Weak oceanic density stratification can generate internal waves under external perturbations. Oscillating bubbles, a perturbation source, can induce notable internal waves; however, their generation mechanisms and evolution characteristics remain unclear. Therefore, to numerically investigate the interaction between an oscillating bubble and a weakly density-stratified fluid, a multi-material Arbitrary Lagrangian-Eulerian (ALE) model coupling both is established assuming a two-layer model. Meanwhile, a novel experimental method is proposed to investigate bubble dynamics in density-stratified fluids for model validation, with both results agreeing well. Based on this model, bubble morphological evolution, jet formation, migration, interfacial liquid column development and collapse, and internal wave generation and propagation are analyzed in detail, revealing the physical mechanism by which oscillating bubbles induce internal waves. Results indicate that in a weakly stratified environment, the pressure gradient still dominates upward bubble jet generation. The jet and subsequent migration trigger the interfacial liquid column. Vertical shear generated during liquid column collapse subsequently excites longer-lasting internal waves. Furthermore, the Atwood number's effects on bubble radius increment, jet velocity, the area and potential energy of the interfacial liquid column, and internal wave height and period are determined. These findings provide theoretical and technical support for understanding ocean internal wave characteristics.

Multiple cavitations generated by near-field underwater explosions can cause significant structural damage, and its generation mechanisms and evolutionary characteristics are still unclear. Therefore, the characteristics of multiple cavitations near plates in underwater explosions are investigated experimentally and numerically. Multiple cavitations near air-backed plates with varying impedances are explored experimentally through a cavitation apparatus, and the effectiveness of Arbitrary Lagrangian-Eulerian method considering multiple cavitations in underwater explosions is validated by the experimental results. Based on the numerical method, the generation processes and evolutionary characteristics of multiple cavitations near air-backed plates at different detonation distances and near water-backed plates with different impedances are analyzed, where the influences of the explosion shock wave and bubble dynamics on evolutionary characteristics of multiple cavitations are commendably elucidated. On the basis of the liquid pressure and structural velocity, the generation mechanisms of multiple cavitations near the structure have also been well revealed. The results indicate that: I. The first cavitation is mainly caused by rarefaction wave reflections or transmissions from the structure, which collapses quickly. The second cavitation is driven by negative pressure from liquid stretching due to structural oscillations, which collapses more slowly. II. For air-backed plates, decreasing structural impedance increases the first cavitation diameter and delays second cavitation. Smaller detonation distances result in larger diameters and longer durations for cavitations. III. For water-backed plates, when impedance is lower than water, cavitation diameters and durations increase as impedance decreases. However, when impedance exceeds water's, cavitation generation becomes difficult. IV. The third cavitation follows similar generation and evolution patterns as the second. These findings provide theoretical and technical support for revealing the complex mechanical mechanisms in near-field underwater explosions.

In this study, we systematically focus on the coupling mechanism between the free surface and array bubbles. The method of underwater electric discharge was utilized to synchronously generate the array bubbles. The current array design consists of three collinear bubbles arranged horizontally beneath the free surface. High-speed photography shows distinct bubble dynamics and water spike evolution patterns for different bubble-free surface stand-off distances of gamma(b) and gamma(f). Numerous distinct and novel phenomena were identified. Quantitative analyses are performed on the jet velocities of array bubbles and the width and rising velocity of the water spikes at different stand-off distances. It is shown that for small gamma(b) less than 1.0, the bubbles would merge as well as the water spike being formed. As gamma(b) increases, the integrated water spike is observed to be separated, resulting in three water spikes arising on the free surface. Rich shapes of water spikes with the required width or height can be produced by controlling the stand-off distances associated with the array bubbles. The findings can provide a probable reference for predicting dynamics of the water spikes caused by array oscillating bubbles.

Lightweight protective structures face a critical challenge in simultaneously mitigating high-speed kinetic energy projectiles while maintaining structural efficiency. Honeycomb array perforated steel (HAPS) exhibits distinct protective performance against explosively formed projectiles (EFPs) compared to conventional bullets. A smooth particle hydrodynamics finite-element model numerical simulation and an experimental verification method were used to study the ballistic performance. An analysis was performed to assess the impact of the HAPS arrangement and EFP impact points on protective capabilities. The findings reveal that the protective efficacy is most pronounced when HAPS is placed between two layers of target panels. In the embedding damage mode, the maximum deformation of the back panel in the sandwich structure with HAPS decreased by 52.7 % compared with the HAPS front configuration. In the penetration mode, the ballistic limit velocity increased by 9.9 % compared with the HAPS front configuration. Moreover, the impact location and of the EFP and the cell size of HAPS influences the EFP's penetration capability, with the asymmetric contact between the HAPS and the EFP enhancing the resistance of the structure. Petallike perforations were observed at the rear of the HAPS. These discoveries provide insight into the development of protective structures and offer valuable perspectives for structural design and applications in related fields.

