水下爆炸冲击波数值仿真研究

胡亮亮 黄瑞源 李世超 秦健 王金相 荣光

胡亮亮, 黄瑞源, 李世超, 秦健, 王金相, 荣光. 水下爆炸冲击波数值仿真研究[J]. 高压物理学报, 2020, 34(1): 015102. doi: 10.11858/gywlxb.20190773
引用本文: 胡亮亮, 黄瑞源, 李世超, 秦健, 王金相, 荣光. 水下爆炸冲击波数值仿真研究[J]. 高压物理学报, 2020, 34(1): 015102. doi: 10.11858/gywlxb.20190773
HU Liangliang, HUANG Ruiyuan, LI Shichao, QIN Jian, WANG Jinxiang, RONG Guang. Shock Wave Simulation of Underwater Explosion[J]. Chinese Journal of High Pressure Physics, 2020, 34(1): 015102. doi: 10.11858/gywlxb.20190773
Citation: HU Liangliang, HUANG Ruiyuan, LI Shichao, QIN Jian, WANG Jinxiang, RONG Guang. Shock Wave Simulation of Underwater Explosion[J]. Chinese Journal of High Pressure Physics, 2020, 34(1): 015102. doi: 10.11858/gywlxb.20190773

水下爆炸冲击波数值仿真研究

doi: 10.11858/gywlxb.20190773
基金项目: 国家自然科学基金(11802001,11402266,11672138);装备预研基金(614260404021801);中国空气动力研究与发展中心超高速碰撞研究中心开放基金(20190303);中央高校基本科研业务费专项资金项目(30916011348)
详细信息
    作者简介:

    胡亮亮(1995-),男,硕士研究生,主要从事水下爆炸数值仿真研究.E-mail: 18362906302@163.com

    通讯作者:

    黄瑞源(1984-),男,博士,讲师,主要从事爆炸力学与冲击动力学研究.E-mail: ryhuang@njust.edu.cn

  • 中图分类号: O383

Shock Wave Simulation of Underwater Explosion

  • 摘要: 由于在水下爆炸冲击波的数值仿真研究中,水的状态方程、人工黏性系数和网格尺寸对数值计算结果影响很大,采用常规TNT炸药的水下爆炸为例,以冲击波的峰值压力和比冲量为衡量指标,研究了这3个主要影响因素对数值仿真结果的影响。首先,通过采用常用的5种水的状态方程进行系列仿真,给出了各种状态方程的适用范围;其次,讨论了人工黏性系数对计算结果的影响,并给出了一次与二次人工黏性系数的建议取值范围;最后,通过对不同炸药当量及不同网格尺寸开展系列运算,从而得到不同炸药当量在满足工程计算精度要求下所对应的建议网格尺寸,并得到了不同炸药当量所对应的建议网格尺寸的表达式。

     

  • 图  采用不同状态方程得到的峰值压力计算结果

    Figure  1.  Calculated peak pressure results using different equations of states

    图  采用不同状态方程得到的比冲量计算结果

    Figure  2.  Calculated specific impulse results obtained with different equations of states

    图  调整一次项黏性系数得到的计算结果

    Figure  3.  Calculated results obtained by adjusting the viscosity coefficient of the primary term

    图  调整二次项黏性系数得到的计算结果

    Figure  4.  Calculated results obtained by adjusting the viscosity coefficient of the quadratic term

    图  一次黏性系数对不同当量工况的影响

    Figure  5.  Effects of primary viscosity coefficient under different equivalent conditions

    图  采用不同网格下得到的峰值压力

    Figure  6.  Peak pressure obtained under different grids

    图  采用不同网格下得到的比冲量

    Figure  7.  Specific impulse obtained under different grids

    图  网格尺寸对不同炸药当量水下爆炸数值仿真的影响

    Figure  8.  Influence of grid size on different explosive equivalents numerical simulation of underwater explosion

    图  炸药当量与适宜网格尺寸的关系

    Figure  9.  Relationship between explosive equivalent and suitable grid size

    图  10  数值仿真得到的冲击波时程曲线与试验对比

    Figure  10.  Numerical and experimental comparison of shock wave time history curve

    表  1  TNT炸药的主要参数[16]

    Table  1.   Main parameters of TNT explosives[16]

    A/GPaB/GPaR1R2ωρ0/(kg∙m–3)e/(J∙kg–1)
    371.23.2314.150.950.316304.19 ×106
    下载: 导出CSV

    表  2  常用Mie-Grüneisen状态方程不同形式的参数

    Table  2.   Commonly used parameters of the Mie-Grüneisen equation of state

    Equation of stateC0/(km·s–1)S1S2S3${\gamma _0} $a
    SNL[20]1.6471.9200 0 0
    HULL[21]1.4831.75000.28 0
    Steiberg[22]1.4802.56–1.9860.226 8 0.50 2.67
    下载: 导出CSV

    表  3  Autodyn程序提供的水多项式状态方程参数[12, 23]

    Table  3.   Polynomial state equation parameters of water provided by the Autodyn program[12, 23]

