高马赫数激波作用下单模界面的Richtmyer-Meshkov不稳定性数值模拟

高士清 邹立勇 唐久棚 李季 林健宇

高士清, 邹立勇, 唐久棚, 李季, 林健宇. 高马赫数激波作用下单模界面的Richtmyer-Meshkov不稳定性数值模拟[J]. 爆炸与冲击, 2024, 44(7): 073201. doi: 10.11883/bzycj-2023-0458
引用本文: 高士清, 邹立勇, 唐久棚, 李季, 林健宇. 高马赫数激波作用下单模界面的Richtmyer-Meshkov不稳定性数值模拟[J]. 爆炸与冲击, 2024, 44(7): 073201. doi: 10.11883/bzycj-2023-0458
GAO Shiqing, ZOU Liyong, TANG Jiupeng, LI Ji, LIN Jianyu. Numerical simulation of single-mode Richtmyer-Meshkov instability caused by high-Mach number shock wave[J]. Explosion And Shock Waves, 2024, 44(7): 073201. doi: 10.11883/bzycj-2023-0458
Citation: GAO Shiqing, ZOU Liyong, TANG Jiupeng, LI Ji, LIN Jianyu. Numerical simulation of single-mode Richtmyer-Meshkov instability caused by high-Mach number shock wave[J]. Explosion And Shock Waves, 2024, 44(7): 073201. doi: 10.11883/bzycj-2023-0458

高马赫数激波作用下单模界面的Richtmyer-Meshkov不稳定性数值模拟

doi: 10.11883/bzycj-2023-0458
基金项目: 国家自然科学基金重大研究计划培育项目(92052108, 12202419);冲击波物理与爆轰物理全国重点实验室稳定支持项目(JCKYS2022212006, JCKYS2023212003)
详细信息
    作者简介:

    高士清(1998- ),男,硕士,gaoshiqing21@gscaep.ac.cn

    通讯作者:

    林健宇(1988- ),男,博士,副研究员,linjiany@mail.ustc.edu.cn

  • 中图分类号: O354.5

Numerical simulation of single-mode Richtmyer-Meshkov instability caused by high-Mach number shock wave

  • 摘要: 为了研究高马赫数激波冲击下的单模界面Richtmyer-Meshkov (RM)不稳定性,特别是高马赫数激波带来的热化学非平衡效应的影响,采用基于有限体积方法的二维高温非平衡流动程序,利用自适应非结构网格模拟了空气中高马赫数激波冲击两侧温度不同的单模界面导致的RM不稳定现象。研究中涵盖了轻/重界面和重/轻界面2 种情况,涉及的激波马赫数范围分别为6~9和8~11。对比了冻结流、热非平衡流和热化学非平衡流3种气体模式下的流场演化过程,揭示了扰动增长和增长率的变化规律。通过对比扰动增长的线性理论和非线性理论,分析了初始激波马赫数和初始扰动尺度的变化对RM不稳定性的影响,同时讨论了涡量场分布和环量的演化规律。结果表明,与冻结流相比,热化学非平衡流中透射激波、反射波及界面速度明显不同,扰动振幅增长率峰值降低,界面增长率脉动减弱,界面不稳定性增长速度变慢。通过对比多种理论模型和本文的数值模拟结果,发现Zhang-Sohn模型相对于其他模型更适用于高马赫数激波作用下的单模界面RM不稳定性问题。对涡量场的研究发现,有2个较强的涡量生成区域,一个位于界面上,另一个位于透射激波波后,这同低马赫数下涡量主要在界面上生成的结论显著不同。此外,热化学非平衡流中环量的幅值大小低于冻结流中的结果,这与热化学非平衡流中扰动的增长低于冻结流的结论对应。
  • 图  1  激波冲击轻/重单模界面初始示意图

    Figure  1.  Schematic of shock wave impact on a light/heavy single-mode interface

    图  2  正激波后的压力和密度分布

    Figure  2.  Pressure and density distributions after the normal shock wave

    图  3  不同网格尺度下重/轻界面的振幅增长率

    Figure  3.  Amplitude growth rates at different grid resolutions for the heavy/light interface

    图  4  轻/重界面时的界面和压力场演化

    Figure  4.  Evolution of interface and pressure field for the light/heavy interface

    Top: FG; middle: TNG; bottom: TCNG.

