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Coupled Richtmyer–Meshkov and Kelvin–Helmholtz instability on a shock-accelerated inclined single-mode interface

Published online by Cambridge University Press:  02 October 2024

Qing Cao ,
Jiaxuan Li Open the ORCID record for Jiaxuan Li [Opens in a new window] ,
He Wang Open the ORCID record for He Wang [Opens in a new window] ,
Zhigang Zhai Open the ORCID record for Zhigang Zhai [Opens in a new window]  and
Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window]
Qing Cao
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Jiaxuan Li
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
He Wang*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Zhigang Zhai*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Xisheng Luo
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China State Key Laboratory of High-Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

The coupling of Richtmyer–Meshkov instability (RMI) and Kelvin–Helmholtz instability (KHI), referred to as RM-KHI, on a shock-accelerated inclined single-mode air–SF$_6$ interface is studied through shock-tube experiments, focusing on the evolution of the perturbation distributed along the inclined interface. To clearly capture the linear (overall linear to nonlinear) evolution of RM-KHI, a series of experiments with a weak (relatively strong) incident shock is conducted. For each series of experiments, various $\theta _{i}$ (angle between incident shock and equilibrium position of the initial interface) are considered. The nonlinear flow features manifest earlier and develop faster when $\theta _{i}$ is larger and/or shock is stronger. In addition, the interface with $\theta _{i}>0^{\circ }$ evolves obliquely along its equilibrium position under the effect of KHI. RMI dominates the early-time amplitude evolution regardless of $\theta _{i}$ and shock intensity, which arises from the discrepancy in the evolution laws between RMI and KHI. KHI promotes the post-early-stage amplitude growth and its contribution is related positively to $\theta _{i}$. An evident exponential-like amplitude evolution behaviour emerges in RM-KHI with a relatively strong shock and large $\theta _{i}$. The linear model proposed by Mikaelian (Phys. Fluids, vol. 6, 1994, pp. 1943–1945) is valid for RM-KHI within the linear period. In contrast, the adaptive vortex model (Sohn et al., Phys. Rev. E, vol. 82, 2010, p. 046711) can effectively predict both the interface morphology and overall amplitude evolutions from the linear to nonlinear regimes.

JFM classification

Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 996 , 10 October 2024 , A37
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© The Author(s), 2024. Published by Cambridge University Press

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References

Abd-El-Fattah, A.M. & Henderson, L.F. 1978 a Shock waves at a fast-slow gas interface. J. Fluid Mech. 86, 15–32.10.1017/S0022112078000981CrossRefGoogle Scholar
Abd-El-Fattah, A.M. & Henderson, L.F. 1978 b Shock waves at a slow-fast gas interface. J. Fluid Mech. 89, 79–95.10.1017/S0022112078002475CrossRefGoogle Scholar
Abd-El-Fattah, A.M., Henderson, L.F. & Lozzi, A. 1976 Precursor shock waves at a slow-fast gas interface. J. Fluid Mech. 76, 157–176.10.1017/S0022112076003182CrossRefGoogle Scholar
