Bubble Dynamics Characteristics Near Double-Layer Cylindrical Structures with a Hole Based on PIV Experiments
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摘要: 近场水下爆炸冲击波破坏双壳体潜艇外壳结构后，后续的气泡脉动和射流载荷会对潜艇的内壳体继续造成严重毁伤，因此研究破口附近的气泡脉动和气泡载荷特性具有重要意义。基于受冲击波毁伤后的双壳体潜艇结构，制作预制圆形破口的双层圆柱结构模型，将电火花装置作为气泡发生源，开展了不同爆距参数（爆距与气泡的最大直径之比）和不同破口参数（破口直径与气泡的最大直径之比）条件下气泡与带破口双层圆柱结构的相互作用实验。通过高速摄影机捕捉气泡在双层圆柱结构附近的脉动和射流形成过程，采用粒子图像测速技术对爆炸流场速度进行测试，得到气泡溃灭后产生的水射流速度，同时采用压力传感器测量内层圆柱壳壁面处的压力载荷。实验结果表明：爆距参数决定了内板壁面所受压力的载荷形式、气泡溃灭后是否产生有效射流以及产生的射流速度；当爆距参数在一定范围内时，破口参数影响气泡的脉动以及气泡溃灭后产生的水射流方向。Abstract: After the outer shell of the double-shell submarine is damaged by the near-field underwater explosion shock wave, the subsequent bubble pulsation and jet load will continue to cause serious damage to the inner shell of the submarine. Therefore, it is of great significance to study the characteristics of bubble pulsation and bubble load near the hole. Based on the double-shell submarine structure damaged by the shock wave, a double-layer cylindrical structure model with a prefabricated circular hole is made. Using an electric spark device as the bubble generator, the interaction experiments between bubbles and double-layer cylindrical structure with a hole under different explosion distance parameters (the ratio of explosion distance to the maximum diameter of bubbles) and different hole parameters (the ratio of hole diameter to the maximum diameter of bubbles) are carried out. A high-speed camera is used to capture the bubble pulsation and jet formation process near the double-layer cylindrical structure. The particle image velocimetry technology is used to test the velocity of the explosion flow field to obtain the jet velocity after the bubble collapse. At the same time, a pressure sensor is used to measure the pressure load on the inner cylindrical shell wall. The experimental results show that the detonation distance parameters determine the form of pressure load on the inner wall, whether effective jet is generated after the bubble collapse, and the jet velocity. When the detonation distance parameters are within a certain range, the hole parameters will affect the bubble pulsation and the direction of the water jet generated after the bubble collapse.
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图 4 参照组实验（工况1）的气泡脉动过程
Figure 4. Bubble pulsation process of the reference group experiment (Case 1)
图 6 实验工况3气泡最大收缩速度测量结果
Figure 6. Measurement results of maximum bubble contraction velocity of Case 3
图 7 自由场条件下不同工况的压力时程曲线
Figure 7. Pressure-time history curves of different cases under free field conditions
图 8 自由场和模型2的压力-爆距曲线对比
Figure 8. Comparison of pressure-explosion distance curves between the free field and Model 2
图 9 不同爆距下模型2的压力时程曲线
Figure 9. Pressure-time history curves of Model 2 with different γ
图 13 γ = 0.2时不同模型破口附近的气泡脉动形态
Figure 13. Bubble pulsation patterns near different models with γ = 0.2
图 14 γ = 0时不同模型破口附近的气泡脉动形态
Figure 14. Bubble pulsation patterns near different models with γ = 0
图 16 几种典型工况下瞬时射流速度的PIV结果
Figure 16. Jet velocities obtaied by PIV for several typical cases
图 17 γ = 0.2时不同模型破口附近的气泡射流形态
Figure 17. Bubble jet pattern near different models with γ = 0.2
表 1 双层圆柱模型的尺寸以及参数
Table 1. Dimensions and parameters of the double layered cylindrical model
Model No. Outer radius/mm Inner radius/mm Plate thickness/mm dW/mm dN/mm 1 70 45 5 10 6 2 70 45 5 20 6 3 70 45 5 30 6 
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表 2 模型1～模型3的实验工况
Table 2. Experimental cases for Model 1–Model 3
Model Case $ \lambda $ $ \gamma $ 1 M1-1 0.2 0 M1-2 0.2 0.1 M1-3 0.2 0.2 M1-4 0.2 0.3 M1-5 0.2 0.4 M1-6 0.2 0.6 M1-7 0.2 0.8 2 M2-1 0.4 0 M2-2 0.4 0.1 M2-3 0.4 0.2 M2-4 0.4 0.3 M2-5 0.4 0.4 M2-6 0.4 0.6 M2-7 0.4 0.8 3 M3-1 0.6 0 M3-2 0.6 0.1 M3-3 0.6 0.2 M3-4 0.6 0.3 M3-5 0.6 0.4 M3-6 0.6 0.6 M3-7 0.6 0.8
