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The accurate estimation of deep-sea explosion loads is challenging due to the extreme conditions such as the ultra-hydrostatic pressure. The traditional Geers–Hunter model has acceptable accuracy in calculating underwater explosion load in conventional water depth, but it is not effective in deep-sea explosions. The model established by Zhang is applied to the underwater explosion load calculation in ultra-deep water. The model's accuracy is validated by both the deep-sea and the conventional explosion experimental results published and the Eulerian finite element method numerical results. The results show that, compared to the Geers–Hunter model, the present model can not only accurately calculate the conventional conditions, but also has better accuracy for calculating deep-sea explosion shock wave and bubble load, by providing more accurate shock wave attenuation and smoother connection between shock wave stage and bubble pulsation stage in deep sea. [ABSTRACT FROM AUTHOR]

The pulsating bubble near different boundaries demonstrates various dynamics. In this study, the three-dimensional Eulerian finite element method with the adaptive mesh refinement technique was used to investigate the interaction between a bubble and a free surface near a solid wall, including the toroidal bubble motion after the jet impact. The impact pressure on the solid wall was investigated, and the changing trend of pressure peak reverses when the initial depth of the bubble center is between 0.7 and 0.9 times the bubble's maximum radius. Throughout the process, competition occurs between the Bjerknes effects of the free surface and solid wall, which leads to the nonspherical pulsation of the bubble. Different collapsing forms of bubbles, i.e., the strong jet, weak jet, and crescent-type forms, were identified. Greater depth may result in a reduced height of a free surface water column, which is described in a fitting curve. Additionally, inclination of the solid wall can cause the free surface to exhibit a side hump or groove phenomenon. But for a large-scale bubble, no groove phenomenon of the free surface occurred, and the bubble collapsed in a horn-shaped form with two jets in the upward and downward directions. [ABSTRACT FROM AUTHOR]

The shock wave and bubble dynamics of an underwater explosion are significant in various fields. When the charge is non-spherical, the detonation process will remarkably affect the shock wave formation and the subsequent bubble motion. In this work, the underwater explosion of a cylindrical explosive is investigated numerically with the Eulerian finite-element method combined with the programed burn model treating the detonation process. The present model is validated by comparing the simulated results with the experimental ones. Then, several cases with different slenderness of the explosive charge in various buoyancy environments are simulated and analyzed. The results demonstrate a notable variation of the shock wave in different directions. The shock wave will reach the highest pressure peak and shortest pulse width at a certain angle determined by the ratio between the speeds of the detonation wave and the shock wave. Furthermore, the non-spherical initial expansion of the bubble casts a significant influence on the subsequent bubble evolution. Three typical jet morphologies are identified with different combinations of buoyancy parameter and oblateness ratios of the bubble, featured by a slightly oblique upward jet penetrating the bubble, a laminar jet that failed to penetrate the bubble continuously, and a pair of opposite horizontal jets penetrating the bubble. Meanwhile, the horizontal jets that happen under a weak buoyancy environment will reduce the upward migration. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The interaction of an oscillating bubble and a nearby liquid–liquid interface is a complex multiphase problem that has many potential applications. In this work, the behavior of a bubble initially between two different liquids (i.e., with a stand-off distance of zero) is investigated numerically and is shown to exhibit a high degree of nonlinearity. A numerical model based on an Eulerian finite-element method is established. It is validated by simulating a nonspherical collapse of a bubble in the gravity field and comparing the results with those obtained in the experiment. Then, several cases of interaction between an oscillating bubble and a liquid–liquid interface are simulated with different initial conditions. It is confirmed that the density interface tends to induce the bubble to develop a jet that drills into the heavier liquid during the bubble collapse phase. The nondimensional period of oscillation increases with increasing density ratio of the two liquids, and an annular jet impacts, generating a pressure peak, when the density ratio exceeds 1.5. When the effect of gravity is taken into account, it is found that the annular impact is enhanced while the downward jet is weakened. In addition, a significantly sized bubble is split from the main bubble by the impact of the annular jet. When the buoyancy parameter exceeds a threshold value, gravity comes to dominate the bubble motion, and neither an annular jet nor a downward jet will develop. If the buoyancy parameter is large enough, the bubble migrates upward and detaches from the liquid–liquid interface during the collapse phase. [ABSTRACT FROM AUTHOR]

