截锥形弹体在液体介质中运动速度衰减规律分析

孔祥韶 石干 王旭阳 周红昌 吴卫国

孔祥韶, 石干, 王旭阳, 周红昌, 吴卫国. 截锥形弹体在液体介质中运动速度衰减规律分析[J]. 爆炸与冲击, 2021, 41(1): 013301. doi: 10.11883/bzycj-2020-0075
引用本文: 孔祥韶, 石干, 王旭阳, 周红昌, 吴卫国. 截锥形弹体在液体介质中运动速度衰减规律分析[J]. 爆炸与冲击, 2021, 41(1): 013301. doi: 10.11883/bzycj-2020-0075
KONG Xiangshao, SHI Gan, WANG Xuyang, ZHOU Hongchang, WU Weiguo. On velocity attenuation of a truncated cone-shaped projectile vertically penetrating through liquid[J]. Explosion And Shock Waves, 2021, 41(1): 013301. doi: 10.11883/bzycj-2020-0075
Citation: KONG Xiangshao, SHI Gan, WANG Xuyang, ZHOU Hongchang, WU Weiguo. On velocity attenuation of a truncated cone-shaped projectile vertically penetrating through liquid[J]. Explosion And Shock Waves, 2021, 41(1): 013301. doi: 10.11883/bzycj-2020-0075

截锥形弹体在液体介质中运动速度衰减规律分析

doi: 10.11883/bzycj-2020-0075
基金项目: 装备预研教育部联合基金(青年人才)(6141A02033108)
详细信息
    作者简介:

    孔祥韶(1983- ),男,博士,教授,博士生导师,kongxs@whut.edu.cn

  • 中图分类号: O353.4

On velocity attenuation of a truncated cone-shaped projectile vertically penetrating through liquid

  • 摘要: 水面舰船被动防护体系中液舱的主要功能之一是阻止高速弹体(爆炸破片)对内部重要结构、设备和人员的威胁,高速弹体打击液舱的过程包含着复杂的能量传递与耗散。为了分析弹体形状对其在液体介质中运动速度衰减的影响, 开展了一系列不同头形因数的截锥形弹体在不同入水速度下弹体垂直侵彻液体介质过程的数值模拟,得到了垂直侵彻液体介质时弹体速度衰减特性,发现高速弹体在液体介质中运动的阻力因数与弹体形状和无量纲速度有关。基于对系列数值模拟计算结果的拟合分析,提出了计及头形因数的截锥形弹体 垂直侵彻液体介质时的速度衰减经验公式,通过开展数值算例分析验证了公式计算结果的可靠性。本文中提出的经验公式可实现对高速弹体在液体介质中速度衰减的准确快速计算,为舰船防护液舱结构设计提供一定的参考。
  • 图  1  截锥形弹体示意图

    Figure  1.  Schematic diagram of a truncated cone-shaped projectile

    图  2  不同头形因数截锥形弹体有限元模型

    Figure  2.  Finite element models for truncated cone-shaped projectiles with different head type coefficients

    图  3  针对弹体直径为12.65 mm,长度为25.4 mm,入水初速度为603 m/s时,试验与数值计算的空泡尺寸

    Figure  3.  Comparison of cavitation sizes obtained experimentally and numerically for the projectile with the diameter of 12.65 cm and the length of 25.4 cm, water entering at 603 m/s

    图  4  长度为25.4 mm的弹体在两种入水速度工况下位移和速度的变化

    Figure  4.  Changes of displacement and velocity of the projectile with the length of 25.4 mm at two initial velocities of water entry

    图  5  长度为38.1 mm的弹体在两种入水速度工况下位移和速度的变化

    Figure  5.  Changes of displacement and velocity of the projectile with the length of 38.1 mm at two initial velocities of water entry

    图  6  不同头形因数的截锥形弹体在不同入水速度工况下速度随入水距离的衰减

    Figure  6.  Velocity attenuation of truncated cone-shaped projectiles with different head coefficients with water-entry distance at different initial velocities of water entry

    图  7  不同入水速度下,$\psi = 0$的截锥形弹体阻力因数与${v_{\rm{b}}}/{v_0}$的关系

    Figure  7.  Resistance factor varying with ${v_{\rm{b}}}/{v_0}$ for the truncated cone-shaped projectile with $\psi = 0$ at different water-entry velocities

    图  8  对于头形因数不同的截锥形弹体,参数a0a1与马赫数$Ma$的关系

    Figure  8.  Changes of parameters a0 and a1 with Mach number $Ma$ for the truncated cone-shaped projectiles with different head shape factors