    图  5  重/轻界面时的界面和压力场演化

    Figure  5.  Evolution of interface and pressure field for the heavy/light interface

    Top: FG; middle: TNG; bottom: TCNG.

    图  6  激波与轻/重和重/轻界面作用界面及波系随时间的变化

    Figure  6.  Positions of the interfaces and wave systems of the shock wave-light/heavy and -heavy/light interface interaction at different times

    The positions of the interface, transmitted and reflected shock waves are indicated in red, black and blue, respectively.

    图  7  轻/重界面振幅的数值模拟结果与理论解的对比

    Figure  7.  Comparison of the amplitudes of the light/heavy interface between numerical simulation results and theoretical solutions

    图  8  重/轻界面振幅的数值模拟结果与理论解的对比

    Figure  8.  Comparison of the amplitudes of the heavy/light interface between numerical simulation results and theoretical solutions

    图  9  不同气体模式中轻/重界面振幅及其振幅增长率对比

    Figure  9.  Comparison of amplitudes and amplitude growth rates of the light/heavy interface among different gas models

    图  10  不同气体模式中重/轻界面振幅及其振幅增长率对比

    Figure  10.  Comparison of amplitudes and amplitude growth rates of the heavy/light interface among different gas models

    图  11  不同初始扰动尺度下轻/重界面振幅增长对比

    Figure  11.  Comparison of amplitude growths of the light/heavy interface among different initial disturbance scales

    图  12  不同初始扰动尺度下重/轻界面振幅增长对比

    Figure  12.  Comparison of amplitude growths of the heavy/light interface among different initial disturbance scales

    图  13  不同激波马赫数时轻/重界面振幅增长对比

    Figure  13.  Comparison of amplitude growths of the light/heavy interfaces at different Mach numbers of shock waves

    图  14  不同激波马赫数时重/轻界面振幅增长对比

    Figure  14.  Comparison of amplitude growths of the heavy/light interface at different Mach numbers of shock waves

    图  15  不同时刻冻结流中轻/重界面涡量场和涡量生成项

    Figure  15.  Vorticity field and generation terms of the light/heavy interface in frozen gas at different times

    Top: vorticity field; bottom: vorticity generation term.

    图  16  不同时刻冻结流中重/轻界面涡量场与涡量生成项

    Figure  16.  Vorticity field and generation terms of the heavy/light interface in frozen gas at different times

    Top: vorticity field; bottom: vorticity generation term.

    图  17  冻结流中轻/重和重/轻界面环量的演化

    Figure  17.  Evolution of circulations of the light/heavy and heavy/light interfaces in frozen gas

    图  18  不同气体模式轻/重和重/轻界面环量演化

    Figure  18.  Evolution of circulations of the light/heavy and heavy/light interfaces in different gases

    表  1  初始条件

    Table  1.   Initial conditions

    界面类型气体模式Msa0/mm界面类型气体模式Msa0/mm
    轻/重界面冻结流6, 7, 8, 90.75, 7.5, 75重/轻界面冻结流8, 9, 10, 110.75, 7.5, 75
    热非平衡流热非平衡流
    热化学非平衡流热化学非平衡流
    下载: 导出CSV