Abgrall, R. & Karni, S. 2001 Computations of compressible multifluids. J. Comput. Phys. 169, 594–623.10.1006/jcph.2000.6685CrossRefGoogle Scholar
Banerjee, R., Mandal, L., Khan, M. & Gupta, M.R. 2012 Effect of viscosity and shear flow on the nonlinear two fluid interfacial structures. Phys. Plasmas 19, 122105.10.1063/1.4769728CrossRefGoogle Scholar
Betti, R. & Hurricane, O.A. 2016 Inertial-confinement fusion with lasers. Nat. Phys. 12, 435–448.CrossRefGoogle Scholar
Billig, F.S. 1993 Research on supersonic combustion. J. Propul. Power 9, 499–514.CrossRefGoogle Scholar
Chen, C., Xing, Y., Wang, H., Zhai, Z. & Luo, X. 2023 Experimental study on Richtmyer-Meshkov instability at a light-heavy interface over a wide range of Atwood numbers. J. Fluid Mech. 975, A29.CrossRefGoogle Scholar
Collins, B.D. & Jacobs, J.W. 2002 PLIF flow visualization and measurements of the Richtmyer-Meshkov instability of an air/SF$_6$ interface. J. Fluid Mech. 464, 113–136.CrossRefGoogle Scholar
Ding, J., Si, T., Chen, M., Zhai, Z., Lu, X. & Luo, X. 2017 On the interaction of a planar shock with a three-dimensional light gas cylinder. J.Fluid Mech. 828, 289–317.10.1017/jfm.2017.528CrossRefGoogle Scholar
Drazin, P.G. & Reid, W.H. 1981 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Edwards, M.J., et al. 2011 The experimental plan for cryogenic layered target implosions on the National Ignition Facility – the inertial confinement approach to fusion. Phys. Plasmas 18, 051003.10.1063/1.3592173CrossRefGoogle Scholar
Feng, L., Xu, J., Zhai, Z. & Luo, X. 2021 Evolution of shock-accelerated double-layer gas cylinder. Phys. Fluids 33, 086105.10.1063/5.0062459CrossRefGoogle Scholar
Glendinning, S.G., et al. 2003 Effect of shock proximity on Richtmyer-Meshkov growth. Phys. Plasmas 10, 1931–1936.10.1063/1.1562165CrossRefGoogle Scholar
de Gouvello, Y., Dutreuilh, M., Gallier, S., Melguizo-Gavilanes, J. & Mevel, R. 2021 Shock wave refraction patterns at a slow-fast gas-gas interface at superknock relevant conditions. Phys. Fluids 33, 116101.10.1063/5.0066345CrossRefGoogle Scholar
Guo, X., Zhai, Z., Si, T. & Luo, X. 2019 Bubble merger in initial Richtmyer-Meshkov instability on inverse-chevron interface. Phys. Rev. Fluids 4, 092001.CrossRefGoogle Scholar
Haines, B.M., Vold, E.L., Molvig, K., Aldrich, C. & Rauenzahn, R. 2014 The effects of plasma diffusion and viscosity on turbulent instability growth. Phys. Plasmas 21, 092306.CrossRefGoogle Scholar
Harding, E.C., Hansen, J.F., Hurricane, O.A., Drake, R.P., Robey, H.F., Kuranz, C.C., Remington, B.A., Bono, M.J., Grosskopf, M.J. & Gillespie, R.S. 2009 Observation of a Kelvin–Helmholtz instability in a high-energy-density plasma on the Omega laser. Phys. Rev. Lett. 103, 045005.10.1103/PhysRevLett.103.045005CrossRefGoogle Scholar
Helmholtz, H. 1868 On discontinuous movements of fluids. Phil. Mag. 36, 337–346.CrossRefGoogle Scholar
Henderson, L.F. 1966 The refraction of a plane shock wave at a gas interface. J. Fluid Mech. 26, 607–637.10.1017/S0022112066001435CrossRefGoogle Scholar
Henderson, L.F. 2014 The refraction of shock pairs. Shock Waves 24, 553–572.10.1007/s00193-014-0513-8CrossRefGoogle Scholar
Henderson, L.F., Colella, P. & Puckett, E.G. 1991 On the refraction of shock waves at a slow-fast gas interface. J. Fluid Mech. 224, 1–27.CrossRefGoogle Scholar
Hurricane, O.A. 2008 Design for a high energy density Kelvin–Helmholtz experiment. High Energy Dens. Phys. 4, 97–102.10.1016/j.hedp.2008.02.002CrossRefGoogle Scholar
