Explosion Bubble Research Articles

Reduced-Scale Experiment Study on the Protective Mechanism of Foam Coating Against Underwater Explosion Bubble Jet

Reduced-Scale Experiment Study on the Protective Mechanism of Foam Coating Against Underwater Explosion Bubble Jet

A Framework of Runge–Kutta, Discontinuous Galerkin, Level Set and Direct Ghost Fluid Methods for the Multi-Dimensional Simulation of Underwater Explosions

This work describes the development of a hybrid framework of Runge–Kutta (RK), discontinuous Galerkin (DG), level set (LS) and direct ghost fluid (DGFM) methods for the simulation of near-field and early-time underwater explosions (UNDEX) in early-stage ship design. UNDEX problems provide a series of challenging issues to be solved. The multi-dimensional, multi-phase, compressible and inviscid fluid-governing equations must be solved numerically. The shock front in the solution field must be captured accurately while maintaining the total variation diminishing (TVD) properties. The interface between the explosive gas and water must be tracked without letting the numerical diffusion across the material interface lead to spurious pressure oscillations and thus the failure of the simulation. The non-reflecting boundary condition (NRBC) must effectively absorb the wave and prevent it from reflecting back into the fluid. Furthermore, the CFD solver must have the capability of dealing with fluid–structure interactions (FSI) where both the fluid and structural domains respond with significant deformation. These issues necessitate a hybrid model. In-house CFD solvers (UNDEXVT) are developed to test the applicability of this framework. In this development, code verification and validation are performed. Different methods of implementing non-reflecting boundary conditions (NRBCs) are compared. The simulation results of single and multi-dimensional cases that possess near-field and early-time UNDEX features—such as shock and rarefaction waves in the fluid, the explosion bubble, and the variation of its radius over time—are presented. Continuing research on two-way coupled FSI with large deformation is introduced, and together with a more complete description of the direct ghost fluid method (DGFM) in this framework will be described in subsequent papers.

Theoretical and experimental study of bubble dynamics in underwater explosions

The development of analytical theory and experimental methods for understanding the correlation between the explosive properties and bubble dynamic characteristics in underwater explosions has important engineering application value for underwater weapons and ships. Based on the assumption of an instantaneous explosive detonation, we introduced the Jones–Wilkins–Lee equation of state to describe the high-pressure state in an explosion bubble and established the initial conditions for the bubble dynamics calculations. Considering the high-Mach-number flow and high pressure at the initial boundary of the explosion bubble, the Lezzi–Prosperetti equation with second-order Mach accuracy was used. Thus, an analytical model and a calculation method of the explosion bubble dynamics for an explosive detonation were established. This direct link between the detonation parameters and the bubble features is significant for the subtle design, selection, and optimization of explosives' properties. A micro-equivalent explosive bubble pulsation experiment was carried out in a water tank using a customized experimental system, which can offer nearly boundary-free condition to mitigate the reflective wave effects on bubbles. Three types of explosives were used in the experiment: the Research Department explosive (RDX), the Pentaerythritol tetranitrate (PETN), and the Hexanitrohexaazaisowurtzitane (CL20). Finally, the experimental results and the practicability of the experimental system were analyzed. The influence of the explosive type on the dynamic characteristics of the explosion bubbles and the differences between the theoretical and experimental results were compared. The results showed that the proposed explosion bubble dynamics model and calculation method have high accuracy and practicability. The proposed model can be used for explosives with known detonation parameters and equation of state parameters. The detonation parameters, velocity, and pressure are linked to the bubble features pulsation period and the maximum radius directly. The designed experimental system, which is capable of simulating an infinite water for the explosion of micro-equivalent explosives, was stable and easy to use. The work is significant for the subtle design, selection, and optimization of explosives' properties.