    表  2  不同马赫数非平衡距离

    Table  2.   Non-equilibrium distances at different Mach numbers

    界面类型MsLeq/mm界面类型MsLeq/mm
    轻/重界面6582.5重/轻界面8569.4
    7129.69133.0
    841.41047.5
    920.01120.6
    下载: 导出CSV
  • [1] RICHTMYER R D. Taylor instability in shock acceleration of compressible fluids [J]. Communications on Pure and Applied Mathematics, 1960, 13(2): 297–319. DOI: 10.1002/cpa.3160130207.
    [2] MESHKOV E E. Instability of the interface of two gases accelerated by a shock wave [J]. Fluid Dynamics, 1969, 4(5): 101–104. DOI: 10.1007/BF01015969.
    [3] ZHU Y J, YANG Z W, LUO K H, et al. Numerical investigation of planar shock wave impinging on spherical gas bubble with different densities [J]. Physics of Fluids, 2019, 31(5). DOI: 10.1063/1.5092317.
    [4] IGRA D, IGRA O. Shock wave interaction with a polygonal bubble containing two different gases, a numerical investigation [J]. Journal of Fluid Mechanics, 2020, 889: A26. DOI: 10.1017/jfm.2020.72.
    [5] SINGH S, BATTIATO M. Behavior of a shock-accelerated heavy cylindrical bubble under nonequilibrium conditions of diatomic and polyatomic gases [J]. Physical Review Fluids, 2021, 6(4): 044001. DOI: 10.1103/PhysRevFluids.6.044001.
    [6] GEORGIEVSKIY P Y, LEVIN V A, SUTYRIN O G. Interaction of a shock with elliptical gas bubbles [J]. Shock Waves, 2015, 25(4): 357–369. DOI: 10.1007/s00193-015-0557-4.
    [7] KITAMURA K, YUE Z, FUJIMOTO T, et al. Numerical and experimental study on the behavior of vortex rings generated by shock-bubble interaction [J]. Physics of Fluids, 2022, 34(4): 046105. DOI: 10.1063/5.0083596.
    [8] RANJAN D, OAKLEY J, BONAZZA R. Shock-bubble interactions [J]. Annual Review of Fluid Mechanics, 2011, 43: 117–140. DOI: 10.1146/annurev-fluid-122109-160744.
    [9] 郑纯, 何勇, 张焕好, 等. 激波诱导环形SF6气柱演化的机理 [J]. 爆炸与冲击, 2023, 43(1): 013201. DOI: 10.11883/bzycj-2022-0226.

    ZHENG C, HE Y, ZHANG H H, et al. On the evolution mechanism of the shock-accelerated annular SF6 cylinder [J]. Explosion and Shock Waves, 2023, 43(1): 013201. DOI: 10.11883/bzycj-2022-0226.
    [10] GUO X, DING J C, LUO X S, et al. Evolution of a shocked multimode interface with sharp corners [J]. Physical Review Fluids, 2018, 3(11): 114004. DOI: 10.1103/PhysRevFluids.3.114004.
    [11] ZABUSKY N J. Vortex paradigm for accelerated inhomogeneous flows: visiometrics for the Rayleigh-Taylor and Richtmyer-Meshkov environments [J]. Annual Review of Fluid Mechanics, 1999, 31: 495–536. DOI: 10.1146/annurev.fluid.31.1.495.
    [12] LINDL J D, MCCRORY R L, CAMPBELL E M. Progress toward ignition and burn propagation in inertial confinement fusion [J]. Physics Today, 1992, 45(9): 32–40. DOI: 10.1063/1.881318.
    [13] LINDL J, LANDEN O, EDWARDS J, et al. Review of the national ignition campaign 2009–2012 [J]. Physics of Plasmas, 2014, 21(2): 020501. DOI: 10.1063/1.4865400.
    [14] 薛大文, 陈志华, 韩珺礼. 球形重质气体物理爆炸特性 [J]. 爆炸与冲击, 2014, 34(6): 759–763. DOI: 10.11883/1001-1455(2014)06-0759-05.