High-speed vehicles traveling in water will be enveloped by supercavitation, which will have a significant effect on the explosion loads produced by the charge. Therefore, the characteristics of shock wave load, bubble evolution, and bubble loads in underwater explosion when the charge is enveloped by a spherical air layer are investigated using the multi-material Euler method. The effectiveness of the numerical method in simulating shock waves and bubble dynamics is validated by conducting an underwater explosion experiment. The influence of the enveloping air layer and its thickness on the characteristics of underwater explosion loads is analyzed. Besides, a theoretical formula is developed to calculate the transmitted and reflected pressure on the air-water interface, and a predictive formula for the transmitted shock wave peak pressure in water is derived, which are in good agreement with numerical results. These findings demonstrate that multiple pressure waves will be generated when the charge is enveloped by a spherical air layer, and the irregular bubble surface will be formed after the fusion of detonation products and enveloping air. The spherical air layer will diminish the shock wave load and bubble pulsation pressure, and increase the bubble radius and pulsation cycle.

The structural response of the water-back plate under the combined action of shock wave and bubble loads at water depths of 1-300 m is investigated numerically using an arbitrary Lagrange-Euler method. The accuracy of the numerical model is verified by a comparison with the shallow-water experimental results and theoretical results. Specifically, the influences of the water depth and length-to-diameter ratio of the cylindrical charge on the combined damage effect of the shock wave and bubble loads are analysed. The following conclusions are drawn. As water depth increases from 1 m to 300 m, the plastic deformation energy of the water-back plate decreases, meanwhile the permanent deformation mode of a water-backed plate changes from convex to concave under the combined action of shock wave and bubble loads; when the charge has large length-to-diameter, the plastic deformation energy of radial plate under combined action of the shock wave and bubble loads is higher than that of axial plate at water depths of 1-300 m, and both difference decrease with increasing water depth; the combined damage effect of the shock wave and bubble loads can be enhanced in the radial direction by increasing the length-to-diameter ratio in deep-water environments. When the length-to-diameter ratio increases from 1:1 to 8.2:1, the plastic deformation energy of the radial plate gradually increases by 7.58 % from 10.68 to 11.49 J.

This study investigates the deformation characteristics of a ring-stiffened cylindrical shell induced by shock waves and coalesced bubbles in double-charge underwater explosions. A numerical model for coupling underwater multi-point explosion loads with the cylindrical shell is established by the Arbitrary Lagrange Euler method, and underwater explosion experiments with double charges are also conducted. The numerical model's effectiveness is validated by comparing shock wave superposition characteristics, bubble coalescence processes, and bubble pulsation periods with the experimental results. Based on the numerical model, the influences of detonation intervals and layout angles of charge on shock wave superposition effects, temporal and spatial distribution characteristics of shock waves, and the evolution process of coalesced bubbles in underwater explosions with double charges are explored. Additionally, the deformation characteristics of cylindrical shells induced by shock waves and coalesced bubbles for double charges with different detonation intervals and layout angles of charge are analyzed. The results indicate that double charges can induce more substantial deformation on the cylindrical shell at a specific detonation interval than a single charge with equal total mass. During the shock wave phase, the cylindrical shell's deformation decreases nonlinearly with an increased layout angle. Conversely, during the bubble load phase, the deformation of the cylindrical shell shows an approximately linear decrease with an increase in layout angle. A critical angle exists, below which the impact of double charges on the cylindrical shell is more substantial when detonated with an interval than simultaneous detonation.

Interactions between multiple bubbles near a structure are applicable in several fields such as military or industrial engineering. In this paper, interactions between two underwater explosion bubbles near a floating structure are investigated. Experiments were carried out in a cubic explosion tank, with high-speed images to record the expansion, collapse, jet and coalescence between the bubbles. In addition, numerical simulations are performed using Arbitrary Lagrange-Euler (ALE) method, and the simulations on behaviors of the bubbles are consistent with experimental observations. Effects of the bubble–bubble distance and bubble-wall distance on the bubbles’ interactions are discussed. It is found that the jet formation and development are largely dependent on the position and mutual distance between the bubbles. Research findings reported in this paper can provide a reference for multiple bubbles dynamics and the resultant damage on the structure nearby.