Numerical research of water jet characteristics in underwater explosion based on compressible multicomponent flows

Owing to the high-speed motion and high-pressure load characteristics of water jet, explosion bubble plays an important influence on the surrounding structures in underwater explosion (UNDEX). Based on interface compression and density correction treatment, an important compressible multicomponent flow model is proposed and its discrete method is briefly introduced in the study. This method shows a great potential in multicomponent flow, especially in the research of water jet characteristics caused by bubble collapse in underwater explosion. The bubble dynamic behavior caused by a weighted of 0.2 kg charge at a depth of 50 m is researched under the condition of different distance to diameter ratio near a rigid wall. It can be observed that when the bubble shrinks to the minimum volume, the collapsed pressure on the center of the wall (coordinate origin) does not reach the maximum, excluding γ = 0.24. Owing to the strong nonlinearity of the water jet, the characteristics of the pressure load on the wall are very complex. For the example in the study, the maximum water jet velocity under different γ conditions is between 140 and 280 m/s, and the maximum pressure of the bubble collapse on the wall is between 13.8 and 48.0 MPa. Under such a high-speed impact, a local high-pressure zone is formed near the wall, indicating that the impact damage caused by the water jet to nearby structures cannot be ignored in the underwater explosion.

Effect of a rigid structure on the dynamics of a bubble beneath the free surface

The coupling effect between a pulsating bubble and a free surface near a rigid structure is a complicated physical process. In this study, the evolution of an underwater explosion bubble and the free surface near a rigid structure is modeled by the boundary integral method. An approach of “double-node method” is used to maintain the stability of fluid-structure junction in the simulations, and meshes on the free surface and the structure are transformed to an open domain to ensure the calculation accuracy and efficiency. Validations are conducted against an underwater explosion experiment near a rigid structure. As a result, the simulations trace the jetting behavior of the bubble and the rise of the free surface. Finally, the bubble migration and the height of the free surface for different structure draughts are analyzed.

Sagging damage characteristics of hull girder with trapezoidal cross-section subjected to near-field underwater explosion

To investigate the overall damage characteristics and failure modes of a warship subjected to an underwater non-contact near-field explosion, a hull girder with a trapezoidal cross-section was designed, manufactured, and tested. The design criteria and parameters were determined according to the similarity criterion. Dynamic responses of the girder freely floating on water were obtained under varying conditions, including stand-off distance, charge mass, and position of attack. Damage morphologies of the girder model were obtained. Based on our analysis, basic conditions for sagging damage of the hull girder are proposed. The aim of this study was to determine an efficient method of attack resulting in the most severe damage to the ship hull. The experimental results show that the girder mainly exhibits a first-order response when the first wet frequency of the girder is close to the frequency of the explosion bubble pulsation. The largest deformation was observed when the underwater explosion occurred directly below the midspan of the girder compared to other explosions of the same intensity at different attack positions. When the ratio of stand-off to maximum bubble radius (λ) satisfies 0.7 ≤ λ＜2, the bubble mainly causes sagging damage instead of hogging. As λ decreases (1≤ λ＜2), the sagging damage increases under the same charge mass. However, as λ decreases further (0.7≤ λ＜1), the sagging deformation decreases. This is likely due to the impact of the liquid jet formed by the collapsing bubble, which causes the girder deformation to shift from sagging back to hogging deformation. The initial shock wave excites the high-frequency response of the girder structure but contributes very little to the overall velocity and displacement. However, bubble pulsation typically causes a low-frequency response, which will affect the velocity and displacement of the girder. The low-pressure region of the flow field formed by bubble pulsation and resonant coupling between the girder and the bubble are the predominant causes of damage to the overall girder structure.