    XUE D W, CHEN Z H, HAN J L. Physical characteristics of circular heavy gas cloud explosion [J]. Explosion and Shock Waves, 2014, 34(6): 759–763. DOI: 10.11883/1001-1455(2014)06-0759-05.
    [15] RAYLEIGH L. Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density [J]. Proceedings of the London Mathematical Society, 1882, s1-14(1): 170–177. DOI: 10.1112/plms/s1-14.1.170.
    [16] TAYLOR G I. The air wave surrounding an expanding sphere [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1946, 186(1006): 273–292. DOI: 10.1098/rspa.1946.0044.
    [17] MEYER K A, BLEWETT P J. Numerical investigation of the stability of a shock-accelerated interface between two fluids [J]. Physics of Fluids, 1972, 15(5): 753–759. DOI: 10.1063/1.1693980.
    [18] VANDENBOOMGAERDE M, MÜGLER C, GAUTHIER S. Impulsive model for the Richtmyer-Meshkov instability [J]. Physical Review E, 1998, 58(2): 1874–1882. DOI: 10.1103/PhysRevE.58.1874.
    [19] ZHANG Q, SOHN S I. Nonlinear theory of unstable fluid mixing driven by shock wave [J]. Physics of Fluids, 1997, 9(4): 1106–1124. DOI: 10.1063/1.869202.
    [20] SADOT O, EREZ L, ALON U, et al. Study of nonlinear evolution of single-mode and two-bubble interaction under Richtmyer-Meshkov instability [J]. Physical Review Letters, 1998, 80(8): 1654–1657. DOI: 10.1103/PhysRevLett.80.1654.
    [21] DIMONTE G, RAMAPRABHU P. Simulations and model of the nonlinear Richtmyer-Meshkov instability [J]. Physics of Fluids, 2010, 22(1): 014104. DOI: 10.1063/1.3276269.
    [22] ZHANG Q, GUO W X. Universality of finger growth in two-dimensional Rayleigh-Taylor and Richtmyer-Meshkov instabilities with all density ratios [J]. Journal of Fluid Mechanics, 2016, 786: 47–61. DOI: 10.1017/jfm.2015.641.
    [23] 欧阳良琛, 马东军, 孙德军, 等. 单模大扰动的Richtmyer-Meshkov不稳定性 [J]. 爆炸与冲击, 2008, 28(5): 407–414. DOI: 10.11883/1001-1455(2008)05-0407-08.

    OUYANG L C, MA D J, SUN D J, et al. High-amplitude single-mode perturbation evolution of Richtmyer-Meshkov instability [J]. Explosion and Shock Waves, 2008, 28(5): 407–414. DOI: 10.11883/1001-1455(2008)05-0407-08.
    [24] 杨玟, 王丽丽, 周海兵, 等. 用浮阻力模型研究Richtmyer-Meshkov不稳定性诱导混合 [J]. 爆炸与冲击, 2015, 35(3): 423–427. DOI: 10.11883/1001-1455(2015)03-0423-05.

    YANG M, WANG L L, ZHOU H B, et al. Study on mixing induced by Richtmyer-Meshkov instability by using buoyancy-drag model [J]. Explosion and Shock Waves, 2015, 35(3): 423–427. DOI: 10.11883/1001-1455(2015)03-0423-05.
    [25] BROUILLETTE M, BONAZZA R. Experiments on the Richtmyer-Meshkov instability: wall effects and wave phenomena [J]. Physics of Fluids, 1999, 11(5): 1127–1142. DOI: 10.1063/1.869983.
    [26] VETTER M, STURTEVANT B. Experiments on the Richtmyer-Meshkov instability of an air/SF6 interface [J]. Shock Waves, 1995, 4(5): 247–252. DOI: 10.1007/BF01416035.
    [27] JONES M A, JACOBS J W. A membraneless experiment for the study of Richtmyer-Meshkov instability of a shock-accelerated gas interface [J]. Physics of Fluids, 1997, 9(10): 3078–3085. DOI: 10.1063/1.869416.
    [28] MANSOOR M M, DALTON S M, MARTINEZ A A, et al. The effect of initial conditions on mixing transition of the Richtmyer-Meshkov instability [J]. Journal of Fluid Mechanics, 2020, 904: A3. DOI: 10.1017/jfm.2020.620.
    [29] 罗喜胜, 王显圣, 陈模军, 等. 可控肥皂膜气柱界面与激波相互作用的实验研究 [J]. 实验流体力学, 2014, 28(2): 7–13,26. DOI: 10.11729/syltlx20140015.

