Numerical Simulation of Rayleigh-Taylor Instability Perturbation Growth in High-purity Copper Interface

doi:10.3969/j.issn.1000-1093.2020.09.013

Abstract

Abstract: The two-dimensional simulations of Rayleigh-Taylor instability perturbation growth of an initial perturbed copper interface under explosive loading are performed to study the Rayleigh-Taylor instability of metal interface under high pressure and high strain rate loading.A numerical simulation model for the perturbation growth behavior of metal interface is established based on the two-dimensional finite difference code AUTODYN，and the effects of initial perturbed characteristics and material strength property on the perturbation growth behavior of metal interface are mainly analyzed.The simulated results show that the growth of the pre-perturbed copper interface is closely related to its perturbated initial wavelength and amplitude，and a critical amplitude exists.For the stable case，the ultimate perturbation amplitude after a transient phase increases with the increase in the initial wavelength if the initial amplitude is smaller than the critical amplitude; and the growth behavior is opposite for the unstable case when the initial amplitude is larger than the critical amplitude.The initial thickness of plate is also an important factor for perturbation growth，and there is a critical thickness related to initial perturbation characteristics. In the preliminary stage of perturbation growth，the strength of material has no influence on the perturbation amplitude growth，and the yield strength of material can greatly reduce Rayleigh-Taylor growth rate at the later stage of Rayleigh-Taylor instability growth; and the effect of shear module can be neglectful to a certain extent in the period of perturbation growth.

Key words: high-puritycopperinterface, Rayleigh-Taylorinstability, perturbationgrowth, initialperturbationcharacteristic, materialstrength, numericalsimulation

CLC Number:

O389

LI Biyong， PENG Jianxiang， GU Yan， YIN Xiaochun， HE Hongliang. Numerical Simulation of Rayleigh-Taylor Instability Perturbation Growth in High-purity Copper Interface[J]. Acta Armamentarii, 2020, 41(9): 1809-1816.