In order to analyze the influence of a water medium on the forming process and penetration performance of a shaped charge jet, a comparative study was carried out on an underwater shaped charge jet (USCJ) and a shaped charge jet (SCJ) in air. The virtual mass hypothesis is proposed to analyze the forming mechanism of USCJs. The arbitrary Lagrangian–Eulerian algorithm is adopted to carry out a series of simulation calculations considering the impact of standoff height and liner cone angle. The penetration test of the shaped charge jet in two media is carried out, and the experimental results verify the effectiveness of the theory and simulation. The differences of SCJ formation and penetration in air and water are analyzed. The results demonstrate that the USCJ exhibits a higher jet head velocity, higher cumulative kinetic energy, and a greater penetration ability than those of the jet in air. The depth of penetration (DOP) initially increases and subsequently decreases with an increase in the standoff height. The optimal standoff height of the USCJ is approximately 4–4.5 times greater than the charge diameter, whereas the SCJ in air is approximately 3.5–4 times greater than the charge diameter. Additionally, the DOP of the jet decreases at the optimal standoff height with an increase in the cone angle.

以缩比无人水下航行器典型尾部变截面加筋圆柱壳结构为研究对象,应用LS-DYNA软件中ALE算法对水下爆炸冲击波及气泡载荷作用下变截面加筋圆柱壳结构的动态响应进行数值仿真计算.分析了变截面加筋圆柱壳在水下爆炸冲击波及气泡载荷作用下的动态响应,并进一步探讨了冲击因子和爆炸方位对结构损伤特性的影响.结果表明:随着冲击因子的增大,冲击波对变截面加筋圆柱壳结构的损伤逐渐增大,气泡载荷会进一步加大结构的凹陷变形及塑性区域;射流载荷随着冲击因子的增大先增大后减小,在特定冲击因子下射流载荷能够达到最大;冲击波对变截面加筋圆柱壳的损伤效果受方位影响很小,当药包位于变截面加筋圆柱壳正上方时,射流载荷最大,导致结构的最终损伤变形也最大.

In order to study the directional enhancement effect of underwater explosion for cylindrical explosive with large length-to-diameter ratio, based on the experiment and ALE method, the influences of length-to-diameter ratio on the shock wave and bubble load as well as the structural response of nearby water-back copper plate are analysed. Meanwhile, the influence of the explosive weight on the directional enhancement effect is considered. Some instructive conclusions can be drawn. i) As the length-to-diameter ratio increases, the propagation velocity increases in the radial direction and decreases in the axial direction, and the high-pressure area gradually concentrates in the radial direction. ii) In the range of 1:1–8.2:1, increasing the length-to-diameter ratio enhances the shock wave and bubble load in the top direction and facilitates the formation of a stable bubble jet in this direction. iii) Increasing the length-to-diameter ratio enhances the damage effect of combined load in the top and bottom directions. When the length-to-diameter ratio increases from 1:1 to 8.2:1, the maximum plastic deformation of the water-back copper plate is increased by 26.2%. iv) The directional enhancement effect will be more obviously if the maximum bubble radius is larger than the distance between the structure and the explosive.

In marine warfare, the water jets formed by near-field underwater explosions can cause serious local damage to ship structures. With more knowledge on near-field underwater explosions, the phenomenon of water jet has become a hot research topic in recent years. To study the formation mechanism of water jet during near-field explosion under the bottom of a ship, an underwater explosion experiment was carried out, in which 2.5 g of TNT was detonated under the bottom of a clamped square plate at different explosion distances. A high-speed camera was used to record the evolution of the bubble jet. At the same time, a free-field underwater pressure sensor was used to measure the pressure field in the water tank. The experimental results show that with the increase of the burst distance, the process of bubbles evolving to form jets at the bottom of the square plate can be divided into two types; that is, the adsorption type and non-adsorption type. Then, by employing ABAQUS software andusing the CEL method, a series of numerical simulations were carried out for the experiment. The numerical simulation results show that the critical point for the conversion from the adsorption jet to the non-adsorption jet is between 0.821 times the maximum bubble radius and 0.867 times the maximum bubble radius. Because the upper part of the bubble is difficult to expand freely under the barrier of the steel plate, the corresponding burst distance when the bubble is adsorbed is smaller than the maximum bubble radius. By analyzing the velocity cloud diagram at the jet being formed, it is found that with the increase of the burst distance, because the clamped square plate accelerates the process of bubble collapse, the time of jet formation is advanced. The maximum velocity during the formation process of water jet and the velocity when water jet hits the steel plate both increase first and then decrease with the increase of the burst distance, reaching the maximum near the critical point. The maximum jet velocity can reach 621 m/s, the maximum jet velocity when jet hits the steel plate can reach 269 m/s. Because the larger the burst distance, the later the bubble collapses, and the more concentrated the energy in the bubble, which makes the jet velocity larger, but when the burst distance is too large, the Bjerknes effect of the steel plate on the bubble will be weakened, which will reduce the jet velocity. Consequently, a critical point of the burst distance exists, at which the jet velocity renders a maximum.