    LUO X S, WANG X S, CHEN M J, et al. Experimental study of shock interacting with well-controlled gas cylinder generated by soap film [J]. Journal of Experiments in Fluid Mechanics, 2014, 28(2): 7–13,26. DOI: 10.11729/syltlx20140015.
    [30] ZHAI Z G, SI T, LUO X S, et al. On the evolution of spherical gas interfaces accelerated by a planar shock wave [J]. Physics of Fluids, 2011, 23(8). DOI: 10.1063/1.3623272.
    [31] ZHAI Z G, WANG M H, SI T, et al. On the interaction of a planar shock with a light polygonal interface [J]. Journal of Fluid Mechanics, 2014, 757: 800–816. DOI: 10.1017/jfm.2014.516.
    [32] LI J, ZHU Y J, LUO X S. On Type VI-V transition in hypersonic double-wedge flows with thermo-chemical non-equilibrium effects [J]. Physics of Fluids, 2014, 26(8): 086104. DOI: 10.1063/1.4892819.
    [33] 王宏辉, 丁举春, 司廷, 等. 反射激波冲击单模界面的不稳定性实验研究 [J]. 空气动力学学报, 2022, 40(1): 33–40. DOI: 10.7638/kqdlxxb-2021.0153.

    WANG H H, DING J C, SI T, et al. Richtmyer-Meshkov instability of a single-mode interface with reshock [J]. Acta Aerodynamica Sinica, 2022, 40(1): 33–40. DOI: 10.7638/kqdlxxb-2021.0153.
    [34] LIU L L, LIANG Y, DING J C, et al. An elaborate experiment on the single-mode Richtmyer-Meshkov instability [J]. Journal of Fluid Mechanics, 2018, 853: R2. DOI: 10.1017/jfm.2018.628.
    [35] 马迪, 丁举春, 罗喜胜. 重/轻单模界面的Richtmyer-Meshkov不稳定性研究 [J]. 中国科学: 物理学 力学 天文学, 2020, 50(10): 104705. DOI: 10.1360/SSPMA-2020-0034.

    MA D, DING J C, LUO X S. Study on Richtmyer-Meshkov instability at heavy/light single-mode interface [J]. Scientia Sinica Physica, Mechanica & Astronomica, 2020, 50(10): 104705. DOI: 10.1360/SSPMA-2020-0034.
    [36] 刘金宏, 邹立勇, 柏劲松, 等. 激波冲击下air/SF6界面的Richtmyer-Meshkov不稳定性 [J]. 爆炸与冲击, 2011, 31(2): 135–140. DOI: 10.11883/1001-1455(2011)02-0135-06.

    LIU J H, ZOU L Y, BAI J S, et al. Richtmyer-Meshkov instability of shock-accelerated air/SF6 interfaces [J]. Explosion and Shock Waves, 2011, 31(2): 135–140. DOI: 10.11883/1001-1455(2011)02-0135-06.
    [37] PRESTRIDGE K, RIGHTLEY P M, VOROBIEFF P, et al. Simultaneous density-field visualization and PIV of a shock-accelerated gas curtain [J]. Experiments in Fluids, 2000, 29(4): 339–346. DOI: 10.1007/s003489900091.
    [38] 廖深飞, 邹立勇, 刘金宏, 等. 反射激波作用重气柱的Richtmyer-Meshkov不稳定性的实验研究 [J]. 爆炸与冲击, 2016, 36(1): 87–92. DOI: 10.11883/1001-1455(2016)01-0087-06.

    LIAO S F, ZOU L Y, LIU J H, et al. Experimental study of Richtmyer-Meshkov instability in a heavy gas cylinder interacting with reflected shock wave [J]. Explosion and Shock Waves, 2016, 36(1): 87–92. DOI: 10.11883/1001-1455(2016)01-0087-06.
    [39] 黄熙龙, 廖深飞, 邹立勇, 等. 激波与椭圆形重气柱相互作用的PLIF实验 [J]. 爆炸与冲击, 2017, 37(5): 829–836. DOI: 10.11883/1001-1455(2017)05-0829-08.

