EI、Scopus 收录
中文核心期刊
Cui Zhuxuan, Ding Juchun, Si Ting. NUMERICAL STUDY ON THE EVOLUTION OF THREE-DIMENSIONAL CONCAVE CYLINDRICAL INTERFACE ACCELERATED BY REFLECTED SHOCK[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1246-1256. DOI: 10.6052/0459-1879-21-042
Citation: Cui Zhuxuan, Ding Juchun, Si Ting. NUMERICAL STUDY ON THE EVOLUTION OF THREE-DIMENSIONAL CONCAVE CYLINDRICAL INTERFACE ACCELERATED BY REFLECTED SHOCK[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1246-1256. DOI: 10.6052/0459-1879-21-042

NUMERICAL STUDY ON THE EVOLUTION OF THREE-DIMENSIONAL CONCAVE CYLINDRICAL INTERFACE ACCELERATED BY REFLECTED SHOCK

  • Received Date: January 23, 2021
  • The interaction of shock wave with cylindrical interface is fundamental in study of the Richtmyer-Meshkov (RM) instability. Although the RM instability of two-dimensional (2D) cylindrical interfaces under a single shock wave has been extensively studied previously, the interaction of reflected shock (short for reshock) with cylindrical interfaces, especially three-dimensional (3D) cylindrical interfaces has not been investigated thoroughly, with relevant development rules and underlying mechanisms unclear. When the shock wave interacts with the evolving interface after reshock, new baroclinic vorticity appears on the interface and this will have a major influence on the evolution of the interface. In this work, the HOWD (high order WENO and double-flux) solver developed in our group is used to numerically study the reshock effect on the evolution of 2D and 3D concave cylindrical N2/SF6 (inner/outer phases) interfaces with incident planar shock strength of Ma=1.29. This work will focus on the evolution of 2D and 3D concave cylindrical interfaces after the reshock under different reflected distances, which is defined as the distance between the end wall and the center of the gas cylinder. Series of data have been extracted both before and after the reshock, including the schlieren and vorticity images of the evolving gas cylinder and the quantitative data of the geometric position of the feature points on the gas cylinder. The geometrical characteristics of the distorted interface and the generation and distribution of baroclinic vorticity in different stages are analyzed. The results indicate that for different reflected distances, the shapes of the evolving interface and the reshock at the interaction instance affect the generation and distribution of the baroclinic vorticity, resulting in distinct evolution characteristics of the RM instability. For the 3D concave cylindrical interface, the baroclinic vorticity distributed in 3D space at different heights can induce complicated 3D structures of the evolving interface.
  • [1]
    Richtmyer RD. Taylor instability in shock acceleration of compressible fluids. Commun Pure Appl Math, 1960,13(2):297-319
    [2]
    Meshkov EE. Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn, 1969,4(5):101-104
    [3]
    Lindl JD, McCrory RL, Campbell EM. Progress toward ignition and burn propagation in inertial confinement fusion. Phys Today, 1992,45(9):32-40
    [4]
    Lindl JD, Amendt P, Berger RL, et al. The physics basis for ignition using indirect-drive targets on the National Ignition Facility. Phys Plasmas, 2004,11:339-491
    [5]
    徐建于, 黄生洪. 圆柱形汇聚激波诱导Richtmyer-Meshkov不稳定的SPH模拟. 力学学报, 2019,51(4):998-1011

    (Xu Jianyu, Huang Shenghong. Numerical simulation of cylindrical converging shock induced Richtmyer-Meshkov instability with SPH. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(4):998-1011 (in Chinese))
    [6]
    Robey HF, MacGowan BJ, Landen OL, et al. The effect of laser pulse shape variations on the adiabat of NIF capsule implosions. Phys Plasmas, 2013,20:052707
    [7]
    Yang J, Kubota T, Zukoski EE. Application of shock-induced mixing to supersonic combustion. AIAA J, 1993,31(5):854-862
    [8]
    汪洋, 董刚. RM 不稳定过程中预混火焰界面演化及混合区增长预测. 力学学报, 2020,52(6):1655-1665