Numerical simulation of underwater explosion cavitation characteristics based on phase transition model in compressible multicomponent fluids

Underwater explosion cavitation has an important influence on the shock wave, explosion bubble, and structural deformation. The one-fluid model is usually used in underwater explosion cavitation. It is assumed that the cavitation is induced suddenly when the pressure is lower than the saturated pressure. The biggest deficiency of the model is that it is difficult to consider the temperature change in the cavitation domain. It is known that cavitation is sensitive to the temperature. In this paper, we study UNDEX cavitation characteristics based on the two-fluid model proposed by Chiapolino et al. (2017), which holds that the cavitation phenomenon is the result of the phase transition between the gas and liquid phases. This model is composed of the 4-equation model with phase transition relaxation, which is solved by a simple fractional step. In this article, we briefly introduce the compressible multiphase fluids model and successfully extent it to the engineering research field of underwater explosion cavitation. Through the quantitative analysis of the vapor phase content, it is suggested that the initial mass fraction of vapor phase in water should be set to less than 10−7. Meanwhile, it can be observed that the bulk cavitation near the free surface can evolve into a vortex ring until it collapses. Numerical results show that the collapsed pressure cannot be ignored relative to the shock wave in the bulk and local cavitation. Numerical results of this paper display that the phase transition model shows a great prospect of engineering application in underwater explosion cavitation.

Interaction of two out-of-phase underwater explosion bubbles

This study presents an experimental investigation of the dynamic properties of underwater explosion (UNDEX) bubble pairs produced with a range of phase differences Δθ, defined as 2π(t1−t2)/Tosc, where ti (i = 1,2) represents the bubble inception moment and Tosc is the experimentally obtained first period of a single UNDEX bubble. Each bubble was generated by a spherical hexogen explosive charge detonated in a cubical tank and observed via high-speed photography. The phase difference was adjusted by setting different delays between the two detonations, with an accuracy of 1.0 ms. Experiments were conducted with both horizontally and vertically positioned bubble pairs and with single bubbles as well. UNDEX bubble pairs are subject to a larger buoyancy effect than cavitation or spark-generated bubble pairs. The resultant bubble behavior in the bubble–bubble interaction is more complex and is yet to be understood. In our experiments, various bubble parameters, including bubble pulsation periods, bubble elongation ratios, and collapse-induced shock wave pressures bubble, were measured and studied. Dependence of the bubble dynamics on Δθ was found, demonstrating the significant influence of Δθ on the morphology and shock wave pressure of bubble pairs. The findings suggest a method of strengthening or weakening the damage potential of an UNDEX bubble pair based on the proper adjustment of the delay between two detonations. It may also lead to a better understanding of the dynamics of interacting bubbles with buoyancy effects.

AiStudy on the Behavior of an Underwater Explosion Bubble near a Rigid Wall

The dynamic approach to an underwater explosion (UNDEX) is a complex episode that involves shockwave propagation, bubble pulse with high pressure, and water jet impact. This paper proposes linkage of Finite Element Avenue (FEM) and Companion of Eulerian-Lagrangian (CEL) to supply promised data of large deformations and flow simulation of fluid and gas where the bubble interaction is near a stiff wall. To conduct the process, a 7.5 m x 9.0 m Eulerian domain and explosive charges of 10 g, 35 g, and 55 g TNT are built in a free field, respectively. Numerical analysis, as far as a comparison with research from E. Klaseboer, has been given in this study. The important results obtained from the CEL approach imply high expectations. In spite of the fact that this approach is not adequately consistent to totally supplant a live test, it can be utilized as an outline database to anticipate outcomes of managing an UNDEX with a high pressure bubble. The behavioral explosion from an UNDEX bubble near a rigid wall is a prospective contribution in this research. With these results, this technique can be used in further studies to examine UNDEX bubbles in the vicinity of deformable and complex structures.

An improved Kirkwood–Bethe model for calculating near-field shockwave propagation of underwater explosions

To calculate the near-field shockwave propagation of underwater explosions for different explosives quickly and accurately, an improved calculation model, based on the Kirkwood–Bethe theory, is proposed. Based on the detonation theory and shock jump conditions, the model establishes initial equilibrium conditions and an initial shockwave-front state of the explosion bubble interface. By incorporating a second-order Mach-precision bubble dynamics equation, the model determines the physical parameters and enthalpy change functions at the initial expanding stage in real time. By solving the isentropic flow of the enthalpy change function G at varying delay times, a functional relation was established between the enthalpy change function and the pressure at arbitrary flow points and times. The model obtained the near-field shockwave-front peak-pressure spatial distributions of underwater explosions and the pressure decay time constants at arbitrary flow points. The results indicated that the proposed method can quickly and accurately determine the near-field shockwave propagation of underwater explosions for different explosives, with satisfactory agreement with experimental data. The proposed method relates the explosive detonation, explosion bubble expansion, and shockwave propagation, thus connecting the explosive parameters with the shockwave front state parameters.