为分析药柱形状对水下爆炸冲击波演化的影响.针对圆柱形装药中心起爆问题,在理论上建立了炸药与水交界面上初始冲击波压力及其传播方向的二维计算方法,借助于AUTODYN有限元计算程序开展了长径比1:2～10∶ 1的圆柱形TNT在无限水域爆炸的数值模拟,并开展了长径比为1 ∶ 1和2.6 ∶ 1的圆柱形TNT的水下爆炸试验;对比理论、仿真和试验结果,验证了理论模型的合理性和数值模拟的有效性,分析了柱形装药水下爆炸冲击波的传播规律,重点分析了药柱长径比对不同爆距处冲击波压力分布及传播方向的影响.结果表明:圆柱形装药水下爆炸后,冲击波波阵面逐渐从柱形趋向椭球型再趋向球型,当冲击波传播至10倍无量纲爆距时高压区的转移结束;当长径比大于1 ∶ 1时,炸药轴向(端面)的冲击波压力衰减速率大于径向(圆柱面)的衰减速率,冲击波峰值压力随着方向角的增大而单调增长;在1 ∶ 1～5 ∶ 1的长径比和20倍无量纲爆距范围内,增大药柱长径比可定向增强炸药径向的冲击波压力,药柱的形状对冲击波压力分布影响随着爆距增大而减小.

The interactions between bubbles and water waves have important applications in ocean engineering, and their coupling characteristics are strongly associated with the wave phase angle, wavelength, and wave amplitude. Based on the assumption that the liquid is inviscid and incompressible, the coupling characteristics between bubbles and water waves are solved by the Euler equations with the finite volume method, and the bubble surface and water wave surface are tracked by the front tracking method. The accuracy of the numerical method is verified by comparison with a spark-generated bubble experiment. Compared with the bubble near the initially plane free surface, the rising height of the water spike is reduced by water waves in the crest state, where a concave shape forms on the falling water wave during bubble contraction when the wavelength λ≤ 4.00 and the wave amplitude h≥ 0.364. The rising height of the water spike is significantly strengthened by water waves in the trough state with smaller wavelengths and larger wave amplitudes, which produce a thinner and higher water spike. The bubble cycle is shortened by water waves in the crest state with smaller wavelengths and prolonged by water waves in the trough state with smaller wavelengths and larger wave amplitudes. The results presented in this paper provide guidance for the study of underwater explosions in complex water wave environments.

This study aims to investigate the formation characteristics and penetration performance of an underwater conical shaped charge jet. First, a new theoretical model for underwater jet formation is proposed by the virtual mass method. Based on the theoretical model and the ALE algorithm, the influences of standoff height, cone angle, liner thickness and initiation manner on the jet formation characteristics and penetration ability are analyzed. Then the experiments of underwater shaped charge jet are carried out to verify the theoretical and simulation results. Finally some instructive conclusions are drawn: (i) the theoretical model based on the virtual mass method can accurately predict the initial jet parameters and calculate the penetration depth, and the error between the theoretical and experimental results is less than 8%. (ii) The penetration depth initially increases and then decreases with increasing standoff height. The optimal standoff height is approximately 4–4.5 times the charge diameter. (iii) at the optimal standoff height, the penetration depth decreases with the increase of the cone angle, and the optimal cone angle is 40°–50°. (iv) The penetration depth decreases with increasing the liner thickness, and the jet shape and penetration depth formed by the ring initiation manner are better.