References

［1］ RAYLEIGH L.Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density［J］.Proceedings of the London Mathematical Society，1882，14（1）:170-177.
［2］ TAYLOR G I.The stability of liquid surface when accelerated in a direction perpendicular to their planes I［J］.Proceedings of the Royal Society of London. Series A，Mathematical and Physical Sciences，1950，201（1065）: 192-196.
［3］张维岩，叶文华，吴俊峰，等.激光间接驱动聚变内爆流体不稳定性研究［J］.中国科学:物理学力学天文学，2014，44(1):1-23.
ZHANG W Y，YE W H，WU J F，et al. Hydrodynamic instabilities of laser indirect-drive inertial-confinement-fusion implosion［J］.Scientia Sinica(Physica， Mechanica & Astronomica)， 2014， 44(1): 1-23. (in Chinese)
［4］刘军，冯其京，周海兵.柱面内爆驱动金属界面不稳定性的数值模拟研究［J］.物理学报，2014，63(15):155201-1-155201-6.
LIU J，FENG Q J，ZHOU H B. Simulation study of interface instability in metals driven by cylindrical implosion ［J］. Acta Physica Sinica， 2014，63(15):155201-1-155201-6.(in Chinese)
［5］ 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):5302-5305.
［6］ MIKAELIAN K O. Solution to Rayleigh-Taylor instabilities: bubbles，spikes，and their scalings ［J］.Physical Review E，2014，89(5): 3009-3015.
［7］ WHITE J.Experimental investigation of the Rayleigh-Taylor instability［D］.Madison，GA，US：University of Wisconsin-Madison，2011.
［8］ WANG T，LIU J H，BAI J S，et al.Experimental and numerical investigation of inclined air/SF6 interface instability under shock wave［J］.Applied Mathematics and Mechanics(English Edition)，2012，33(1):37-50.
［9］ GONZLEZ-GUTIRREZ L M，DE ANDREA GONZLEZ A.Numerical computation of the Rayleigh-Taylor instability for a viscous fluid with regularized interface properties［J］.Physical Review E，2019，100(1):3101-3109.
［10］王涛，汪兵，林健宇，等.“反尖端”界面不稳定性数值计算分析［J］.高压物理学报，2019，33(1):47-56.
WANG T，WANG B，LIN J Y，et al. Computational analysis of RM instability with inverse chevron interface［J］.Chinese Journal of High Pressure Physics，2019，33(1):47-56. (in Chinese)
［11］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.
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.(in Chinese)
［12］ BARNES J F，BLEWETT P J，MCQUEEN R G，et al. Taylor instability in solids［J］.Journal of Applied Physics，1974，45(2):727-732.
［13］ MILES J W.Taylor instability of a flat plate：GAMD-7335［R］. San Diego，CA, US：Department of Commerce，1966.
［14］ DRUCKER D C.“Taylor instability” of surface of an elastic-plastic plate［J］.Mechanics Today，1980，5:37-47.
［15］ SWEGLE J W， ROBINSON A C. Acceleration instability in elastic-plastic solids. I. numerical simulations of plate acceleration ［J］. Journal of Applied Physics，1989，66(7):2838-2858.
［16］沈飞，王辉，李彪彪，等.拉拔成型无氧铜管在爆轰加载下的膨胀及断裂特性研究［J］.兵工学报，2019，40(8):1634-1640.
SHEN F，WANG H，LI B B，et al.Research on the expansion and fracture characteristics of drawing-molded oxygen-free copper tubes under detonation loading［J］.Acta Armamentarii，2019，40(8): 1634-1640.(in Chinese)
［17］ BIRKHOFF G. Helmholtz and Taylor instability ［C］∥Proceedings of Symposia in Applied Mathematics.New York，NY，US:American Mathematical Society，1962：55-76.
［18］ COLVIN J D，LEGRAND M，REMINGTON B A，et al.A model for instability growth in accelerated solid metals［J］.Journal of Applied Physics，2003，93(9):5287-5301.
［19］ BAI X B，WANG T，ZHU Y X，et al. Expansion of linear analysis of Rayleigh-Taylor interface instability of metal materials ［J］. World Journal of Mechanics，2018，8(4):94-106.
［20］刘旭红，黄西成，陈裕泽，等.强动载荷下金属材料塑性变形本构模型评述［J］.力学进展，2007，37(3):361-374.
LIU X H，HUANG X C，CHEN Y Z，et al. A review on constitutive models for plastic deformation of metal materials under dynamic loading［J］.Advances in Mechanics，2007，37(3):361-374. (in Chinese)
［21］谭华.实验冲击波物理导引［M］.北京:国防工业出版社，2007.
TAN H.Introduction to experimental shock-wave physics［M］.Beijing:National Defense Industry Press，2007.(in Chinese)
［22］ MORRIS C E，FRITZ J N.Relation of the “solid Hugoniot” to the “fluid Hugoniot” for aluminum and copper［J］.Journal of Applied Physics，1980，51(2):1244-1246.
［23］ KALANTAR D H，REMINGTON B A，COLVIN J D，et al. Solid-state experiments at high pressure and strain rate ［J］. Physics of Plasmas，2000，7(5):1999-2006.
［24］ PARK H S，REMINGTON B A，BECKER R C，et al. Strong stabilization of the Rayleigh-Taylor instability by material strength at megabar pressures［J］.Physics of Plasmas，2010，17(5):6314-6322.