    A1/GPaA2 /GPaA3 /GPaT1 /GPaT2/GPaB0B1
    2.29.5414.572.200.280.28
    下载: 导出CSV

    表  4  Dytran中水的多项式状态方程的参数[2425]

    Table  4.   Polynomial state equations parameters of water in Dytran[2425]

    a1/GPaa2/GPaa3/GPab0b1b2b3
    2.0029.2248.7670.493 41.393 700
    下载: 导出CSV

    表  5  1 kg炸药无限水域爆炸冲击波峰值压力

    Table  5.   Shock wave peak pressure of 1 kg explosive infinite water fields explosion MPa

    State equation of waterR/R0
    7101520253035
    Autodyn polynomial165.7 95.656.740.631.324.620.3
    Dytran polynomial170.7 97.657.441.231.525.120.8
    Steiberg169.8 97.757.741.631.125.321.1
    SNL218.7123.171.246.236.830.825.7
    HULL182.5106.762.845.234.928.423.7
    Empirical formula196.7115.268.349.438.431.226.2
    下载: 导出CSV

    表  6  1 kg炸药无限水域爆炸冲击波比冲量

    Table  6.   Shock wave impulse of 1 kg explosives infinite water fields explosion N·s·m–2

    State equation of waterR/R0
    7101520253035
    Autodyn polynomial12 522.9 9 116.86 355.14 919.64 033.43 429.32 989.7
    Dytran polynomial12 284.8 8 943.46 234.24 826.03 956.73 364.12 932.8
    Steiberg12 130.7 8 831.36 156.04 765.53 907.13 321.92 896.0
    SNL13 237.3 9 636.96 717.65 200.24 263.53 624.93 160.2
    HULL11 976.6 8 719.16 077.94 704.93 857.53 279.72 859.2
    Empirical formula14 007.710 197.87 108.65 502.94 511.73 835.93 344.1
    下载: 导出CSV

    表  7  5种常用水的状态方程的适用范围与特点

    Table  7.   Applicable scope and characteristics of common five kinds of state equations for water

    State equation of waterScope of application
    Autodyn polynomialThe overall error of the peak pressure is too large, and the far field error is larger than the near field. The near field error of the specific impulse calculation is smaller than the far field.
    Dytran polynomialThe near-field peak pressure error is small, the specific impulse error is large, the far-field peak pressure error is large, and the specific impulse error is small.
    SteibergThe near-field peak pressure error is small, the specific impulse error is large, the far-field peak pressure error is large, and the specific impulse error is small.
    SNLThe mid-field attenuation of the pressure peak is fast, and the far-field error is small. The difference between the near-field and the far-field error is not large, which is suitable for far-field calculation.
    Empirical formulaThe pressure peak error is small overall, and the specific impulse error is gradually increased from near to far, suitable for near-field calculation.
    下载: 导出CSV

    表  8  人工黏性对计算结果的影响

    Table  8.   Artificial viscosity effects on calculation results

    Artificial viscosity coefficientRecommended range
    of values
    Impact on calculation results
    Primary viscosity coefficient0.005–0.040The peak pressure of the underwater shock wave has a great influence, the contrast impulse has little effect, the primary viscosity coefficient increases, and the peak pressure decreases.
    Secondary viscosity coefficient0.8–1.0Less influence on peak pressure and specific impulse.
    下载: 导出CSV

    表  9  1 kg炸药采用不同网格尺寸得到的峰值压力

    Table  9.   Peak pressure of 1 kg explosive with different grid sizes MPa

    Grid size/mmR/R0
    7101520253035
    2188.8110.665.647.436.830.025.2
    5179.0104.862.144.934.9 28.4 23.9
    8161.3 94.556.040.531.425.621.5
    12135.7 81.546.135.726.521.518.1
    15112.1 65.738.927.121.917.814.9
    20 85.6 52.428.720.716.113.111.0
    Empirical formula196.7115.268.349.438.431.226.2
    下载: 导出CSV

    表  10  1 kg炸药采用不同网格尺寸得到的比冲量

    Table  10.   Specific impulse of 1 kg explosive with different grid sizes N·s·m–2

    Grid size/mmR/R0
    7101520253035
    212 228.810 197.76 205.84 803.93 938.63 348.72 919.4
    512 004.6 8 902.66 092.04 715.93 866.53 287.32 865.9
    812 172.7 8 739.46 177.34 781.93 920.63 333.32 906.0
    1211 752.4 8 861.85 964.14 616.83 785.33 218.32 805.7
    1511 472.3 8 555.95 821.94 506.83 695.03 141.62 738.8
    2011 822.5 8 351.95 999.64 644.43 807.83 237.42 822.4
    Empirical formula14 007.710 197.87 108.65 502.94 511.73 835.93 344.1
    下载: 导出CSV

    表  11  不同炸药当量下适宜网格尺寸

    Table  11.   Appropriate grid size for different explosive equivalents

    Explosive equivalent/kgSuitable grid size/mm
    0.11.5
    0.53
    15
    1010
    5016
    10020
    50035
    1 00050
    下载: 导出CSV
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