Pressure hulls is an essential part of the deep-sea submersible and may implode to emit shock pressure wave. This paper establishes a deep-sea implosion model based on the Eulerian finite element method, and two implosion conditions, ellipsoidal and egg-shaped, are studied. It is found that the pressure load at the gauging point in the long semi-axis direction is always greater than that in the short semi-axis direction when the two models implosion. Introducing the radius ratio β , it is found that the pressure load after the implosion of the two models increases first and then decreases with the increase of β. Then the dimensionless number M a is introduced to simulate the change of pressure load under implosion in different water depths. It is found that pressure peak P m ∗ decreases by a factor of M a − 0. 5 as M a increases, and the time T m ∗ to reach the pressure peak increases linearly with the rise of M a. Therefore, the pressure load caused by implosion can be reduced by reasonably selecting the radius ratio of the pressure hull. In addition, the implosion load when a plurality of pressure hulls are arranged together can be reduced by organizing them along the short semi-axis direction. • Based on the Eulerian finite element method, ellipsoidal and egg-shaped implosion models are established. • The implosion load in the long radius of the pressure hull is greater than that in the short radius. • The implosion load increases first and then decreases with the increase of the radius ratio. • The characteristic of implosion load at different sea depths is studied. [ABSTRACT FROM AUTHOR]

• The improved Eulerian finite-element method considers viscosity. • Studying the coupling between a bubble and liquid-liquid interface systematically. • The pressure peaks caused by bubbles are nonlinearly related to viscosity and buoyancy. The bubble dynamics are of great significance in the scientific community and have wide applications. Due to the complex coupling effect, high nonlinearities arise when the bubble is initiated at a liquid-liquid interface. Based on the Eulerian finite element method, the coupling model of a bubble and the liquid-liquid interface is established considering the viscosity and is verified by comparing with the experiments. It is found that the bubble only generates a downward jet at a large Reynolds number. In contrast, a pinch-off effect occurs due to an annular jet impact, which generates two opposite jets at a small Reynolds number. And the bubble migrates upward with the increase of buoyancy parameters. Moreover, through dynamic analysis, we find three reasons for the pressure peaks above the bubble: the annular jet impact, the downward jet impact, and the upward jet passing the measuring point. It is found that the pressure peaks are nonlinearly related to viscosity and buoyancy, and they can enhance each other to generate higher pressure peaks. [ABSTRACT FROM AUTHOR]

Marine structures operating in the deep-sea, such as submersibles and photomultiplier tubes, bear enormous hydrostatic pressure of deep-sea, which may cause structural damage and implosion. And a pressure wave will emit from the collapse of the cavity and pose a threat to nearby structures. On the basis of the Eulerian finite element method, the numerical model of multiphase flow for deep-sea implosion is established in this paper. The numerical method is verified by comparing the results with those from Keller equation and literature. The physical process under the spherical simplification is firstly analyzed in our work. The basic phenomena are studied, and the pressure changes under different distances and Mach numbers are given. Subsequently, the basic physical process and pressure distribution under cylindrical simplification are introduced. Then, the bubble evolutions under different Mach numbers and initial aspect ratios are given. In the early stage of bubble movement, a rarefaction wave will radiate to the surrounding. The multi-peak phenomenon will occur in the cylindrical model because of the bubble sides breakage and the bubble pulsation. Finally, asymmetric three-dimensional cylindrical bubble implosion near the solid wall with different standoff distances are present in this paper, where the typical oblique jet is observed and analyzed. • Based on the EFEM, the numerical model of deep-sea implosion is established. • The spherical and cylindrical implosion model are analyzed by different parameters. • Three-dimensional cylindrical bubble implosion near the solid wall are present. [ABSTRACT FROM AUTHOR]

