Simple Method for the Calculation of Bubble Pulsation Period in Underwater Explosion
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摘要: 将爆轰产物状态方程与气泡运动方程相结合，提出了一种水下爆炸气泡脉动周期的数值计算方法，能够快速计算不同炸药水下爆炸的气泡脉动周期。结果表明：采用JWL状态方程与采用
$\gamma$ 律状态方程的气泡周期计算方法相比，前者计算TNT炸药水下爆炸气泡脉动周期的误差更小，计算误差小于3%；通过对比RS211炸药水下爆炸实验结果，进一步验证了该数值计算方法对含铝炸药水下爆炸气泡脉动周期的计算同样具有良好的适用性。Abstract: Based on the detonation product state equation and the Rayleigh-Plesset equation, this paper proposed a numerical method for calculating the bubble pulsation period of underwater explosions. We can quickly calculate the bubble pulsation period of underwater explosions of different explosives. Compared with the bubble period calculation method using the JWL equation of state and the γ equation of state, the former has a smaller error (less than 3%) for TNT explosives. Additionally, by comparing the results of the RS211 explosive underwater explosion experiment, it is further verified that the numerical calculation method has good applicability for aluminum-containing explosives. -
图 3 两种状态方程的计算值与实测值的相对偏差曲线
Figure 3. Error curves between calculated values of the two state equations and the measured results
$A/$GPa $B/$GPa $ {R}_{1} $ $ {R}_{2} $ $\omega$ ${\,\rho }{_{0}} /$(kg·m−3) 371.2 3.231 4.485 0.79 0.30 1580 
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表 2 不同药量TNT气泡周期实测值与计算值结果对比
Table 2. Comparison of the measured and calculated results of bubble pulsation period of TNT explosive
m/g ${T}{_{\rm s} }$/ms ${T}{_{\rm b1}}$/ms $\delta{_1}$/% ${T}{_{\rm b2}}$/ms $\delta{_2}$/% 200 145.19 154.17 6.18 149.94 3.27 300 166.13 175.62 5.71 170.78 2.92 400 182.85 192.50 5.27 188.17 2.91 600 210.00 220.79 5.14 215.69 2.71 800 231.97 243.31 4.88 237.60 2.43 1000 250.11 261.33 4.48 255.10 1.99
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$A/$GPa $B/$GPa $ {R}_{1} $ $ {R}_{2} $ $ \omega $ ${\,\rho }{_{0} }/$(kg·m−3) 758 8.51 4.9 1.1 0.2 1630
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表 4 RS211炸药水下爆炸气泡脉动周期计算和实验结果对比
Table 4. Comparison of calculated and experimental results of bubble pulsation period of RS211 explosive
h/m m/g ${T}{_{\rm s}}$/ms ${T}{_{\rm b2} }$/ms $\delta$/% 5 1076 258.5 262.4 1.51 5 1067 257.8 261.7 1.51 5 5000 400.0 409.8 2.45 12 3000 273.3 269.1 −1.54
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