Orlicz, G. & Prestridge, K. 2008 An experimental investigation of mixing mechanisms in shock-accelerated flow. J. Fluid Mech. 611, 131–150.CrossRefGoogle Scholar
Vandenboomgaerde, M., Gauthier, S. & Mügler, C. 2002 Nonlinear regime of a multimode Richtmyer–Meshkov instability: a simplified perturbation theory. Phys. Fluids 14 (3), 1111–1122.CrossRefGoogle Scholar
Vandenboomgaerde, M., Mügler, C. & Gauthier, S. 1998 Impulsive model for the Richtmyer–Meshkov instability. Phys. Rev. E 58 (2), 1874.CrossRefGoogle Scholar
Velikovich, A.L. & Dimonte, G. 1996 Nonlinear perturbation theory of the incompressible Richtmyer–Meshkov instability. Phys. Rev. Lett. 76 (17), 3112.CrossRefGoogle ScholarPubMed
Velikovich, A. & Phillips, L. 1996 Instability of a plane centered rarefaction wave. Phys. Fluids 8 (4), 1107–1118.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., Zou, L., Wu, Q. & Luo, X. 2018 Review of experimental Richtmyer–Meshkov instability in shock tube: from simple to complex. Proc. Inst. Mech. Engng C 232, 2830–2849.CrossRefGoogle Scholar
Zhang, Q. 1998 Analytical solutions of Layzer-type approach to unstable interfacial fluid mixing. Phys. Rev. Lett. 81 (16), 3391.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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, 47–61.CrossRefGoogle Scholar
Zhang, Q. & Sohn, S.I. 1997 Nonlinear theory of unstable fluid mixing driven by shock wave. Phys. Fluids 9, 1106–1124.CrossRefGoogle 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
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., Glendinning, S.S., Skinner, A.A., Huntington, C., Hurricane, O.A., Dimits, A.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., et al. 2021 Rayleigh–Taylor and Richtmyer–Meshkov instabilities: a journey through scales. Physica D 423, 132838.CrossRefGoogle Scholar