The water jet produced by underwater explosion bubbles during the contraction stage can produce a strong impact on the nearby structure, and its impact characteristics are significantly associated with the explosion distance and azimuth angle. Experiment and ALE method are used to investigate its impact characteristics on the plate structure at different explosion distances and azimuth angles. Through experiments, the coupling process between bubbles and plate structure was recorded, and the accuracy of the numerical method is verified. The results show that when the explosion distance increases, the water jet angle decreases nonlinearly. Due to the inclined water jet, there is an offset distance between the center of the high-stress area induced by the water jet and the geometric center of the plate, and it increases with the increase of explosion distance, while the maximum plate stress decreases gradually. When the azimuth angle α changes from 90° to 0° and then to −90°, the water jet angle θ, the maximum stress and deflection of the plate decrease firstly and then increase. Compared with the negative azimuth angle α, the water jet can produce a stronger impact on the plate when the azimuth angle α is positive.

在2 m×2 m×2 m水箱中分别采用两种引爆方式对2.5 g、5 g和10 g圆柱形装药TNT进行了水下爆炸实验,得到了不同工况下冲击波和气泡脉动的压力时程曲线以及相应的气泡脉动过程.实验结果表明:使用电雷管对主装药进行引爆时,炸药并未完全起爆,冲击波峰值压力均小于经验公式计算得到的理论值,二者间平均误差为25.92％;而使用电雷管以及传爆药柱对主装药进行引爆后,炸药完全起爆,冲击波峰值压力与经验公式间的平均误差降低至4.37％,且整体较为稳定.在此基础上,对比两种引爆方式下的各项爆炸特性,发现炸药的不完全起爆会导致其爆炸后的气泡脉动周期和气泡膨胀最大半径有所减小,冲击波峰值压力、冲击波能以及气泡能明显降低,但对气泡脉动峰值压力的影响并不明显.

An underwater multipoint synchronous explosion can enhance the damage effect of an underwater explosion shock wave on a structure. This study investigates the damage effect of an underwater multipoint synchronous explosion on an air-backed clamped circular plate. First, we derive the theoretical formula for the superposition of underwater explosion shock wave pressure. A numerical simulation was conducted using the ALE (Arbitrary Lagrange-Euler) algorithm to investigate the damage effect of underwater explosion shock wave pressure on a clamped circular plate, and an experiment was conducted in a tank. By changing the conditions (explosive distance, explosive spacing, and number of explosives), the damage effect of an underwater multipoint synchronous explosion on an air-backed clamped circular plate was thoroughly investigated. The results show that the shock wave pressure of an underwater two-point synchronous explosion has a nonlinear superposition effect that is approximately 1.48–2.52 times greater than that of a single-point explosion. As the distances between the explosives and between the explosives and the plate decrease, the damage effect increases. When the total mass of the explosives is constant, the synchronous explosion of eight explosives has the greatest damage effect on the clamped circular plate.

The bubble motion in the shallow water environment has significant applications in underwater explosion and seabed exploration, where the bubble characteristics are mainly associated with the two types of stand-off distance parameters γf and γs (the parameters are defined in Section 2.3). Based on the assumption that the liquid is inviscid and incompressible, the influences of γf and γs on the coupling characteristics between the bubble and the free surface in the shallow water environment are solved by the Euler equations with the finite volume method, and the bubble surface and the free surface are tracked by the front tracking method. For the case γs = 0.8, (i) the water spike always keeps rising during the bubble expansion and contraction when γf<1.25, (ii) the water spike velocity increases with the decrease of γf, and the maximum bubble jet velocity is generated when γf = 0.8, (iii) the bubble top elongated is no longer obvious when γf>1.5. For the case γf = 0.6, (i) the toroidal bubble is split into two sub-toroidal bubbles when γs≤ 0.6 and γs≥1.1, (ii) the water spike velocity and the step pressure decrease with the increase of γs.

Bubble has significant applications in ocean engineering. Aiming at the difficulty of conducting the underwater explosion bubble experiment with large charge in deep water, this paper adopts a new way to deal with this problem. On the basis of similarity theory, it is found that by considering the scaling relationship of gravitational acceleration, the explosion bubble with small charge in shallow water can satisfy the similar relationship with the explosion bubble with large charge in deep water. Therefore, the dynamic characteristics of the explosion bubble with large charge in deep water can be realized by changing the gravitational acceleration. With the assumption that the liquid is inviscid and incompressible, the bubble dynamics are solved by the Euler equations with the finite volume method, and the motion of the bubble interface is tracked by the front tracking method. Based on this model, the bubble collapse characteristics near a solid wall under different hypergravity environments are studied systematically. The results show that the bubble motion, the formation position of the bubble jet, the liquid jet velocity, and the pressure induced by the bubble will change significantly under different hypergravity environments.