Study on bubble collapse near a solid wall under different hypergravity environments

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.

An engineering application of Prosperetti and Lezzi equation to solve underwater explosion bubbles

The dynamic behaviors of underwater explosion bubbles differ for different explosives. The explosive characteristic parameters will result in a greater impact on the motion characteristics of the bubbles. Based on the bubble dynamics equation established by Prosperetti and Lezzi [“Bubble dynamics in a compressible liquid. Part 1. First-order theory,” J. Fluid Mech. 168, 457âĂŞ-478 (1986); “Bubble dynamics in a compressible liquid. Part 2. Second-order theory,” J. Fluid Mech. 185, 289âĂŞ-321 (1987)], we proposed an initial condition and an equation of state (EOS) form applicable for calculating the underwater explosion bubble dynamics of different explosives. With the assumption of instantaneous detonation and initial shock wave formation at the gas–liquid boundary, we calculated the initial state of the bubble boundary and established the initial condition for calculating explosion bubbles. Using the Jones–Wilkins–Lee EOS for different explosives, we constructed an isentropic EOS with a polytropic exponent that varied with density. We calculated and analyzed the differences in the initial expansions and the subsequent oscillations of underwater explosion bubbles with different explosives as well as the effects of different explosive parameters on the explosion bubble dynamics. This study showed that the proposed initial condition and the EOS form with a polytropic exponent that varied with density yielded good calculation accuracy and achieve close association of the underwater explosion bubbles with the properties of the explosive detonation and the characteristics of the detonation products. In addition, the explosion bubbles differed in the initial expansion, where the bubbles produced by explosives with higher densities and greater detonation velocities expanded more rapidly.

An effective method for modeling the load of bubble jet in underwater explosion near the wall

Due to the nonlinear effects such as strong impact and complex movement of gas-water interface in the process of water jet in underwater explosion, there is no suitable method to calculate the load of water. This work presents a novel and efficient method for modeling underwater-explosion-induced bubble jet near the wall. In this method, compressible multiphase five-equation model with interface compression and density correction is solved by a finite volume method, while a fifth-order accuracy Weighted Essentially Non-Oscillation (WENO) reconstruction and HLLC approximate Riemann solver are employed to discretize the convective terms, and 3rd order TVD Runge-Kutta scheme is used to discretize the temporal term. This method is validated by conducting one-dimensional benchmarking problems and two-dimensional cases. It is found that the results predicted by our method agree well with those from different sources. Finally, the proposed method is applied to simulate underwater explosion bubble jet near the wall. It shows that the generation, development and collapse of the water jet can be well captured, confirming that the five-equation model is effective for modeling bubble jet load near the wall.

Characteristics of wall pressure generated by bubble jets in an underwater explosion

