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In this work, we established a novel theory for the dynamics of oscillating bubbles such as cavitation bubbles, underwater explosion bubbles, and air bubbles. For the first time, we proposed bubble dynamics equations that can simultaneously take into consideration the effects of boundaries, bubble interaction, ambient flow field, gravity, bubble migration, fluid compressibility, viscosity, and surface tension while maintaining a unified and elegant mathematical form. The present theory unifies different classical bubble equations such as the Rayleigh–Plesset equation, the Gilmore equation, and the Keller–Miksis equation. Furthermore, we validated the theory with experimental data of bubbles with a variety in scales, sources, boundaries, and ambient conditions and showed the advantages of our theory over the classical theoretical models, followed by a discussion on the applicability of the present theory based on a comparison to simulation results with different numerical methods. Finally, as a demonstration of the potential of our theory, we modeled the complex multi-cycle bubble interaction with wide ranges of energy and phase differences and gained new physical insight into inter-bubble energy transfer and coupling of bubble-induced pressure waves. [ABSTRACT FROM AUTHOR]

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. [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]

Summary: The Runge‐Kutta discontinuous Galerkin method together with a refined real‐ghost fluid method is incorporated into an adaptive mesh refinement environment for solving compressible multifluid flows, where the level set method is used to capture the moving material interface. To ensure that the Riemann problem is exactly along the normal direction of the material interface, a simple and efficient modification is introduced into the original real‐ghost fluid method for constructing the interfacial Riemann problem, and the initial conditions of the Riemann problem are obtained directly from the solution polynomials of the discontinuous Galerkin finite element space. In addition, a positivity‐preserving limiter is introduced into the Runge‐Kutta discontinuous Galerkin method to suppress the failure of preserving positivity of density or pressure for the problems involving strong shock wave or shock interaction with material interface. For interfacial cells in adaptive mesh refinement, the data transfer between different grid levels is achieved by using a L2 projection approach along with the least squares fitting. Various numerical cases, including multifluid shock tubes, underwater explosions, and shock‐induced collapse of a underwater air bubble, are computed to assess the capability of the present adaptive positivity‐preserving RKDG‐GFM approach, and the simulated results show that the present approach is quite robust and can provide relatively reasonable results across a wide variety of flow regimes, even for problems involving strong shock wave or shock wave impacting high acoustic impedance mismatch material interface. [ABSTRACT FROM AUTHOR]

In this study, we establish a full coupling model (FCM) to simulate strong bubble-sphere interactions based on a three-dimensional boundary integral method. Different from the conventional loose coupling model (LCM), FCM adopts several auxiliary functions to deal with the mutual dependence between the hydrodynamic force and the sphere acceleration. In addition, the weighted moving least square method, a mesh density control scheme and an adaptive mesh refinement scheme are implemented to improve the quality of mesh on the deformable bubble surface. To validate the present model, convergence tests on different mesh sizes and time steps are conducted at first. The numerical results are also compared with the axisymmetric model, in which consistent results have been achieved. We further make comparisons between the numerical results and those from several experiments under different boundary conditions. For weak interaction cases, both LCM and FCM can give the results that have good agreement with the experiment data. As the interaction effects become stronger, the advantage of the FCM over the LCM becomes increasingly obvious. Particularly, when the pulsating bubble is in contact with the sphere surface, the essential physical features of the experiments can be well reproduced by the FCM while the predictions by the LCM are significantly different from the experiment. The present 3D model can be further extended to study more complex underwater contact explosions, cavitation inception on a structure and airgun bubble dynamics. • A full coupling model is established to simulate strong bubble-sphere interaction based on 3D boundary integral method. • Auxiliary functions are introduced to deal with the mutual dependence between the force and the sphere acceleration. • By using some latest numerical techniques, the interaction between a sphere and an attached bubble is simulated. • The essential physical features of some experiments are well reproduced by the present 3D model. [ABSTRACT FROM AUTHOR]