    HUANG X L, LIAO S F, ZOU L Y, et al. Experiment on interaction of shock and elliptic heavy-gas cylinder by using PLIF [J]. Explosion and Shock Waves, 2017, 37(5): 829–836. DOI: 10.11883/1001-1455(2017)05-0829-08.
    [40] NIEDERHAUS C E, JACOBS J W. Experimental study of the Richtmyer-Meshkov instability of incompressible fluids [J]. Journal of Fluid Mechanics, 2003, 485: 243–277. DOI: 10.1017/s002211200300452x.
    [41] COLLINS B D, JACOBS J W. PLIF flow visualization and measurements of the Richtmyer-Meshkov instability of an air/SF6 interface [J]. Journal of Fluid Mechanics, 2002, 464: 113–136. DOI: 10.1017/s0022112002008844.
    [42] WALCHLI B, THORNBER B. Reynolds number effects on the single-mode Richtmyer-Meshkov instability [J]. Physical Review E, 2017, 95(1): 013104. DOI: 10.1103/PhysRevE.95.013104.
    [43] BAI X, DENG X L, JIANG L. A comparative study of the single-mode Richtmyer-Meshkov instability [J]. Shock Waves, 2018, 28(4): 795–813. DOI: 10.1007/s00193-017-0764-2.
    [44] WONG M L, LIVESCU D, LELE S K. High-resolution Navier-Stokes simulations of Richtmyer-Meshkov instability with reshock [J]. Physical Review Fluids, 2019, 4(10): 104609. DOI: 10.1103/PhysRevFluids.4.104609.
    [45] 柏劲松, 李平, 王涛, 等. 可压缩多介质粘性流体的数值计算 [J]. 爆炸与冲击, 2007, 27(6): 515–521. DOI: 10.11883/1001-1455(2007)06-0515-07.

    BAI J S, LI P, WANG T, et al. Computation of compressible multi-viscosity-fluid flows [J]. Explosion and Shock Waves, 2007, 27(6): 515–521. DOI: 10.11883/1001-1455(2007)06-0515-07.
    [46] 张君鹏, 翟志刚. 不同强度平面激波冲击下正方形air/SF6界面演化的数值研究 [J]. 中国科学: 物理学 力学 天文学, 2016, 46(6): 064701. DOI: 10.1360/SSPMA2015-00561.

    ZHANG J P, ZHAI Z G. Numerical investigation on air/SF6 square block accelerated by planar shock with different strengths [J]. Scientia Sinica: Physica, Mechanica and Astronomica, 2016, 46(6): 064701. DOI: 10.1360/SSPMA2015-00561.
    [47] SOHN S I. Effects of surface tension and viscosity on the growth rates of Rayleigh-Taylor and Richtmyer-Meshkov instabilities [J]. Physical Review E, 2009, 80(5): 055302. DOI: 10.1103/PhysRevE.80.055302.
    [48] GROOM M, THORNBER B. Reynolds number dependence of turbulence induced by the Richtmyer-Meshkov instability using direct numerical simulations [J]. Journal of Fluid Mechanics, 2021, 908: A31. DOI: 10.1017/jfm.2020.913.
    [49] 张忠珍, 王继海. k-D-a-B模型和Richtmyer-Meshkov不稳定性的数值模拟 [J]. 爆炸与冲击, 1997, 17(3): 199–206.

    ZHANG Z Z, WANG J H. Turbulent mixing model and numerical simulation of Richtmyer-Meshkov instability [J]. Explosion and Shock Waves, 1997, 17(3): 199–206.
    [50] ATTAL N, RAMAPRABHU P. Numerical investigation of a single-mode chemically reacting Richtmyer-Meshkov instability [J]. Shock Waves, 2015, 25(4): 307–328. DOI: 10.1007/s00193-015-0571-6.
    [51] 陈霄, 董刚, 蒋华, 等. 多次激波诱导正弦扰动预混火焰界面失稳的数值研究 [J]. 爆炸与冲击, 2017, 37(2): 229–236. DOI: 10.11883/1001-1455(2017)02-0229-08.