The loading of bubble jet is an important part of the whole loading induced by the middle-field and near-field underwater explosion. Due to the fact that the period of the bubble jet is extremely short and the jet occurs inside the complicated underwater explosion bubble, it is hard to investigate the bubble jet through the direct underwater explosion bubble. Therefore, simplifying underwater explosion bubble jet into a high-speed water column has been widely adopted by many researchers to investigate the bubble jet. Based on the in-cavity explosion, a new high-speed water jet experimental methodology was proposed, and the experimental device design, method and system were presented as well. The details about how to carry out the pertinent experiments were also illustrated. Based on the proposed experimental system, the experimental research on high-speed water jet under different conditions were carried out. It is found that the shapes of the generated high-speed water jet vary with the outlet position and the depth of the cavity. Three experiments with three different cavity depths but same outlet position, and other two experiments with same cavity depth but different outlet positions were carried out. According to the results, the shape of the water jet generated in the experiments with short cavity depth and surface-above outlet position cannot meet the requirements of the investigation. The influence of outlet position and depth of the cavity on the shape of the water jet was investigated and the mechanism of the water jet shape was analyzed. According to the requirements of the investigation of the bubble jet wall pressure, the adoptable outlet position and cavity depth were got. In the experiments, the piezoelectric wall pressure sensor was used to measure the wall pressure of the water jet. The whole water jet wall pressure can be divided into two phases: the initial impact pressure period and the later hydrodynamical pressure period. According to the results, the outlet position and the depth of the cavity are the two main factors affecting on the shape of the water jet. The initial impact pressure of the water jet meets the water hammer theory. The proposed water jet experimental methodology based on the in-cavity explosion can be used to investigate the shape of the high-speed water jet and wall pressure characteristics including the underwater explosion bubble jet.

Experimental and numerical investigation on the dynamic response of a simplified open floating slender structure subjected to underwater explosion bubble

A simplified open floating slender structure is used to investigate the dynamic behaviors of the warship in this paper. The deformation and damage mechanisms of the simplified open floating slender structure subjected to the underwater explosion are studied using the experiment and the Coupled Eulerian-Lagrangian (CEL) method. Firstly, a validation for the CEL method is carried out, where the numerical results agree well with the results in experiment. Subsequently, in order to analyze the deformation and damage characteristics of the simplified open floating slender structure subjected to the underwater explosion, a series of cases for different detonation distances and different charge weights are carried out. In the cases, the results indicate that the deformation and damage of the simplified open floating slender structure are mainly induced by the bubble, and the damage induced by the shock wave is not obvious. For small charge weight and large detonation distance, the whipping motion is the main deformation form of the simplified open floating slender structure. When the charge weight increases or the detonation distance decreases to a critical value, the simplified floating slender structure is damaged in a longitudinal bending mode with a plastic hinge generated in the middle region.

Numerical study on strong nonlinear interactions between spark-generated underwater explosion bubbles and a free surface

In this study, strong nonlinear interactions of one and two underwater explosion bubbles with a free surface are numerically studied using an axisymmetrical fully compressible three-phase homogeneous model. The bubble interfaces and free surface are captured by solving two interface advection equations of vapor and air phases. The numerical results are validated via comparisons with the experimental results. The single-bubble case is validated first, and good quantitative and qualitative agreements are achieved. Special features of the interactions, such as jet impact, toroidal bubble, and primary and secondary water spike, are observed in our numerical model. The detailed pressure and velocity contours during the interaction process are obtained and can better reveal the mechanism underlying the bubbles and free surface dynamics. Afterward, the characteristics of the motion of the free surface and the bubbles are investigated considering different non-dimensional standoff parameters. Four distinct patterns of free surface motion are identified. Next, strong interactions between two bubbles and a free surface are simulated. The essential physical phenomena, such as coalesced bubble, annular residual, and bubble splitting, are reproduced well in the representative experiments. Finally, a parametric study reveals the dependence of the center water spike on the interaction between the bubbles and the free surface.

The Application of CEL Technique to Simulate the Behavior of an Underwater Explosion Bubble in the Vicinity of a Rigid Wall

The dynamic process of an underwater explosion (UNDEX) is a complex phenomenon that involves several facets. After detonation, the shockwave radially propagates at a high speed and strikes nearby structures. Subsequently, bubble oscillation may substantially damage the structures because of the whipping effect, water jet impact, and bubble pulse. This paper presents an application of explicit finite element analyses to simulate the process of an UNDEX bubble in the vicinity of rigid wall, in which the coupled Eulerian-Lagrangian (CEL) approach was developed to overcome the difficulties regarding the classical finite element method (FEM), large deformations, and flow simulation of fluid and gas. The results demonstrate that the method is well suited to manage the UNDEX bubble problem and can be used to model the major features of the bubble dynamics. Furthermore, the behavior of an UNDEX bubble near a rigid wall was also examined in the present study, which showed that the migration of the bubble and the development of the water jet are influenced strongly by the standoff distance between the initial bubble position and the wall. This method can be used in future studies to examine UNDEX bubbles in the vicinity of deformable and complex structures.