The propagation of the shock wave across multilayer structures during underwater explosion is a very complex physical phenomenon, involving violent fluid-structure interaction (FSI) problems. In this paper, the coupled Eulerian–Lagrangian (CEL) method in AUTODYN is used to simulate the process of shock wave propagation and solve FSI problems. Firstly, the governing equation and the treatment of fluid and structure interface of the CEL method are briefly reviewed. Afterwards, two underwater explosion numerical models are established, and the results are compared with the empirical formula and experimental data, respectively, to verify the reliability of numerical solutions. The results obtained by this method show good agreements with those of the empirical formula and experiment. Furthermore, the model of the multilayer structures composed of two hemispherical shells and the fluid filled between the shells subjected to underwater explosion is established, and the pressure characteristics of the shock wave propagating across the multilayer structures are analyzed regarding the wave reflection and transmission. Finally, the effects of the shell thickness and the filled fluid type among the multilayer structures on the wave reflection and transmission are studied. [ABSTRACT FROM AUTHOR]

Abstract Underwater explosion in free field is investigated in this paper numerically. With the multiphase interface captured by the Volume of Fluid (VOF) method, the Eulerian finite element method (EFEM) for underwater explosion is established. The MUSCL algorithm to advect the element centered variables is modified to maintain its conservativeness in the axisymmetric model, and the second order Early Time Approximation (ETA 2) is adopted to deal with the non-reflecting boundary condition of the computational domain. By comparing with the experiment results, the numerical model is proved in both shockwave and bubble oscillation simulation. With the numerical model, 2 underwater explosion cases with different initial depths are simulated and the near-field pressure characteristics are analyzed. The near-field bubble pulsation load exhibits noteworthy asymmetry around the bubble, which is attributed to the 2 high pressure regions above and beneath the bubble, respectively. By comparing the evolution of bubbles with different buoyancy parameters, it is found that the increase of the buoyancy parameter can delay the penetration and extend the collapse of the bubble. Highlights • The present numerical model can predict both the shockwave and bubble pulsation load with good accuracy. • The non-reflecting boundary condition based on ETA2 works well in the underwater explosion simulation. • The MUSCL algorithm is modified for the convection in the axisymmetric model. • The asymmetry of the pulsation load is generated by the 2 high pressure regions caused by gravity and the jet impact. [ABSTRACT FROM AUTHOR]

Two-bubble interaction is the most fundamental problem in multi-bubbles dynamics, which is crucial in many practical applications involving air-gun arrays and underwater explosions. In this paper, we experimentally and numerically investigate coalescence, collapse, and rebound of non-buoyant bubble pairs below a rigid wall. Two oscillating vapor bubbles with similar size are generated simultaneously near a rigid wall in axisymmetric configuration using the underwater electric discharge method, and the physical process is captured by a high-speed camera. Numerical simulations are conducted based on potential flow theory coupled with the boundary integral method. Our numerical results show excellent agreement with the experimental data until the splashing of the jet impact sets in. With different ranges of γbw (the dimensionless distance between the rigid wall and the nearest bubble center), the interaction between the coalesced bubble and the rigid wall is divided into three types, i.e., “weak,” “intermediate,” and “strong.” As γbw decreases, the contact point of the two axial jets migrates toward the wall. In “strong interaction” cases, only an upward jet towards the upper rigid wall forms and a secondary jet with a larger width appears at the base of the first jet. The collapsing coalesced bubble in a toroidal form splits into many smaller bubbles due to the instabilities and presents as bubble clouds during the rebounding phase, which may lead to a weakened pressure wave because the focusing energy associated with the collapsing bubble is disintegrated. [ABSTRACT FROM AUTHOR]