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表 3 炸药的材料模型及状态方程参数
Table 3. Material model and equation of state parameter of the explosive
$ {\rho }_{0} $/($ \mathrm{k}\mathrm{g}\cdot {\mathrm{m}}^{-3} $) $ D_{\mathrm{C}\mathrm{J}} $/$ \left(\mathrm{m}\cdot {\mathrm{s}}^{-1}\right) $ $ p_{\mathrm{C}\mathrm{J}} $/GPa EZ/GPa A/GPa B/GPa $ {R}_{1} $ $ {R}_{2} $ $ \omega $ 1630 6930 21.0 7.17 373.7 3.74 4.15 0.9 0.35
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表 4 水的材料模型及状态方程参数
Table 4. Material model and equation of state parameter of water
$ {\rho }_{0} $/($ \mathrm{k}\mathrm{g}\cdot {\mathrm{m}}^{-3} $) $ {C}_{0} $/GPa $ {C}_{1} $/GPa $ {C}_{2} $/GPa $ {C}_{3} $/GPa $ {C}_{4} $ $ {C}_{5} $ $ {C}_{6} $ EC $ 1010 $ $ 1.01\times {10}^{-4} $ 2.036 8.432 8.014 0.4934 1.3937 0 $ 2.05\times {10}^{-4} $
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表 5 实验与数值模拟结果对比
Table 5. Comparison between experimental and simulation results
db Tb vb Exp./cm Sim./cm Error/% Exp./ms Sim./ms Error/% Exp./(m·s−1) Sim./(m·s−1) Error/% 5.00 4.99 0.2 4.80 4.42 8.5 43.118 49.069 12.1
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表 6 自由场压力测量实验结果
Table 6. Experimental results of free field pressure measurement
Case DF/cm Shock wave pressure/MPa Pressure of bubble secondary wave/MPa F-1 4 0.573 7.692 F-2 5 0.454 5.818 F-3 6 0.372 4.772 F-4 7 0.291 3.798 F-5 8 0.261 2.482
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表 7 模型2的压力实验结果
Table 7. Pressure experiment results of Model 2
Case D/cm $ \gamma $ Shock wave
pressure/MPaPressure of secondary
wave/MPaPressure of triple
wave/MPaBubble jet
load/MPaM-1 1 0.2 0.594 3.575 1.025 M-2 2 0.4 0.466 2.085 1.297 M-3 3 0.6 0.381 6.325 2.338 0.404 M-4 4 0.8 0.284 7.317 3.032 M-5 5 1.0 0.267 2.332 0.372
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表 8 模型1的气泡脉动实验结果
Table 8. Bubble pulsation experiment results of Model 1
Case $ \gamma $ Maximum bubble
diameter/cmBubble pulsation
period/msJet direction Instantaneous jet
velocity/($ \mathrm{m}\cdot {\mathrm{s}}^{-1} $)Mean jet velocity/
($ \mathrm{m}\cdot {\mathrm{s}}^{-1} $)M1-1 0 4.50 4.0 Upward and downward 34.75 19.55 M1-2 0.1 4.95 4.5 Upward and downward 41.44 25.56 M1-3 0.2 5.08 4.9 Upward and downward 38.56 17.49 M1-4 0.3 4.95 5.0 Upward and downward 38.88 12.68 M1-5 0.4 5.02 5.1 Upward and downward 41.68 12.01 M1-6 0.6 5.01 5.0 Upward 24.51 7.85 M1-7 0.8 5.02 4.9
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表 9 模型2的气泡脉动实验结果
Table 9. Bubble pulsation experiment results of Model 2
Case $ \gamma $ Maximum bubble
diameter/cmBubble pulsation
period/msJet direction Instantaneous jet
velocity/($ \mathrm{m}\cdot {\mathrm{s}}^{-1} $)Mean jet velocity/
($ \mathrm{m}\cdot {\mathrm{s}}^{-1} $)M2-1 0 4.97 4.4 Upward and downward 44.74 25.08 M2-2 0.1 4.95 4.8 Upward and downward 42.18 23.03 M2-3 0.2 5.15 5.0 Upward and downward 44.31 17.88 M2-4 0.3 5.05 4.9 Upward and downward 42.01 12.94 M2-5 0.4 5.00 4.7 Upward 40.13 10.42 M2-6 0.6 5.19 5.1 Upward 5.61 M2-7 0.8 5.00 5.0
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表 10 模型3的气泡脉动实验结果
Table 10. Bubble pulsation experiment results of Model 3
Case $ \gamma $ Maximum bubble
diameter/cmBubble pulsation
period/msJet direction Instantaneous jet
velocity/($ \mathrm{m}\cdot {\mathrm{s}}^{-1} $)Mean jet velocity/
($ \mathrm{m}\cdot {\mathrm{s}}^{-1} $)M3-1 0 5.37 4.8 Upward 40.91 30.49 M3-2 0.1 4.90 4.9 Upward 43.17 26.92 M3-3 0.2 4.75 5.0 Upward 42.79 16.37 M3-4 0.3 5.01 5.0 Upward 46.51 17.69 M3-5 0.4 4.95 4.8 Upward 28.76 9.38 M3-6 0.6 4.98 4.9 Upward 2.88 M3-7 0.8 5.00 5.0
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