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Experimental study on a light–heavy interface evolution induced by two successive shock waves

Published online by Cambridge University Press:  06 December 2022

He Wang Open the ORCID record for He Wang [Opens in a new window] ,
Qing Cao ,
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]
He Wang
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Qing Cao
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
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: sanjing@ustc.edu.cn
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Abstract

Richtmyer–Meshkov instability induced by two successive shock waves is experimentally studied in a specific shock tube. To create two successive shock waves synchronously, a driver section is added between the driver and driven sections of the standard shock tube, and an electronically controlled membrane rupture equipment is adopted. The shock-tube flow after the membranes rupture is well described by combining the shock relations, isentropic wave relations with compatibility relations across the contact surface (region). The new shock tube is capable of generating two successive shock waves with controllable strengths and time interval, and provides a relatively ‘clean’ wave system. Then the developments of single-mode light–heavy interfaces with different initial conditions induced by two successive shock waves are investigated. The initial amplitudes are all small enough such that the first-shocked interface is within the linear growth regime at the arrival of the second shock. The results show that if the pre-second-shock perturbation amplitude is small, the linear, nonlinear and modal evolutions of the double-shocked interface can be reasonably predicted by the existing models proposed for predicting the perturbation growth induced by a single shock. For the double-shocked interface, the second shock provides an additional perturbation velocity field to the original one introduced by the first shock impact. The validity of the linear superposition model indicates that the linear superposition of these two perturbation velocity fields is satisfied. Therefore, a double-shocked interface evolves similarly to a single-shocked interface provided that their postshock amplitudes and linear growth rates are the same.