Abstract: Numerical and experimental methods are combined in this paper to study the bubble dynamics generated by an underwater charge explosion with different initial charge shape, detonating styles and boundary conditions. Outdoor experiments are carried out to employ sunlight with the assistant of lamplight to get clearer pictures of bubble motion. The results show that the charge detonating stage is not finished instantly but takes some time to explode fully. The explosion begins from its detonating end and finishes at the other end, which results in its uneven distribution of initial normal velocity. So instead of following the traditional method of treating the charge explosion instantly, a real charge explosion model is built in this paper with the combination of LS-DYNA and the boundary element method (BEM). LS-DYNA is used to solve the charge initial detonation and the BEM to solve its subsequent bubble motion. The linking relationship between these two methods is modeled. The convergence study has been firstly taken with different meshes. In this paper, charges with a different slenderness ratio from 0.99 to 20 are chosen to carry out the experiments and their corresponding numerical results are put forward. It can be found in both experimental and numerical results that the initial charge shape and its detonating style would affect its following bubble dynamic behavior. When the cylindrical charge is horizontally installed and end detonated, an oblique jet leaned to the detonating end would be formed and a horizontal migration process is also observed during the whole bubble pulsating stage. The bubble dynamic behaviors near different solid boundaries are further studied and the numerical results coincide well with the experimental ones. [Copyright &y& Elsevier]

Abstract: Highly dependent on boundary conditions, the behaviors of underwater explosion (UNDEX) bubbles would be quite unusual near boundaries that are discontinuous with abrupt changes in shape, e.g. ship structures that have already been deformed by previous attacks. The oscillation features of the UNDEX bubble near the bilge with a circular opening representing previous deformation are studied experimentally with electric-spark-generated bubbles and high-speed photographing. The bubble behaviors are found highly dependent on two non-dimensional variables, D and Φ, representing the opening-bubble distance and the opening diameter, respectively. Seven distinctive oscillation scenarios are summarized from 180 experiments, namely the ‘rim-constrained oscillation’, the ‘inward jet’, the ‘outward jet’, the ‘bump and dimple’, the ‘quasi-spherical oscillation’, the ‘spherical oscillation with jet’ and the ‘spherical oscillation without jet’. The occurrence domains of the scenarios are identified as functions of D and Φ. Significantly affected by the opening, the bubble behaviors are quite different from that near a non-opening bilge; the bubble jet might not be formed, or even develop from inside the bilge, which indicates that the bubble load on the bilge should be re-evaluated. Finally the speeds, initiation time and displacements of the jets in different scenarios are measured and noticeable variation trends are found. [Copyright &y& Elsevier]

In the underwater-shock environment, cavitation occurs near the structural surface. The dynamic response of fluid-structure interactions is influenced seriously by the cavitation effects. It is also the difficulty in the field of underwater explosion. With the traditional boundary element method and the finite element method (FEM), it is difficult to solve the nonlinear problem with cavitation effects subjected to the underwater explosion. To solve this problem, under the consideration of the cavitation effects and fluid compressibility, with fluid viscidity being neglected, a 3D numerical model of transient nonlinear fluid-structure interaction subjected to the underwater explosion is built. The fluid spectral element method (SEM) and the FEM are adopted to solve this model. After comparison with the FEM, it is shown that the SEM is more precise than the FEM, and the SEM results are in good coincidence with benchmark results and experiment results. Based on this, combined with ABAQUS, the transient fluid-structure interaction mechanism of the 3D submerged spherical shell and ship stiffened plates subjected to the underwater explosion is discussed, and the cavitation region and its influence on the structural dynamic responses are presented. The paper aims at providing references for relevant research on transient fluid-structure interaction of ship structures subjected to the underwater explosion. [ABSTRACT FROM AUTHOR]