    (Wang Yang, Dong Gang. Interface evolutions and growth predictions of mixing zone on premixed flame interface during RM instability. Chinese Journal of Theoretical and Applied Mechanics, 2020,52(6):1655-1665 (in Chinese))
    [9]
    Arnett WD, Bahcall JN, Kirshner RP, et al. Supernova 1987A. Annu Rev Astron Astrophys, 2003,27(1):629-700
    [10]
    Luo XS, Liang Y, Si T, et al. Effects of non-periodic portions of interface on Richtmyer-Meshkov instability. Journal of Fluid Mechanics, 2019,861:309-327
    [11]
    Guo X, Zhai ZG, Si T, et al. Bubble merger in initial Richtmyer-Meshkov instability on inverse-chevron interface. Physical Review Fluids, 2019,4(9):092001
    [12]
    刘金宏, 邹立勇, 曹仁义 等. 绕射激波和反射激波作用下N2/SF6界面R-M不稳定性实验研究. 力学学报, 2014,46(3):475-479

    (Liu Jinhong, Zou Liyong, Cao Renyi, et al. Experimentally study of the Richtmyer-Meshkov instability at N2/SF6 flat interface by diffracted incident shock waves and reshock. Chinese Journal of Theoretical and Applied Mechanics, 2014,46(3):475-479 (in Chinese))
    [13]
    Ding JC, Liang Y, Chen MJ, et al. Interaction of planar shock wave with three-dimensional heavy cylindrical bubble. Physics of Fluids, 2018,30(10):106109
    [14]
    Ding JC, Si T, Chen MJ, et al. On the interaction of planar shock with three-dimensional light gas cylinder. Journal of Fluid Mechanics, 2017,828:289-317
    [15]
    Haas JF, Sturtevant B. Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities. Journal of Fluid Mechanics, 1987,181:41-76
    [16]
    Ou JF, Ding JC, Luo XS, et al. Effects of Atwood number on shock focusing in shock-cylinder interaction. Experiments in Fluids, 2018,59(2):29-39
    [17]
    Ou JF, Zhai ZG. Effects of aspect ratio on shock-cylinder interaction. Acta Mechanica Sinica, 2019,35(1):61-69
    [18]
    Zou LY, Liao SF, Liu CL, et al. Aspect ratio effect on shock-accelerated elliptic gas cylinders. Physics of Fluids, 2016,28(3):036101
    [19]
    丛洲洋, 郭旭, 司廷. 反射激波诱导界面不稳定性研究进展. 中国科学: 物理学力学天文学, 2020,50:104703

    (Cong Zhouyang, Guo Xu, Si Ting. Advances in interfacial instability induced by reshock. Sci Sin-Phys Mech Astron, 2020,50:104703 (in Chinese))
    [20]
    Hill DJ, Pantano C, Pullin DI. Large-eddy simulation and multiscale modeling of a Richtmyer-Meshkov instability with reshock. Journal of Fluid Mechanics, 2006,557:29-61
    [21]
    Latini M, Schilling O, Don WS. Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer-Meshkov instability. Journal of Computational Physics, 2007,221(2):805-836
    [22]
    Schilling O, Latini M. High-order WENO simulations of three-dimensional reshocked Richtmyer-Meshkov instability to late times: dynamics, dependence on initial conditions, and comparisons to experimental data. Acta Math Sci, 2010,30(2):595-620
    [23]
    Haehn N, Weber C, Oakley J, et al. Experimental investigation of a twice-shocked spherical gas inhomogeneity with particle image velocimetry. Shock Waves, 2011,21(3):225-231
    [24]
    Jacobs JW, Krivets VV, Tsiklashvili V, et al. Experiments on the Richtmyer-Meshkov instability with an imposed, random initial perturbation. Shock Waves, 2013,23(4):407-413
    [25]
    Si T, Zhai ZG, Yang JM, et al. Experimental studies of reshocked spherical gas interfaces. Physics of Fluids, 2012,24(5):054101
    [26]
    Mohaghar M, Carter J, Musci B, et al. Evaluation of turbulent mixing transition in a shock-driven variable-density flow. Journal of Fluid Mechanics, 2017,831:779-825
    [27]
    Brouillette M, Sturtevant B. Growth induced by multiple shock waves normally incident on plane gaseous interfaces. Physica D, 1989,37(1-3):248-263
    [28]
    Shankar SK, Kawai S, Lele SK. Two-dimensional viscous flow simulation of a shock accelerated heavy gas cylinder. Physics of Fluids, 2011,23(2):024102
    [29]
    Quirk JJ, Karni S. On the dynamics of a shock-bubble interaction. Journal of Fluid Mechanics, 1996,318:129-163
    [30]
    Niederhaus JHJ, Greenough JA, Oakley JG, et al. A computational parameter study for the three-dimensional shock-bubble interaction. Journal of Fluid Mechanics, 2008,594:85-124
    [31]
    Shankar SK, Lele SK. Numerical investigation of turbulence in reshocked Richtmyer-Meshkov unstable curtain of dense gas. Shock Waves, 2014, 24(1): 79-95
    [32]
    张赋, 翟志刚, 司廷 等. 反射激波作用下重气柱界面演化的PIV 研究. 实验流体力学, 2014,28(5):13-17