    图  9  $a$系列参数与头形因数$\psi $的关系

    Figure  9.  Series parameters of a varyied with head shape factor $\psi $

    图  10  入水速度为400 m/s,头形因数不同的弹丸,速度随入水距离衰减的模拟结果与公式计算结果的比较

    Figure  10.  Comparison of velocity attenuation with distance between numerical simulation and formula calculation for the projectiles with different head shape factors at the initial water-entry velocity of 400 m/s

    图  11  头形因数为1/6,入水速度不同的弹丸,速度随入水距离衰减的模拟结果与公式计算结果的比较

    Figure  11.  Comparison of velocity attenuation with distance between numerical simulation and formula calculation for the projectile with the head shape factor of 1/6 at different initial water-entry velocities

    表  1  水的状态方程各项参数[14]

    Table  1.   Parameters of equation of state for water[14]

    ${A_1}{\rm{/GPa}}$${A_{\rm{2}}}{\rm{/GPa}}$${A_3}{\rm{/GPa}}$${B_0}$${B_1}$${T_1}{\rm{/GPa}}$${T_2}{\rm{/GPa}}$$ {\rho }_{0}\rm{/(kg}·{\rm{m}}^{\rm{-3}}\rm{)}$
    2.29.5414.570.280.282.201 000
    下载: 导出CSV

    表  2  数值计算工况

    Table  2.   Numerical calculation conditions

    工况$\psi $v0/(m·s−1)工况$\psi $v0/(m·s−1)工况$\psi $v0/(m·s−1)工况$\psi $v0/(m·s−1)
    1-104002-11/34003-12/34004-11400
    1-206502-21/36503-22/36504-21650
    1-309002-31/39003-32/39004-31900
    1-401 1502-41/31 1503-42/31 1504-411 150
    1-501 4002-51/31 4003-52/31 4004-511 400
    下载: 导出CSV

    表  3  不同工况下的参数${a_0}$${a_1}$的数值

    Table  3.   Values of parameters ${a_0}$ and ${a_1}$ under different working conditions

    $\psi $拟合参数v0/(m·s−1)
    40065090011501400
    0a00.6170.6120.6330.5870.367
    a1−0.217−0.212−0.223−0.1530.128
    1/3a00.3290.4590.4770.4400.288
    a1−0.019−0.158−0.168−0.1130.077
    2/3a00.7680.7070.7840.7140.553
    a1−0.387−0.297−0.394−0.289−0.082
    1a01.2161.2041.5271.3821.416
    a1−0.344−0.345−0.823−0.580−0.640
    下载: 导出CSV

    表  4  参数${a_0}$${a_1}$的拟合结果

    Table  4.   Fitting results of parameters ${a_0}$ and ${a_1}$

    $\psi $a01a02a03a04a05a11a12a13a14a15
    00.847−1.4592.575−0.707−0.887−0.3760.918−1.096−1.0591.743
    1/3−0.6116.078−13.02512.9015.0551.060−7.04215.285−15.1965.971
    2/32.810−15.06737.573−38.34213.579−3.24621.137−52.93254.463−19.504
    18.033−53.017141.081−153.41858.737−10.54779.685−213.159232.929−89.548
    下载: 导出CSV

    表  5  ${a_{ij}}$系列参数的拟合结果

    Table  5.   Fitting results of ${a_{ij}}$ series parameters

    ${a_{ij}}$${a_{ij}}_0$${a_{ij}}_1$${a_{ij}}_2$
    ${a_0}_1$0.693−7.53615.031
    ${a_{02}}$−0.86449.585−102.332
    ${a_{03}}$1.908−128.117267.957
    ${a_{04}}$−0.654136.681−289.498
    ${a_{05}}$0.814−32.00088.221
    ${a_1}_1$−0.2399.212−19.657
    ${a_1}_2$0.628−70.273149.620
    ${a_1}_3$−1.463185.983−397.312
    ${a_1}_4$0.187−201.803433.298
    ${a_1}_5$1.00177.280−167.088
    下载: 导出CSV
  • [1] 孔祥韶. 爆炸载荷及复合多层防护结构响应特性研究[D]. 武汉: 武汉理工大学, 2013: 1-26.DOI: 10.7666/d.Y2364126.
    [2] LEE M, LONGORIA R G, WILSON D E. Cavity dynamics in high-speed water entry [J]. Physics of Fluids, 1997, 9(3): 540–550. DOI: 10.1063/1.869472.
    [3] 李营, 张磊, 朱海清, 等. 爆炸破片在液舱中的速度衰减特性研究 [J]. 中国造船, 2016, 57(1): 127–137. DOI: 10.3969/j.issn.1000-4882.2016.01.014.