    CHEN X, DONG G, JIANG H, et al. Numerical studies of sinusoidally premixed flame interface instability induced by multiple shock waves [J]. Explosion and Shock Waves, 2017, 37(2): 229–236. DOI: 10.11883/1001-1455(2017)02-0229-08.
    [52] WRIGHT C E, ABARZHI S I. Effect of adiabatic index on Richtmyer-Meshkov flows induced by strong shocks [J]. Physics of Fluids, 2021, 33(4): 046109. DOI: 10.1063/5.0041032.
    [53] SAMULYAK R, PRYKARPATSKYY Y. Richtmyer-Meshkov instability in liquid metal flows: influence of cavitation and magnetic fields [J]. Mathematics and Computers in Simulation, 2004, 65(4/5): 431–446. DOI: 10.1016/j.matcom.2004.01.019.
    [54] 郝鹏程, 冯其京, 胡晓棉. 内爆加载金属界面不稳定性的数值分析 [J]. 爆炸与冲击, 2016, 36(6): 739–744. DOI: 10.11883/1001-1455(2016)06-0739-06.

    HAO P C, FENG Q J, HU X M. A numerical study of the instability of the metal shell in the implosion [J]. Explosion and Shock Waves, 2016, 36(6): 739–744. DOI: 10.11883/1001-1455(2016)06-0739-06.
    [55] 王涛, 汪兵, 林健宇, 等. 柱形汇聚几何中内爆驱动金属界面不稳定性 [J]. 爆炸与冲击, 2020, 40(5): 052201. DOI: 10.11883/bzycj-2019-0150.