JFM classification

Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 953 , 25 December 2022 , A15
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Copyright
© The Author(s), 2022. 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.Google Scholar
Bates, J.W. 2004 Initial-value-problem solution for isolated rippled shock fronts in arbitrary fluid media. Phys. Rev. E 69, 056313.CrossRefGoogle ScholarPubMed
Betti, R. & Hurricane, O.A. 2016 Inertial-confinement fusion with lasers. Nat. Phys. 12, 435–448.CrossRefGoogle Scholar
Betti, R., Zhou, C.D., Anderson, K.S., Perkins, L.J., Theobald, W. & Solodov, A.A. 2007 Shock ignition of thermonuclear fuel with high areal density. Phys. Rev. Lett. 98, 155001.10.1103/PhysRevLett.98.155001CrossRefGoogle ScholarPubMed
Brouillette, M. 2002 The Richtmyer–Meshkov instability. Annu. Rev. Fluid Mech. 34, 445–468.10.1146/annurev.fluid.34.090101.162238CrossRefGoogle Scholar
Brouillette, M. & Sturtevant, B. 1989 Growth induced by multiple shock waves normally incident on plane gaseous interfaces. Physica D 37, 248–263.10.1016/0167-2789(89)90133-4CrossRefGoogle Scholar
Buttler, W.T., et al. 2014 a Explosively driven two-shockwave tools with applications. J. Phys.: Conf. Ser. 500, 112014.Google Scholar
Buttler, W.T., et al. 2014 b Second shock ejecta measurements with an explosively driven two-shockwave drive. J. Appl. Phys. 116, 103519.CrossRefGoogle Scholar
Charakhch'yan, A.A. 2000 Richtmyer–Meshkov instability of an interface between two media due to passage of two successive shocks. J. Appl. Mech. Tech. Phys. 41, 23–31.Google Scholar
Charakhch'yan, A.A. 2001 Reshocking at the non-linear stage of Richtmyer–Meshkov instability. Plasma Phys. Control. Fusion 43, 1169–1179.Google Scholar
Cherne, F.J., Hammerberg, J.E., Andrews, M.J., Karkhanis, V. & Ramaprabhu, P. 2015 On shock driven jetting of liquid from non-sinusoidal surfaces into a vacuum. J. Appl. Phys. 118, 185901.10.1063/1.4934645CrossRefGoogle Scholar
Dimonte, G., Frerking, C.E., Schneider, M. & Remington, B. 1996 Richtmyer–Meshkov instability with strong radiatively driven shocks. Phys. Plasmas 3, 614–630.Google Scholar
Dimonte, G. & Ramaprabhu, P. 2010 Simulations and model of the nonlinear Richtmyer–Meshkov instability. Phys. Fluids 22, 014104.CrossRefGoogle Scholar
Glass, I.I. & Hall, J.G. 1959 Handbook of supersonic aerodynamics. Section 18. Shock tubes. NAVORD R-1488. US Government Printing Office, Washington, DC.Google Scholar
Goncharov, V.N. 1999 Theory of the ablative Richtmyer–Meshkov instability. Phys. Rev. Lett. 82, 2091–2094.Google Scholar
Goncharov, V.N., Knauer, J.P., McKenty, P.W., Radha, P.B., Sangster, T.C., Skupsky, S., Betti, R., McCrory, R.L. & Meyerhofer, D.D. 2003 Improved performance of direct-drive inertial confinement fusion target designs with adiabat shaping using an intensity picket. Phys. Plasmas 10, 1906–1918.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
Han, Z. & Yin, X. 1993 Shock Dynamics: Fluid Mechanics and its Application. Kluwer Academic Publishers and Science Press.CrossRefGoogle Scholar
Ishizaki, R., Nishihara, K., Sakagami, H. & Ueshima, Y. 1996 Instability of a contact surface driven by a nonuniform shock wave. Phys. Rev. E 53, R5592–R5595.CrossRefGoogle ScholarPubMed
Karkhanis, V. & Ramaprabhu, P. 2019 Ejecta velocities in twice-shocked liquid metals under extreme conditions: a hydrodynamic approach. Matter Radiat. Extrem. 4, 044402.10.1063/1.5088162CrossRefGoogle Scholar
Karkhanis, V., Ramaprabhu, P., Buttler, W.T., Hammerberg, J.E., Cherne, F.J. & Andrews, M.J. 2017 Ejecta production from second shock: numerical simulations and experiments. J. Dyn. Behav. Mater. 3, 265–279.CrossRefGoogle Scholar
Karkhanis, V., Ramaprabhu, P., Cherne, F.J., Hammerberg, J.E. & Andrews, M.J. 2018 A numerical study of bubble and spike velocities in shock-driven liquid metals. J. Appl. Phys. 123, 025902.Google Scholar
Kuranz, C.C., et al. 2018 How high energy fluxes may affect Rayleigh–Taylor instability growth in young supernova remnants. Nat. Commun. 9, 1564.10.1038/s41467-018-03548-7CrossRefGoogle ScholarPubMed
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.Google 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