第41卷第9期2020 年9月
兵工学报ACTA ARMAMENTARII
Vol.41No.9Sep.2020

[1]	WANG Ge， ZHANG Chun， LIN Zhiwei， WANG Baohua， TAN Hu， CHEN Chen. Research on's Opening Distance of AHEAD Ammunition [J]. Acta Armamentarii, 2022, 43(S1): 115-120.
[2]	L Dailong， CHEN Shaosong， XU Yihang， QIU Jiawei. Aerodynamic Characteristics of Close-coupled Canard Missile [J]. Acta Armamentarii, 2022, 43(6): 1316-1325.
[3]	WANG Danyu, NAN Fengqiang, LIAO Xin, XIAO Zhongliang, DU Ping, WANG Binbin. Effect of Flame Inhibitor of the Muzzle Flame of Large Caliber Gun [J]. Acta Armamentarii, 2022, 43(2): 273-278.
[4]	XU Gancheng, YUAN Weize, CHEN Linheng, LI Chengxue, XIE Xuhu, NIE Mengqi. Seismic Collapse Resitance of NFB700 High-strength Steel Plate [J]. Acta Armamentarii, 2022, 43(2): 391-400.
[5]	LU Kuan， RAO Xiang， WANG Huamei， ZHANG Qian. The Influences of Different Mooring Systems on the Hydrodynamic Performance of Buoy [J]. Acta Armamentarii, 2022, 43(1): 120-130.
[6]	CHENG Shenshen, TAO Ruyi, WANG Hao, XUE Shao, LIN Qingyu. Dampling Characteristics of Projectile in Engraving Process of Nylon Sealing Band [J]. Acta Armamentarii, 2021, 42(9): 1847-1857.
[7]	GUAN Dian, LI Shipeng, LIU Zhu, WANG Ningfei. Influence of Lateral Acceleration on Ignition Transients of Solid Rocket Motor [J]. Acta Armamentarii, 2021, 42(9): 1877-1887.
[8]	WANG Danyu, NAN Fengqiang, LIAO Xin, XIAO Zhongliang, DU Ping, WANG Binbin. Characteristics of Muzzle Flow Field of Large Caliber Gun Considering Chemical Reaction [J]. Acta Armamentarii, 2021, 42(8): 1624-1630.
[9]	TAN Meijing， YANG Guang， LI Yu， ZHOU Yu， CAO Zhanwei， YAN Hao， TAN Zijing. Influence of Rectifying Wedge on the Flow Structure and Aerodynamic Heating Environment around All-movable Rudder [J]. Acta Armamentarii, 2021, 42(8): 1648-1659.
[10]	CHENG Yuansheng， XIE Jieke， LI Zhe， LIU Jun， ZHANG Pan. Damage Response Characteristics of UHMWPE/aluminum Foam Composite Sandwich Panel Subjected to CombinedBlast and Fragment Loadings [J]. Acta Armamentarii, 2021, 42(8): 1753-1762.
[11]	GAO Feng, ZHANG Ze. Review on Performance Evaluation of Solid Rocket Motors with Charge Defects [J]. Acta Armamentarii, 2021, 42(8): 1789-1802.
[12]	LIU Qingyang, LEI Juanmian. Numerical Simulation of Aerodynamic Interference of Close-coupled Highly Swept-back Wings at Transonic Velocity [J]. Acta Armamentarii, 2021, 42(7): 1412-1423.
[13]	DU Huachi， ZHANG Xianfeng， LIU Chuang， XIONG Wei， LI Pengcheng， CHEN Haihua. Trajectory Characteristics of Projectile Obliquely Penetrating into Steel Target with Multi-layer Space Structure [J]. Acta Armamentarii, 2021, 42(6): 1204-1214.
[14]	WANG Mengxin， CHEN Ruiying， WANG Jinxiang. Protective Properties of Porous Foam Aluminum Sandwich Composite Plate under the Combined Action of Fragment and ShockWave [J]. Acta Armamentarii, 2021, 42(5): 1041-1052.
[15]	TONG Ding, TIAN Hongyan, LIU Xinyuan, LIU Ye, GAO Chao, LI Xin. Effect of Inlet Bend Pipe on the Centrifugal Compressor Performance and Its Optimization Design [J]. Acta Armamentarii, 2021, 42(4): 706-714.