    LI Y, ZHANG L, ZHU H Q, et al. Velocity attenuation of blast fragments in water tank [J]. Shipbuilding of China, 2016, 57(1): 127–137. DOI: 10.3969/j.issn.1000-4882.2016.01.014.
    [4] 沈晓乐, 朱锡, 侯海量, 等. 高速破片侵彻防护液舱试验研究 [J]. 中国舰船研究, 2011, 6(3): 12–15. DOI: 10.3969/j.issn.1673-3185.2011.03.003.

    SHEN X L, ZHU X, HOU H L, et al. Experimental study on penetration properties of high velocity fragment into safety liquid cabin [J]. Chinese Journal of Ship Research, 2011, 6(3): 12–15. DOI: 10.3969/j.issn.1673-3185.2011.03.003.
    [5] 郭子涛. 弹体入水特性及不同介质中金属靶的抗侵彻性能研究[D]. 哈尔滨: 哈尔滨工业大学, 2012: 21-36.DOI: 10.7666/d.D241209.
    [6] ZHAO B L, ZHAO J G, CUI C Y, et al. Growth model of cavity generated by the projectile impacting liquid-filled tank [J]. Defence Technology, 2020, 16(3): 609–616. DOI: 10.1016/j.dt.2019.09.013.
    [7] ZHANG Y, LI X B, LI S Y. Research on the velocity attenuation characteristics of the fragments during high-speed water entry [C] // Proceedings of the 37th International Conference on Ocean, Offshore and Arctic Engineering. Madrid: ASME, 2018.DOI: 10.1115/OMAE2018-78665.
    [8] VARAS D, ZAERA R, LÓPEZ-PUENTE J. Numerical modelling of partially filled aircraft fuel tanks submitted to Hydrodynamic Ram [J]. Aerospace Science and Technology, 2012, 16(1): 19–28. DOI: 10.1016/j.ast.2011.02.003.
    [9] BIRKHOFF G, CAYWOOD T E. Fluid flow patterns [J]. Journal of Applied Physics, 1949, 20(7): 646–659. DOI: 10.1063/1.1698450.
    [10] 孔祥韶, 吴卫国, 刘芳, 等. 舰船舷侧防护液舱对爆炸破片的防御作用研究 [J]. 船舶力学, 2014, 18(8): 996–1004. DOI: 10.3969/j.issn.1007-7294.2014.08.015.

    KONG X S, WU W G, LIU F, et al. Research on protective effect of guarding fluid cabin under attacking by explosion fragments [J]. Journal of Ship Mechanics, 2014, 18(8): 996–1004. DOI: 10.3969/j.issn.1007-7294.2014.08.015.
    [11] LECYSYN N, BONY-DANDRIEUX A, APRIN L, et al. Experimental study of hydraulic ram effects on a liquid storage tank: analysis of overpressure and cavitation induced by a high-speed projectile [J]. Journal of Hazardous Materials, 2010, 178(1/2/3): 635–643. DOI: 10.1016/j.jhazmat.2010.01.132.
    [12] JOHNSON G R, COOK W H. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures [C] // Proceedings of the 7th International Symposium on Ballistics. Netherlands: The Hague, 1983.
    [13] 陈刚, 陈忠富, 陶俊林, 等. 45钢动态塑性本构参量与验证 [J]. 爆炸与冲击, 2005, 25(5): 451–456. DOI: 10.11883/1001-1455(2005)05-0451-06.

    CHEN G, CHEN Z F, TAO J L, et al. Investigation and validation on plastic constitutive parameters of 45 steel [J]. Explosion and Shock Waves, 2005, 25(5): 451–456. DOI: 10.11883/1001-1455(2005)05-0451-06.
    [14] 李晓杰, 张程娇, 王小红, 等. 水的状态方程对水下爆炸影响的研究 [J]. 工程力学, 2014, 31(8): 46–52. DOI: 10.6052/j.issn.1000-4750.2013.03.0180.

    LI X J, ZHANG C J, WANG X H, et al. Numerical study on the effect of equations of state of water on underwater explosions [J]. Engineering Mechanics, 2014, 31(8): 46–52. DOI: 10.6052/j.issn.1000-4750.2013.03.0180.
  • 加载中
图(11) / 表(5)
计量
  • 文章访问数:  540
  • HTML全文浏览量:  227
  • PDF下载量:  72
  • 被引次数: 0
出版历程
  • 收稿日期:  2020-03-20
  • 修回日期:  2020-06-24
  • 刊出日期:  2021-01-05

目录

    /

    返回文章
    返回