Hurricane, O.A., et al. 2012 Validation of a turbulent Kelvin–Helmholtz shear layer model using a high-energy-density OMEGA laser experiment. Phys. Rev. Lett. 109, 155004.CrossRefGoogle ScholarPubMed
Jacobs, J.W. & Krivets, V.V. 2005 Experiments on the late-time development of single-mode Richtmyer-Meshkov instability. Phys. Fluids 17, 034105.CrossRefGoogle Scholar
Jahn, R.G. 1956 The refraction of shock waves at a gaseous interface. J. Fluid Mech. 1, 457–489.10.1017/S0022112056000299CrossRefGoogle Scholar
Jiang, G.S. & Shu, C.W. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202–228.CrossRefGoogle Scholar
Kelly, R.E. 1965 The stability of an unsteady Kelvin–Helmholtz flow. J. Fluid Mech. 22, 547–560.CrossRefGoogle Scholar
Kerr, R.M. 1988 Simulation of Rayleigh–Taylor flows using vortex blobs. J. Comput. Phys. 76, 48–84.CrossRefGoogle Scholar
Krasny, R. 1986 Desingularization of periodic vortex sheet roll-up. J. Comput. Phys. 65, 292–313.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
Layzer, D. 1955 On the instability of superposed fluids in a gravitational field. Astrophys. J. 122, 1–12.CrossRefGoogle Scholar
Li, J., Cao, Q., Wang, H., Zhai, Z. & Luo, X. 2023 New interface formation method for shock-interface interaction studies. Exp. Fluids 64, 170.10.1007/s00348-023-03710-yCrossRefGoogle Scholar
Liang, Y., Zhai, Z., Ding, J. & Luo, X. 2019 Richtmyer-Meshkov instability on a quasi-single-mode interface. J. Fluid Mech. 872, 729–751.10.1017/jfm.2019.416CrossRefGoogle Scholar
Lindl, J., Landen, O., Edwards, J., Moses, E. & Team, N. 2014 Review of the national ignition campaign 2009–2012. Phys. Plasmas 21, 020501.10.1063/1.4865400CrossRefGoogle 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, R2.10.1017/jfm.2018.628CrossRefGoogle Scholar
Luo, X., Dong, P., Si, T. & Zhai, Z. 2016 The Richtmyer-Meshkov instability of a ‘V’ shaped air/SF$_6$ interface. J. Fluid Mech. 802, 186–202.CrossRefGoogle Scholar
Maeda, K., et al. 2010 An asymmetric explosion as the origin of spectral evolution diversity in type Ia supernovae. Nature 466, 82–85.10.1038/nature09122CrossRefGoogle ScholarPubMed
Malamud, G., Shimony, A., Wan, W.C., Di Stefano, C.A., Elbaz, Y., Kuranz, C.C., Keiter, P.A., Drake, R.P. & Shvarts, D. 2013 A design of a two-dimensional, supersonic KH experiment on OMEGA-EP. High Energy Dens. Phys. 9, 672–686.10.1016/j.hedp.2013.06.002CrossRefGoogle Scholar
Matsuoka, C. & Nishihara, K. 2006 Vortex core dynamics and singularity formations in incompressible Richtmyer-Meshkov instability. Phys. Rev. E 73, 026304.CrossRefGoogle ScholarPubMed
McFarland, J., Greenough, J. & Ranjan, D. 2014 a Simulations and analysis of the reshocked inclined interface Richtmyer-Meshkov instability for linear and nonlinear interface perturbations. Trans. ASME J. Fluids Engng 136, 071203.CrossRefGoogle Scholar
McFarland, J., Reilly, D., Creel, S., McDonald, C., Finn, T. & Ranjan, D. 2014 b Experimental investigation of the inclined interface Richtmyer-Meshkov instability before and after reshock. Exp. Fluids 55, 1–14.CrossRefGoogle Scholar
McFarland, J.A., Greenough, J.A. & Ranjan, D. 2011 Computational parametric study of a Richtmyer-Meshkov instability for an inclined interface. Phys. Rev. E 84, 026303.CrossRefGoogle ScholarPubMed