    (Zhang Bin, Zhai Zhigang, Si Ting, et al. Experimental study on the evolution of heavy gas cylinder under reshock condition by PIV method. Journal of Experiments in Fluid Mechanics, 2014,28(5):13-17 (in Chinese))
    [33]
    何惠琴, 翟志刚, 司廷 等. 反射激波作用下两种重气柱界面不稳定性实验研究. 实验流体力学, 2014,28(6):56-60

    (He Huiqin, Zhai Zhigang, Si Ting, et al. Experimental study on the reshocked RM instability of two kinds of heavy gas cylinder. Journal of Experiments in Fluid Mechanics, 2014,28(6):56-60 (in Chinese))
    [34]
    王显圣, 司廷, 罗喜胜 等. 反射激波冲击重气柱的RM不稳定性数值研究. 力学学报, 2012,44(4):664-672

    (Wang Xiansheng, Si Ting, Luo Xisheng, et al. Numerical study on the RM instability of a heavy-gas cylinder interacted with reshock. Chinese Journal of Theoretical and Applied Mechanics, 2012,44(4):664-672 (in Chinese))
    [35]
    沙莎, 陈志华, 薛大文. 激波冲击R22重气柱所导致的射流与混合研究. 物理学报, 2013,62(14):144701

    (Sha Sha, Chen Zhihua, Xue Dawen. The generation of jet and mixing induced by the interaction of shock wave with R22 cylinder. Acta Phys Sin, 2013,62(14):144701 (in Chinese))
    [36]
    丁举春. 汇聚Richtmyer-Meshkov不稳定性的实验与数值研究. [博士论文]. 合肥: 中国科学技术大学, 2016

    (Ding Juchun. Experimental and numerical study on converging Richtmyer-Meshkov instability. [PhD Thesis]. Hefei: University of Science and Technology of China, 2016 (in Chinese))
    [37]
    Liu XD, Osher S, Chan T. Weighted Essentially Non-oscillatory schemes. Journal of Computational Physics, 1994,115(1):200-212
    [38]
    Schilling O, Latini M, Don WS. Physics of reshock and mixing in single-mode Richtmyer-Meshkov instability. Phys Rev E, 2007,76(2):026319
    [39]
    Wang XS, Yang DG, Wu JQ, et al. Interaction of a weak shock wave with a discontinuous heavy-gas cylinder. Physics of Fluids, 27(6): 064104, 2015
    [40]
    王显圣. 极小曲面特征界面的Richtmyer-Meshkov不稳定性研究. [博士论文]. 合肥: 中国科学技术大学, 2013

