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Asymptotic matching modal model on Richtmyer–Meshkov instability

Published online by Cambridge University Press:  26 December 2024

Jiaxuan Li Open the ORCID record for Jiaxuan Li [Opens in a new window] ,
Chenren Chen ,
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]
Jiaxuan Li
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Chenren Chen
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 State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, 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

An asymptotic matching modal model is established based on the singular perturbation method for predicting mode evolution in single- and dual-mode interfaces accelerated by a shock wave. The startup process is incorporated into the model to provide a complete description of the mode evolution after the shock impact. Through considering the feedback from high-order harmonic to the third-order harmonic, the model accuracy is improved and the model divergence is prevented. In addition, the model can evaluate the mutual-coupling effect on the amplitude variations of high-order harmonics besides the ‘beat modes’. To validate the model, experiments on both light–heavy and heavy–light interfaces subject to a shock wave are conducted, and both single- and dual-mode interfaces formed by the soap-film technique are involved. The interface profiles extracted from mode decomposition and predicted by the model show high consistency with the experimental counterparts. Good agreement of the mode amplitude growths between the experiments and theoretical predictions shows the superiority of the model, especially for the heavy–light interface.

JFM classification

Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1002 , 10 January 2025 , A16
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Anderson, J.D. 1990 Modern Compressible Flow: With Historical Perspective. McGraw-Hill.Google Scholar
Chapman, P.R. & Jacobs, J.W. 2006 Experiments on the three-dimensional incompressible Richtmyer–Meshkov instability. Phys. Fluids 18, 074101.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
Chen, Q., Li, L., Zhang, Y. & Tian, B. 2019 Effects of the Atwood number on the Richtmyer–Meshkov instability in elastic–plastic media. Phys. Rev. E 99, 053102.CrossRefGoogle ScholarPubMed
Chu, Y., Wang, Z., Qi, J., Xu, Z. & Li, Z. 2022 Numerical performance assessment of double-shell targets for Z-pinch dynamic hohlraum. Matt. Radiat. Extrem. 7, 035902.CrossRefGoogle Scholar
Cobos Campos, F. & Wouchuk, J.G. 2014 Analytical asymptotic velocities in linear Richtmyer–Meshkov-like flows. Phys. Rev. E 90, 053007.CrossRefGoogle ScholarPubMed
Cobos Campos, F. & Wouchuk, J.G. 2016 Analytical scalings of the linear Richtmyer–Meshkov instability when a shock is reflected. Phys. Rev. E 93, 053111.CrossRefGoogle Scholar
Di Stefano, C., Rasmus, A., Doss, F., Flippo, K., Hager, J., Kline, J. & Bradley, P. 2017 Multimode instability evolution driven by strong, high-energy-density shocks in a rarefaction-reflected geometry. Phys. Plasmas 24, 052101.CrossRefGoogle Scholar
Dimonte, G., Nagori, M., Ramaprabhu, P. & Boureima, I. 2024 Simulations and models for the Richtmyer–Meshkov instability with broadband perturbations. Phys. Fluids 36, 025143.CrossRefGoogle Scholar
Dimonte, G. & Ramaprabhu, P. 2010 Simulations and model of the nonlinear Richtmyer–Meshkov instability. Phys. Fluids 22, 014104.CrossRefGoogle Scholar
Elbaz, Y. & Shvarts, D. 2018 Modal model mean field self-similar solutions to the asymptotic evolution of Rayleigh–Taylor and Richtmyer–Meshkov instabilities and its dependence on the initial conditions. Phys. Plasmas 25, 062126.CrossRefGoogle Scholar
Fraley, G. 1986 Rayleigh–Taylor stability for a normal shock wave-density discontinuity interaction. Phys. Fluids 29, 376–386.CrossRefGoogle Scholar
Gao, X., Guo, X., Zhai, Z. & Luo, X. 2024 Interfacial instabilities driven by co-directional rarefaction and shock waves. J. Fluid Mech. 980, A20.CrossRefGoogle Scholar
Ge, J., Li, H., Zhang, X. & Tian, B. 2022 Evaluating the stretching/compression effect of Richtmyer–Meshkov instability in convergent geometries. J. Fluid Mech. 946, A18.CrossRefGoogle Scholar
Guo, X., Cong, Z., Si, T. & Luo, X. 2022 Shock-tube studies of single- and quasi-single-mode perturbation growth in Richtmyer–Meshkov flows with reshock. J. Fluid Mech. 941, A65.CrossRefGoogle Scholar
Haan, S.W. 1991 Weakly nonlinear hydrodynamic instabilities in inertial fusion. Phys. Fluids B 3, 2349–2355.CrossRefGoogle Scholar
Hurricane, O.A., Patel, P.K., Betti, R., Froula, D.H., Regan, S.P., Slutz, S.A., Gomez, M.R. & Sweeney, M.A. 2023 Physics principles of inertial confinement fusion and US program overview. Rev. Mod. Phys. 95, 025005.CrossRefGoogle Scholar