McFarland, J.A., Greenough, J.A. & Ranjan, D. 2013 Investigation of the initial perturbation amplitude for the inclined interface Richtmyer-Meshkov instability. Phys. Scr. T155, 014014.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. 1994 Oblique shocks and the combined Rayleigh–Taylor, Kelvin–Helmholtz, and Richtmyer-Meshkov instabilities. Phys. Fluids 6, 1943–1945.CrossRefGoogle Scholar
Mohaghar, M., Carter, J., Musci, B., Reilly, D., McFarland, J. & Ranjan, D. 2017 Evaluation of turbulent mixing transition in a shock-driven variable-density flow. J. Fluid Mech. 831, 779–825.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, 595–635.10.1017/jfm.2019.330CrossRefGoogle Scholar
Niederhaus, C.E. & Jacobs, J.W. 2003 Experimental study of the Richtmyer-Meshkov instability of incompressible fluids. J. Fluid Mech. 485, 243–277.CrossRefGoogle Scholar
Nourgaliev, R.R., Sushchikh, S.Y., Dinh, T.N. & Theofanous, T.G. 2005 Shock wave refraction patterns at interfaces. Intl J. Multiphase Flow 31, 969–995.CrossRefGoogle Scholar
Nuckolls, J., Wood, L., Thiessen, A. & Zimmerman, G. 1972 Laser compression of matter to super-high densities: thermonuclear (CTR) applications. Nature 239, 139–142.CrossRefGoogle Scholar
Pellone, S., Di Stefano, C.A., Rasmus, A.M., Kuranz, C.C. & Johnsen, E. 2021 Vortex-sheet modeling of hydrodynamic instabilities produced by an oblique shock interacting with a perturbed interface in the HED regime. Phys. Plasmas 28, 022303.CrossRefGoogle Scholar
Polachek, H. & Seeger, R.J. 1951 On shock-wave phenomena-refraction of shock waves at a gaseous interface. Phys. Rev. 84, 922–929.10.1103/PhysRev.84.922CrossRefGoogle Scholar
Pullin, D.I. 1982 Numerical studies of surface-tension effects in nonlinear Kelvin–Helmholtz and Rayleigh–Taylor instability. J. Fluid Mech. 119, 507–532.CrossRefGoogle Scholar
Rangel, R.H. & Sirignano, W.A. 1988 Nonlinear growth of Kelvin–Helmholtz instability: effect of surface tension and density ratio. Phys. Fluids 31, 1845–1855.CrossRefGoogle Scholar
Rangel, R.H. & Sirignano, W.A. 1991 The linear and nonlinear shear instability of a fluid sheet. Phys. Fluids A 3, 2392–2400.CrossRefGoogle Scholar
Rasmus, A.M., et al. 2018 Shock-driven discrete vortex evolution on a high-Atwood number oblique interface. Phys. Plasmas 25, 032119.CrossRefGoogle Scholar
Rasmus, A.M., et al. 2019 Shock-driven hydrodynamic instability of a sinusoidally perturbed, high-Atwood number, oblique interface. Phys. Plasmas 26, 062103.CrossRefGoogle Scholar
Reilly, D., McFarland, J., Mohaghar, M. & Ranjan, D. 2015 The effects of initial conditions and circulation deposition on the inclined-interface reshocked Richtmyer-Meshkov instability. Exp. Fluids 56, 1–16.CrossRefGoogle Scholar
Ren, Z., Wang, B., Xiang, G., Zhao, D. & Zheng, L. 2019 Supersonic spray combustion subject to scramjets: progress and challenges. Prog. Aerosp. Sci. 105, 40–59.CrossRefGoogle Scholar
Richtmyer, R.D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 13, 297–319.10.1002/cpa.3160130207CrossRefGoogle Scholar
Rikanati, A., Oron, D., Sadot, O. & Shvarts, D. 2003 High initial amplitude and high Mach number effects on the evolution of the single-mode Richtmyer-Meshkov instability. Phys. Rev. E 67, 026307.CrossRefGoogle ScholarPubMed
Sadot, O., Rikanati, A., Oron, D., Ben-Dor, G. & Shvarts, D. 2003 An experimental study of the high Mach number and high initial-amplitude effects on the evoltion of the single-mode Richtmyer-Meshkov instability. Laser Part. Beams 21, 341–346.CrossRefGoogle Scholar