Study on the quantitative law of wall pressure caused by mini-charge underwater explosion bubble

The wall pressure caused by underwater explosion is always a key problem in the anti-explosion design of naval ships. Notably, the accurate wall pressure caused by underwater explosion bubble is one of the most difficult parts due to the significant nonlinear deformation of the bubble. In present study, the dynamics of an underwater explosion bubble near a rigid wall are captured by high-speed camera and the wall pressure in the wall center are measured by a pressure transducer. The wall pressure with standoff distance parameter γ=d/Rm from 0.38 to 1.54 are recorded, where d represents the vertical distance from the explosive charge center to the wall center, and Rm is the maximum radius of bubble. According to the previous study and the experimental data in this paper, when γ<1.2, the load on the wall center has obvious double-peak phenomenon, that is, the composition of the re-entrant jet load and the bubble collapse load. To obtain the quantitative law of wall pressure caused by mini-charge underwater explosion bubble, we proposed a mathematical model to describe the time-pressure curve when γ<1.2. And according to the conclusion in our previous study (Chen et al., 2018), based on the boundary element method (BEM), the space distribution of the wall pressure was obtained.

Numerical analysis of the interaction of two underwater explosion bubbles using the compressible Eulerian finite-element method

This paper presents numerical investigations of the nonlinear interactions between two underwater explosion (UNDEX) bubbles using the compressible Eulerian finite-element method (EFEM). The volume of fluid method is applied to capture the multi-fluid interface. In this model, the high-temperature and high-pressure gaseous products inside the UNDEX bubble are described by the equation of state for Jones–Wilkins–Lee, which allows us to consecutively simulate the propagation of the primary explosion shock wave and multi-period bubble pulsations. To verify the efficiency and accuracy of the present model, comparisons with experimental data are performed, showing that both the dynamic behaviors of oscillating bubbles and the pressure profiles of primary shock waves, bubble pulsations, and jetting loads are highly consistent. In addition, it is found that the EFEM model can satisfactorily reproduce the complex characteristics of interacting bubbles, such as the coalescence and splitting that occur during later pulsating cycles in bubbles. On this basis, the effects of the initial bubble–bubble distance γbb and buoyancy parameter δ on the features of bubble interactions and the corresponding pressure loads in the flow field are analyzed and discussed. In particular, the pressure induced by two identical UNDEX bubbles (each generated by detonation of an explosive with weight W) is compared to that induced by a single bubble generated by an explosive with weight W or 2W to provide the basic technical support and reference for the design of multiple-weapon attacks in military engineering applications.

Numerical simulation of the coupled response of stiffened structures subjected to explosion bubble loading

Numerical simulations of the dynamics of explosion bubbles and their interactions with stiffened structures are performed using the three-dimensional boundary integral method (BIM) in conjunction with the finite element method (FEM). The BIM is used to investigate the bubble’s physical characteristics, while the FEM is employed to calculate the structural response. This study aims to develop a procedure that considers multiple factors, such as fluid–structure interactions, non-spherical bubble oscillation, transient dynamic response, and stiffening patterns, to investigate the transient response of a structure subjected to an explosion bubble. Code validation comparisons between the numerical results, the analytically bubble model, and the experimental data are carried out. For the stiffened structure, the results indicate that significant effects of various strengthening strategies on the structural deformation are observed, including modification of the deformation pattern and the bubble loading. The effects of the stiffening schemes on the pressure distributions of the bodies, the bubble dynamics, and the structural response characteristics are investigated, including a higher frequency oscillation superimposed on a lower frequency motion in the vertical direction, during the various bubble evolution phases.