Layzer, D. 1955 On the instability of superposed fluids in a gravitational field. Astrophys. J. 122, 1.CrossRefGoogle Scholar
Li, J., Cao, Q., He, W., Zhai, Z. & Luo, X. 2023 New interface formation method for shock–interface interaction studies. Exp. Fluids 64, 170.CrossRefGoogle Scholar
Li, J., Chen, C., Zhai, Z. & Luo, X. 2024 Effects of compressibility on Richtmyer–Meshkov instability of heavy/light interface. Phys. Fluids 36 (5), 056104.CrossRefGoogle Scholar
Liang, Y. & Luo, X. 2023 Review on hydrodynamic instabilities of a shocked gas layer. Sci. China Phys. Mech. Astron. 66, 104701.CrossRefGoogle Scholar
Lin, C. & Segel, L. 1988 Mathematics Applied to Deterministic Problems in the Natural Sciences. SIAM.CrossRefGoogle Scholar
Liu, C., Zhang, Y. & Xiao, Z. 2023 A unified theoretical model for spatiotemporal development of Rayleigh–Taylor and Richtmyer–Meshkov fingers. J. Fluid Mech. 954, A13.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. 2009 Startup process in the Richtmyer–Meshkov instability. Phys. Fluids 21, 044104.CrossRefGoogle Scholar
Luo, X., Guan, B., Si, T., Zhai, Z. & Wang, X. 2016 Richtmyer–Meshkov instability of a three-dimensional SF$_6$–air interface with a minimum-surface feature. Phys. Rev. E 93 (7), 013101.CrossRefGoogle ScholarPubMed
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., Liang, Y., Si, T. & Zhai, Z. 2018 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. 2020 Richtmyer–Meshkov instability on a dual-mode interface. J. Fluid Mech. 905, A5.CrossRefGoogle Scholar
Luo, X., Wang, X. & Si, T. 2013 The Richtmyer–Meshkov instability of a three-dimensional air/SF$_6$ interface with a minimum-surface feature. J. Fluid Mech. 722, R2.CrossRefGoogle Scholar
Mansoor, M., Dalton, S., Martinez, A., Desjardins, T., Charonko, J. & Prestridge, K. 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
Motl, B., Oakley, J., Ranjan, D., Weber, C., Anderson, M. & Bonazza, R. 2009 Experimental validation of a Richtmyer–Meshkov scaling law over large density ratio and shock strength ranges. Phys. Fluids 21, 126102.CrossRefGoogle 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
Ofer, D., Alon, U., Shvarts, D., McCrory, R. & Verdon, C. 1996 Modal model for the nonlinear multimode Rayleigh–Taylor instability. Phys. Plasmas 3, 3073–3090.CrossRefGoogle Scholar
Prestridge, K. 2018 Experimental adventures in variable-density mixing. Phys. Rev. Fluids 3 (15), 110501.CrossRefGoogle Scholar
Rayleigh, Lord 1882 Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc. 1, 170–177.CrossRefGoogle Scholar
Remington, B., Weber, S., Marinak, M., Haan, S., Kilkenny, J., Wallace, R. & Dimonte, G. 1995 Single-mode and multimode Rayleigh–Taylor experiments on Nova. Phys. Plasmas 2, 241–255.CrossRefGoogle Scholar
Richtmyer, R.D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 13, 297–319.CrossRefGoogle Scholar
Schalles, M. 2023 Experiments on the three-layer Richtmyer–Meshkov instability. Master's thesis, University of Arizona.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., Gauthier, S. & Mügler, C. 2002 Nonlinear regime of a multimode Richtmyer–Meshkov instability: a simplified perturbation theory. Phys. Fluids 14, 1111–1122.CrossRefGoogle Scholar
Vasil'Eva, A., Butuzov, V. & Kalachev, L. 1995 The Boundary Function Method for Singular Perturbation Problems. SIAM.CrossRefGoogle Scholar
Wang, H., Wang, H., Zhai, Z. & Luo, X. 2023 a High-amplitude effect on Richtmyer–Meshkov instability at a single-mode heavy–light interface. Phys. Fluids 35, 126107.CrossRefGoogle Scholar
Wang, H., Wang, H., Zhai, Z. & Luo, X. 2023 b High-amplitude effect on single-mode Richtmyer–Meshkov instability of a light–heavy interface. Phys. Fluids 35, 016106.CrossRefGoogle Scholar
Wouchuk, J.G. 2001 Growth rate of the Richtmyer–Meshkov instability when a rarefaction is reflected. Phys. Plasmas 8, 2890–2907.CrossRefGoogle Scholar
Wouchuk, J.G. & Nishihara, K. 1997 Asymptotic growth in the linear Richtmyer–Meshkov instability. Phys. Plasmas 4, 1028–1038.CrossRefGoogle Scholar
Yang, Y., Zhang, Q. & Sharp, D.H. 1994 Small amplitude theory of Richtmyer–Meshkov instability. Phys. Fluids 6, 1856–1873.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. Engrs C 232, 2830–2849.Google 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, 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. 1997 Nonlinear theory of unstable fluid mixing driven by shock wave. Phys. Fluids 9, 1106–1124.CrossRefGoogle Scholar
Zhou, Y. 2017 Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I. Phys. Rep. 720–722, 1–136.Google Scholar
Zhou, Y., Clark, T.T., Clark, D.S., Gail Glendinning, S., Aaron Skinner, M., 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