Energy dissipation mechanisms of bubble pulsation in compressible fluids have always been a significant aspect of research into bubble dynamics. In this paper, bubble dynamics in compressible fluids are investigated numerically with the Eulerian finite-element method (EFEM), and the energy dissipation due to the wave effects of the compressible surrounding fluid is analyzed. The present model is validated by comparing with experimental results. Results from both the simulation and experiment show that bubble fragmentation also contributes to the energy dissipation, which has seldom been discussed before. It is also shown that the initial discontinuity is significant to the energy dissipation which is non-trivial to simulate in 1-dimensional bubble dynamics equations like the Gilmore equation. Then, the relationship between dissipated energy and bubble maximum radii in adjacent pulsating cycles is formulated to quantitatively evaluate the energy dissipation during a pulsating cycle. At last, based on the linearized theory of the energy conservation of the bubble system, a new non-dimensional parameter M a is modified from the Mach number to represent the energy dissipation due to wave effects. With simulation and discussion on cases with different initial pressure and sound speed, it is found that the dissipated energy is related linearly to M a , which can be used to predict the energy dissipation of a new case. • Bubble dynamics model based on Eulerian FEM with operator split is established and verified by comparing with experiment.. • Energy dissipation of a pulsating bubble is analyzed, which relates the lost energy, radius decrease and fluid compressibility.. • Small bubbles split from main bubble contributes to the energy dissipation.. • Dissipated energy through wave effect is found to be linear related to the modified Mach number.. [ABSTRACT FROM AUTHOR]

In the present paper, the penalty immersed boundary method is improved to resolve the transient fluid–solid interaction problems. The Eulerian finite-element method is chosen as the fluid solver, and the conservation of the total energy is solved to ensure the correct results for discontinuous problems. The penalty immersed boundary method is adopted to couple the fluid and the submerged solid body, which is improved by considering both the normal and tangential relative velocities of the solid surface with an upwind scheme when updating the penetrated depth. With the present model, the simulated results of a 1-dimensional moving piston problem in the ideal gas are compared with the exact solution and the results from the Abaqus to validate the capability of the present method in dealing with shocks. Then, several 3-dimensional problems are simulated and analyzed, including a bubble–sphere interaction problem, and three high-speed water entry problems. The results are compared with experiments and show good agreements. • The penalty immersed boundary method is improved to resolve the fluid–solid interaction problems. • The Eulerian finite-element method is modified to ensure the conservation of the total energy. • The present method perform well in several test cases of fluid–structure interaction. [ABSTRACT FROM AUTHOR]

Violent pulsating bubbles behave diversely in different circumstances. It is a multi-scale problem in both space and time. In 3-D problems, the numerical simulation is usually too expensive to implement in practice with a fixed grid. In this paper, a 3-D multi-fluid model is established based on the Eulerian finite element method and the adaptive mesh refinement technique to investigate the bubble evolution and its toroidal motion near a solid vertical wall. The mixture formula for compressible multi-fluid flow is adopted to ensure conservativeness. By means of the block-based adaptive mesh refinement, the accuracy and the efficiency of the simulation are well balanced. The present model is validated by comparing the results with an underwater explosion experiment and the existing numerical results. The results agree well and a fast convergence is observed. Then, several cases with different buoyancy parameters are simulated, and the toroidal bubble motion and their pressure load on the solid wall are analyzed. The bubble's motion exhibits complex physics, such as the formation of the crescent-shaped bubble, the air cushion effect during the jet penetration, and the nonlinear relationship between the jet impact pressure and the angle between the jet and the opposite bubble surface. • A compressible multi-fluid model is presented for bubble dynamics. • The toroidal bubble motion beside a vertical wall motion is investigated. • The crescent-shape bubble and cushion effect are observed and analyzed. [ABSTRACT FROM AUTHOR]

When a charge explodes in shallow water, the combined effects of free surface and seabed on shockwave propagation and bubble motion are significant. In this paper, an underwater explosion between a deformable seabed and a free surface is numerically investigated. An axisymmetric numerical model is established using the Eulerian Finite Element Method (EFEM) and the Volume of Fluid (VOF) method is used in dealing with the interface. The truncated computational domain boundary adopts the non-reflecting boundary condition. The seabed is regarded as a heavier fluid and density ratio between the seabed and water is used to describe seabed feature in this paper. The present model is validated by comparing with the experiment and shows great results. Then the underwater explosion with different initial conditions are simulated, it is found that deformable seabed has a great impact on bubble when the bubble is near the deformable seabed. And the bubble period and pressure peak of shockwave have a positive relation with the density ratio and initial charge depth. In addition, the annular jet might appear and penetrate the upper surface of the bubble in certain condition, leading to the bubble split during the contraction phase. • The nonlinear interactions between bubble and deformable seabed are shown based on the EFEM. • The deformable seabed has a greater effect on bubble than the free surface when a charge explodes in shallow water. • The shockwave pressure peak and bubble period have a positive relation with the initial charge depth and density ratio. • The annular jet induced by the bubble necking occurs only with an appropriate condition. [ABSTRACT FROM AUTHOR]