Samtaney, R. & Zabusky, N.J. 1994 Circulation deposition on shock-accelerated planar and curved density-stratified interfaces: models and scaling laws. J. Fluid Mech. 269, 45–78.CrossRefGoogle Scholar
Smalyuk, V.A., Sadot, O., Delettrez, J.A., Meyerhofer, D.D., Regan, S.P. & Sangster, T.C. 2005 Fourier-space nonlinear Rayleigh–Taylor growth measurements of 3D laser-imprinted modulations in planar targets. Phys. Rev. Lett. 95, 215001.CrossRefGoogle ScholarPubMed
Smalyuk, V.A., et al. 2020 Recent and planned hydrodynamic instability experiments on indirect-drive implosions on the National Ignition Facility. High Energy Dens. Phys. 36, 100820.CrossRefGoogle Scholar
Sohn, S.-I., Yoon, D. & Hwang, W. 2010 Long-time simulations of the Kelvin–Helmholtz instability using an adaptive vortex method. Phys. Rev. E 82, 046711.10.1103/PhysRevE.82.046711CrossRefGoogle ScholarPubMed
Taub, A.H. 1947 Refraction of plane shock waves. Phys. Rev. 72, 51–60.CrossRefGoogle Scholar
Thompson, W.S. 1871 Hydrokinetic solutions and observations. Phil. Mag. 42, 362–377.10.1080/14786447108640585CrossRefGoogle Scholar
Tryggvason, G. 1988 Numerical simulations of the Rayleigh–Taylor instability. J. Comput. Phys. 75, 253–282.CrossRefGoogle Scholar
Vandenboomgaerde, M., Souffland, D., Mariani, C., Biamino, L., Jourdan, G. & Houas, L. 2014 An experimental and numerical investigation of the dependency on the initial conditions of the Richtmyer–Meshkov instability. Phys. Fluids 26, 024109.CrossRefGoogle Scholar
Velikovich, A.L., Herrmann, M. & Abarzhi, S.I. 2014 Perturbation theory and numerical modelling of weakly and moderately nonlinear dynamics of the incompressible Richtmyer-Meshkov instability. J. Fluid Mech. 751, 432–479.CrossRefGoogle Scholar
Wang, H., Wang, H., Zhai, Z. & Luo, X. 2022 Effects of obstacles on shock-induced perturbation growth. Phys. Fluids 34, 086112.CrossRefGoogle Scholar
Wang, H., Wang, H., Zhai, Z. & Luo, X. 2023 High-amplitude effect on single-mode Richtmyer-Meshkov instability of a light-heavy interface. Phys. Fluids 35, 016106.CrossRefGoogle Scholar
Wang, L., Ye, W., Fan, Z., Li, Y., He, X. & Yu, M. 2009 Weakly nonlinear analysis on the Kelvin–Helmholtz instability. Europhys. Lett. 86, 15002.CrossRefGoogle Scholar
Wang, M., Si, T. & Luo, X. 2013 Generation of polygonal gas interfaces by soap film for Richtmyer-Meshkov instability study. Exp. Fluids 54, 1427–1435.CrossRefGoogle Scholar
Wang, X., Hu, X., Wang, S., Pan, H. & Yin, J. 2021 Linear analysis of Atwood number effects on shear instability in the elastic-plastic solids. Sci. Rep. 11, 18049.CrossRefGoogle ScholarPubMed
Xiang, G. & Wang, B. 2019 Theoretical and numerical studies on shock reflection at water/air two-phase interface: fast-slow case. Intl J. Multiphase Flow 114, 219–228.CrossRefGoogle Scholar
Yang, J., Kubota, T. & Zukoski, E.E. 1993 Application of shock-induced mixing to supersonic combustion. AIAA J. 31, 854–862.10.2514/3.11696CrossRefGoogle 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., Clark, T.T., Clark, D.S., Glendinning, S.G., Skinner, M.A., Huntington, C.M., Hurricane, O.A., Dimits, A.M. & Remington, B.A. 2019 Turbulent mixing and transition criteria of flows induced by hydrodynamic instabilities. Phys. Plasmas 26, 080901.CrossRefGoogle Scholar
Zhou, Y., et al. 2021 Rayleigh–Taylor and Richtmyer-Meshkov instabilities: a journey through scales. Physica D 423, 132838.10.1016/j.physd.2020.132838CrossRefGoogle Scholar