    (Wang Xiansheng. The Richtmyer-Meshkov instability on minimum-surface featured interface. [PhD Thesis]. Hefei: University of Science and Technology of China, 2013 (in Chinese))
    [41]
    Isenberg C. The Science of Soap Films and Soap Bubbles. New York: Dover Publications INC, 1992
  • Related Articles

    [1]Qu Ke, Zheng Wei, Wang Chao, Yu Renshi. NUMERICAL SIMULATION AND THEORETICAL CALCULATION OF THE FORMATION AND EVOLUTION OF THE BACKFLOW BORE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2025, 57(7): 1772-1782. DOI: 10.6052/0459-1879-25-079
    [2]Wang Yuerou, Wang Junfeng, Liu Hailong. NUMERICAL SIMULATION ON BUBBLE RINSING BEHAVIORS UNDER ELECTRIC FIELD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(1): 31-39. DOI: 10.6052/0459-1879-19-193
    [3]Xu Jianyu, Huang Shenghong. NUMERICAL SIMULATION OF CYLINDRICAL CONVERGING SHOCK INDUCED RICHTMYER-MESHKOV INSTABILITY WITH SPH[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(4): 998-1011. DOI: 10.6052/0459-1879-19-041
    [4]Wu Qin, Wang Guoyu, Huang Biao. NUMERICAL METHODS AND TRANSITION INVESTIGATION OF TRANSIENT FLOWS AROUND A PITCHING HYDROFOIL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(1): 60-69. DOI: 10.6052/0459-1879-13-080
    [5]Wang Xiansheng, Si Ting, Luo Xisheng, Yang Jiming. NUMERICAL STUDY ON THE RM INSTABILITY OF A HEAVY-GAS CYLINDER INTERACTED WITH RESHOCK[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, (4): 664-672. DOI: 10.6052/0459-1879-11-245
    [6]Jie Wang, Chunsheng Weng. Numerical calculation of 3-D flow outside multi-tube pulse detonation engine[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(6): 835-841. DOI: 10.6052/0459-1879-2009-6-2008-032
    [7]Z.Y. Gao, Tongxi Yu, D. Karagiozova. Finite element simulation on the mechanical properties of MHS materials[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 39(1): 65-75. DOI: 10.6052/0459-1879-2007-1-2006-198
    [8]AN ADAPTIVE BLOCK IMPLICIT ALGORITHM FOR INCOMPRESSIBLE FLOW CALCULATION IN COMPLEX GEOMETRY BOUNDARY[J]. Chinese Journal of Theoretical and Applied Mechanics, 1997, 29(1): 95-98. DOI: 10.6052/0459-1879-1997-1-1995-200
    [9]A NUMERICEL SIMULATION OF ENERGY DISSIPATION IN PRESSURE CONDUITS WITH TWO PERFORATED PLATES[J]. Chinese Journal of Theoretical and Applied Mechanics, 1995, 27(6): 641-646. DOI: 10.6052/0459-1879-1995-6-1995-479
    [10]NUMERICAL STUDY OF SHOCK WAVE AND TURBULENT BOUNDARY LAYER INTERACTION INDUCED BY FLAT-FACED BLUNT FIN[J]. Chinese Journal of Theoretical and Applied Mechanics, 1993, 25(6): 651-657. DOI: 10.6052/0459-1879-1993-6-1995-690
  • Cited by

    Periodical cited type(3)

    1. 王殿恺,石继林,黄龙呈,文明,张腾飞. 脉冲激光等离子体与正激波相互作用的PIV实验研究. 力学学报. 2023(05): 1063-1074 . 本站查看
    2. 宋家喜,潘书诚. 高马赫数下激波液滴相互作用的数值模拟研究. 力学学报. 2022(09): 2419-2434 . 本站查看
    3. 钟巍,贾雷明,王澍霏,田宙. 一类高效率高分辨率加映射的WENO格式及其在复杂流动问题数值模拟中的应用. 力学学报. 2022(11): 3010-3031 . 本站查看

    Other cited types(1)

Catalog

    Article Metrics

    Article views (1362) PDF downloads (175) Cited by(4)
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return