Pressure Time Formula for Underwater Explosion Based on Pressure Impulse Curve
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摘要: 根据材料受冲击载荷时的压力-冲量函数,推导得到了适用于水下爆炸冲击载荷的压力-时程公式。通过水下爆炸实验方法测量不同药量、不同距离的压力-时程曲线,使用MATLAB软件对实验数据进行拟合。计算拟合的冲击波冲量和能量参数,与通用的Cole与Орленко理论计算结果进行对比,验证拟合曲线的准确性。相较于Cole和Орленко理论,新方法的压力衰减曲线更接近于实验值。计算水下爆炸冲击波的比冲和比冲击波能时,新模型具有较好的计算精度;新模型的比冲量与实验值的误差不超过4%,与Орленко理论相比,精度提高了5%~10%;比冲击波能与实验值的误差不超过1%,计算精度与通用理论相当。Abstract: The theoretical study of the attenuation law of underwater blast shock waves was of great significance for the prediction of the underwater blast power of the combatant. According to the pressure-impulse function when the material was subjected to shock loading, the pressure-time interval curve equation applicable to the shock loading of the underwater explosion was derived. Through the underwater explosion experimental method to measure the pressure time course curve of different amounts of drugs and different distances. Used MATLAB software to curve fit the experimental data, the underwater explosion shock wave attenuation section of the fitted curve. The experimental data were curve-fitted using Cole theoretical equations, Орленко theoretical equations, and the new model equations, respectively, and the fitting resolvability coefficients (R2) of the three equations were obtained. The impulse and energy parameters of the shock waves of the fitted curves were calculated and compared with the results of the general Cole and Орленко theories to verify the accuracy of the fitted curves. The correlation between the pressure decay curves obtained by the new method and the experimental values is closer than that of the exponential and inverse ratio segmental expressions of Cole and Орленко, and the coefficient of determination of the accuracy of the fit is more than 0.988. In calculating the values of the specific impulse and the specific energy of underwater explosive shock waves, the new model has a better accuracy of the calculations. The error between the new model and the experimental values in calculating the specific impulse does not exceed 4%, which is 5-10% higher than the error between the theoretical and experimental values of ОРЛЕНКО. The error of the specific shock wave energy from the experimental value does not exceed 1 percent, and the accuracy of the calculation is comparable to that of the general theory.
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Key words:
- underwater explosion /
- pressure decay /
- fitting /
- p-I curve.
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表 1 3种拟合方法的精度
Table 1. Accuracy of three fitting methods
炸药 组号 R2 a/kPa c/(kPa2·s) 新模型 Cole模型 Орленко模型 9gRDX 1 0.9882 0.9282 0.9854 −0.097 0.053 2 0.9923 0.9363 0.9881 −0.089 0.043 12gRDX 1 0.9936 0.9327 0.9861 −0.210 0.135 2 0.9963 0.9306 0.9861 −0.200 0.133 19gRDX 1 0.9897 0.9274 0.9895 −0.180 0.131 2 0.9908 0.9286 0.9900 −0.160 0.094 表 2 冲量的理论值与实验值
Table 2. Theoretical and experimental values of impulse
炸药 组号 I/(Pa·s) δ1(I)/% δ2(I)/% 实验 新模型 Cole-Орленко模型 9gRDX 1 325.862 320.943 325.575 −1.510 −0.088 2 282.572 279.108 325.575 −1.226 15.28 12gRDX 1 376.875 375.155 326.037 −0.456 −13.49 2 349.426 348.407 326.037 −0.292 −6.694 19gRDX 1 439.536 439.484 431.403 −0.012 −1.850 2 400.488 400.228 431.403 −0.065 7.719 表 3 比冲击波能的理论值与实验值
Table 3. Theoretical and experimental values of specific shock wave energy
炸药 组号 Es/(MJ·kg−1) δ1(Es)/% δ2(Es)/% 实验 新模型 Cole-Орленко模型 9gRDX 1 1.057 1.051 0.929 −0.578 −12.11 2 0.902 0.899 0.929 −0.370 2.993 12gRDX 1 1.171 1.168 1.106 −0.256 −5.551 2 1.087 1.082 1.106 −0.460 1.748 19gRDX 1 0.840 0.836 0.772 −0.429 −8.095 2 0.757 0.754 0.772 −0.396 1.982 -
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