Lindl, J.D. 1998 Inertial Confinement Fusion. Springer.Google Scholar
Lindl, J.D., Amendt, P., Berger, R.L., Glendinning, S.G., Glenzer, S.H., Haan, S.W., Kauffman, R.L., Landen, O.L. & Suter, L.J. 2004 The physics basis for ignition using indirect-drive targets on the national ignition facility. Phys. Plasmas 11, 339–491.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., 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, R2.10.1017/jfm.2013.148CrossRefGoogle Scholar
Meshkov, E.E. 1969 Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 4, 101–104.CrossRefGoogle Scholar
Meshkov, E.E. & Abarzhi, S. 2019 Group theory and Jelly's experiment of Rayleigh–Taylor instability and Rayleigh–Taylor interfacial mixing. Fluid Dyn. Res. 51, 065502.CrossRefGoogle Scholar
Mikaelian, K.O. 1985 Richtmyer–Meshkov instabilities in stratified fluids. Phys. Rev. A 31, 410–419.Google ScholarPubMed
Mikaelian, K.O. 1998 Analytic approach to nonlinear Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Phys. Rev. Lett. 80, 508–511.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
Murakami, M., Nagatomo, H., Azechi, H., Ogando, F., Perlado, M. & Eliezer, S. 2006 Innovative ignition scheme for ICF-impact fast ignition. Nucl. Fusion 46, 99–103.10.1088/0029-5515/46/1/011CrossRefGoogle 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.Google Scholar
Owczarek, J.A. 1964 Fundamentals of Gas Dynamics. International Textbook.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, 297–319.10.1002/cpa.3160130207CrossRefGoogle Scholar
Sun, M. & Takayama, K. 1999 Conservative smoothing on an adaptive quadrilateral grid. J. Comput. Phys. 150, 143–180.CrossRefGoogle Scholar
Tabak, M., Hammer, J., Glinsky, M.E., Kruer, W.L., Wilks, S.C., Woodworth, J., Campbell, E.M., Perry, M.D. & Mason, R.J. 1994 Ignition and high gain with ultrapowerful lasers. Phys. Plasmas 1, 1626–1634.CrossRefGoogle Scholar
Taylor, G.I. 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
Wang, H., Wang, H., Zhai, Z. & Luo, X. 2022 Effects of obstacles on shock-induced perturbation growth. Phys. Fluids 34, 086112.10.1063/5.0099054CrossRefGoogle Scholar
Wang, H. & Zhai, Z. 2020 On regular reflection to Mach reflection transition in inviscid flow for shock reflection on a convex or straight wedge. J. Fluid Mech. 884, A27.CrossRefGoogle Scholar
Wang, H., Zhai, Z. & Luo, X. 2021 Reflection of a converging shock over a double curved wedge. Shock Waves 31, 439–455.CrossRefGoogle Scholar
Wang, H., Zhai, Z., Luo, X., Yang, J. & Lu, X. 2017 A specially curved wedge for eliminating wedge angle effect in unsteady shock reflection. Phys. Fluids 29, 086103.CrossRefGoogle Scholar
Williams, R.J.R. & Grapes, C.C. 2017 Simulation of double-shock ejecta production. J. Dyn. Behav. Mater. 3, 291–299.CrossRefGoogle Scholar
Wu, J., Liu, H. & Xiao, Z. 2021 Refined modelling of the single-mode cylindrical Richtmyer–Meshkov instability. J. Fluid Mech. 908, A9.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., Liang, Y., Liu, L., Ding, J., Luo, X. & Zou, L. 2018 a Interaction of rippled shock wave with flat fast-slow interface. Phys. Fluids 30, 046104.10.1063/1.5024774CrossRefGoogle Scholar
Zhai, Z., Ou, J. & Ding, J. 2019 Coupling effect on shocked double-gas cylinder evolution. Phys. Fluids 31 (9), 096104.CrossRefGoogle Scholar
Zhai, Z., Si, T., Luo, X. & Yang, J. 2011 On the evolution of spherical gas interfaces accelerated by a planar shock wave. Phys. Fluids 23, 084104.CrossRefGoogle Scholar
Zhai, Z., Wang, M., Si, T. & Luo, X. 2014 On the interaction of a planar shock with a light polygonal interface. J. Fluid Mech. 757, 800–816.CrossRefGoogle Scholar
Zhai, Z., Zou, L., Wu, Q. & Luo, X. 2018 b Review of experimental Richtmyer–Meshkov instability in shock tube: from simple to complex. Proc. Inst. Mech. Engrs 232, 2830–2849.Google Scholar
Zhang, F., Si, T., Zhai, Z., Luo, X., Yang, J. & Lu, X. 2016 Reflection of cylindrical converging shock wave over a plane wedge. Phys. Fluids 28, 086101.CrossRefGoogle Scholar
Zhang, J., et al. 2020 Double-cone ignition scheme for inertial confinement fusion. Phil. Trans. R. Soc. A 378, 20200015.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