    WANG T, WANG B, LIN J Y, et al. Numerical investigations of the interface instabilities of metallic material under implosion in cylindrical convergent geometry [J]. Explosion and Shock Waves, 2020, 40(5): 052201. DOI: 10.11883/bzycj-2019-0150.
    [56] SUN P Y, DING J C, HUANG S H, et al. Microscopic Richtmyer-Meshkov instability under strong shock [J]. Physics of Fluids, 2020, 32(2). DOI: 10.1063/1.5143327.
    [57] DELL Z, STELLINGWERF R F, ABARZHI S I. Effect of initial perturbation amplitude on Richtmyer-Meshkov flows induced by strong shocks [J]. Physics of Plasmas, 2015, 22(9): 092711. DOI: 10.1063/1.4931051.
    [58] RIKANATI A, ORON D, SADOT O, et al. High initial amplitude and high Mach number effects on the evolution of the single-mode Richtmyer-Meshkov instability [J]. Physical Review E, 2003, 67(2): 026307. DOI: 10.1103/PhysRevE.67.026307.
    [59] SAMTANEY R, MEIRON D I. Hypervelocity Richtmyer-Meshkov instability [J]. Physics of Fluids, 1997, 9(6): 1783–1803. DOI: 10.1063/1.869294.
    [60] ZANOTTI O, DUMBSER M. High order numerical simulations of the Richtmyer-Meshkov instability in a relativistic fluid [J]. Physics of Fluids, 2015, 27(7): 074105. DOI: 10.1063/1.4926585.
    [61] FURUMOTO G H, ZHONG X L, SKIBA J C. Numerical studies of real-gas effects on two-dimensional hypersonic shock-wave/boundary-layer interaction [J]. Physics of Fluids, 1997, 9(1): 191–210. DOI: 10.1063/1.869162.
    [62] MILLIKAN R C, WHITE D R. Systematics of vibrational relaxation [J]. The Journal of Chemical Physics, 1963, 39(12): 3209–3213. DOI: 10.1063/1.1734182.
    [63] PARK C. Assessment of two-temperature kinetic model for ionizing air [J]. Journal of Thermophysics and Heat Transfer, 1989, 3(3): 233–244. DOI: 10.2514/3.28771.
    [64] PARK C. On convergence of computation of chemically reacting flows [C]//23rd Aerospace Sciences Meeting. Reno: AIAA, 1985: 247. DOI: 10.2514/6.1985-247.
    [65] HARTEN A, LAX P D, LEER B V. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws [J]. SIAM Review, 1983, 25(1): 35–61. DOI: 10.1137/1025002.
    [66] TORO E F. Riemann solvers and numerical methods for fluid dynamics: a practical introduction [M]. Berlin: Springer, 1997. DOI: 10.1007/978-3-662-03490-3.
    [67] BRANDON D M JR. A new single-step implicit integration algorithm with A-stability and improved accuracy [J]. Simulation, 1974, 23(1): 17–29. DOI: 10.1177/003754977402300105.
    [68] JOHNSEN E, COLONIUS T. Implementation of WENO schemes in compressible multicomponent flow problems [J]. Journal of Computational Physics, 2006, 219(2): 715–732. DOI: 10.1016/j.jcp.2006.04.018.
    [69] HOLMES R L, GROVE J W, SHARP D H. Numerical investigation of Richtmyer-Meshkov instability using front tracking [J]. Journal of Fluid Mechanics, 1995, 301: 51–64. DOI: 10.1017/s002211209500379x.
    [70] BROUILLETTE M. The Richtmyer-Meshkov instability [J]. Annual Review of Fluid Mechanics, 2002, 34: 445–468. DOI: 10.1146/annurev.fluid.34.090101.162238.
    [71] COLELLA P, GLAZ H M. Efficient solution algorithms for the Riemann problem for real gases [J]. Journal of Computational Physics, 1985, 59(2): 264–289. DOI: 10.1016/0021-9991(85)90146-9.
    [72] MIKAELIAN K O. Explicit expressions for the evolution of single-mode Rayleigh-Taylor and Richtmyer-Meshkov instabilities at arbitrary Atwood numbers [J]. Physical Review E, 2003, 67(2): 026319. DOI: 10.1103/PhysRevE.67.026319.
    [73] ORON D, ARAZI L, KARTOON D, et al. Dimensionality dependence of the Rayleigh-Taylor and Richtmyer-Meshkov instability late-time scaling laws [J]. Physics of Plasmas, 2001, 8(6): 2883–2889. DOI: 10.1063/1.1362529.
    [74] GONCHAROV V N. Analytical model of nonlinear, single-mode, classical Rayleigh-Taylor instability at arbitrary Atwood numbers [J]. Physical Review Letters, 2002, 88(13): 134502. DOI: 10.1103/PhysRevLett.88.134502.
    [75] ALON U, HECHT J, OFER D, et al. Power laws and similarity of Rayleigh-Taylor and Richtmyer-Meshkov mixing fronts at all density ratios [J]. Physical Review Letters, 1995, 74(4): 534–537. DOI: 10.1103/PhysRevLett.74.534.
    [76] HAAS J F, STURTEVANT B. Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities [J]. Journal of Fluid Mechanics, 1987, 181: 41–76. DOI: 10.1017/s0022112087002003.
    [77] JACOBS J W. The dynamics of shock accelerated light and heavy gas cylinders [J]. Physics of Fluids A: Fluid Dynamics, 1993, 5(9): 2239–2247. DOI: 10.1063/1.858562.
    [78] 王震, 王涛, 柏劲松, 等. 流场非均匀性对非平面激波诱导的Richtmyer-Meshkov不稳定性影响的数值研究 [J]. 爆炸与冲击, 2019, 39(4): 041407041407. DOI: 10.11883/bzycj-2018-0342.

    WANG Z, WANG T, BAI J S, et al. Numerical study of non-uniformity effect on Richtmyer-Meshkov instability induced by non-planar shock wave [J]. Explosion and Shock Waves, 2019, 39(4): 041407. DOI: 10.11883/bzycj-2018-0342.
    [79] NIEDERHAUS J H J, GREENOUGH J A, OAKLEY J G, et al. A computational parameter study for the three-dimensional shock-bubble interaction [J]. Journal of Fluid Mechanics, 2008, 594: 85–124. DOI: 10.1017/s0022112007008749.
  • 加载中
图(18) / 表(2)
计量
  • 文章访问数:  81
  • HTML全文浏览量:  21
  • PDF下载量:  50
  • 被引次数: 0
出版历程
  • 收稿日期:  2023-12-21
  • 修回日期:  2024-04-08
  • 网络出版日期:  2024-04-09
  • 刊出日期:  2024-07-15

目录

    /

    返回文章
    返回