Abstract: Whipping response will happen when a ship is subjected to underwater explosion bubble load. In that condition, the hull would be broken, and even the survivability will be completely lost. A calculation method on the dynamic bending moment of bubble has been put forward in this paper to evaluate the impact of underwater explosion bubble load on the longitudinal strength of surface ships. Meanwhile the prediction equation of bubble dynamic bending moment has been concluded with the results of numerical simulation. With wave effect taken into consideration, the evaluation method of the total damage of a ship has been established. The precision of this evaluation method has been proved through the comparison with calculation results. In order to verify the validity of the calculation results, experimental data of real ship explosion is applied. Prediction equation and evaluation method proposed in this paper are to be used in ship structure design, especially in the preliminary prediction of the ultimate withstanding capability of underwater explosion damage for the integrated ship in preliminary design phase. [Copyright &y& Elsevier]

In the circumstance of underwater explosion, ship equipment's dynamic response characteristics are key factor affecting the working capability and reliability. Numerical simulation is done for the research of time domain dynamic structural response of large scale ship equipments and ship structure on the condition of underwater explosion. The conclusion indicates that integrate analysis result coincides with that from experiments. Meanwhile, integrate analysis is used to determine the characteristic ship cabin structure element length, not only to reduce the amount of calculation but also for good precision. [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]

In the present work, numerical simulation of structural damage subjected to the near-field underwater explosion is carried out by coupling the SPH and RKPM. The fluid solver is established based on the compressible SPH method, while the dynamic response of the structure is calculated based on the RKPM shell formulation. Since large deformation with contact will occur in the underwater explosion problem, a contact detection algorithm for the RKPM shell formulation is proposed. The contact force is calculated based on the volume strain. The fluid-structure interaction solver is established by adopting the normal-flux method, in which the structure is treated as a moving solid boundary for the fluid domain, while the fluid pressure is considered as the load act on the structure surface. Thus, the numerical model for the simulation of structural damage analysis in the underwater explosion is obtained, which is a part of the FSLAB software developed by the FSI laboratory of Harbin Engineering University. Finally, several numerical examples are studied to verify the robustness and accuracy of the present numerical model. • Propose a 3D FSI solver by coupling the SPH and RKPM. • A contact detection algorithm for the RKPM shell formulation is developed. • Fracture of the ship structure subjected to underwater explosion is simulated. • The accuracy and robustness of the FSI solver are verified. [ABSTRACT FROM AUTHOR]

A combined RKDG-FEM approach, using the Runge-Kutta discontinuous Galerkin (RKDG) method [1,2] for fluid simulating and the finite element method (FEM) [3,4] for structure simulating, is developed to study the complex interactions between compressible multiphase flows and deformable steel and composite structures in near-field early-time underwater explosion (UNDEX). The level set method (LSM) [5,6] and the real ghost fluid method (RGFM) [7,8] are applied to capture and treat the moving gas-water interface, respectively. A GFM-based interface treating scheme [9,10] is adopted to treat the fluid-structure interface, achieving the coupling by solving simultaneously the fluid characteristic equation and the structure equation of motion at the material interface to satisfy the kinematic compatibility and pressure equilibrium conditions. The isentropic one-fluid cavitation model in [11] is employed to capture the transient flow cavitation. Accuracy and effectiveness of the combined RKDG-FEM approach are validated by five benchmark cases, and then it is applied to simulate early-time UNDEX problems near a submerged aluminum foam-cored sandwich plate and a monolithic steel plate of equivalent mass. Numerical results show that the sandwich plate has a higher underwater explosion load resistance through absorbing plastic energy by the foam core than the monolithic steel plate of equivalent mass, and that the foam core plays an important role in the fluid-structure interaction (FSI) and flow cavitation effects, which can be exploited to improve the UNDEX mitigation capability of composite sandwich structures. • A combined RKDG-FEM approach is developed for simulating UNDEX problems. • UNDEX involving shock-bubble-structure interactions and flow cavitation is simulated. • Comparison study of UNDEX near steel and composite sandwich structures is conducted. [ABSTRACT FROM AUTHOR]

This work presents experimental and numerical investigations on the nonlinear interaction, coalescence, collapse and rebound of two pulsating bubbles, which are generated by underwater explosions (2.5 g PETN for each). The transient physical phenomena are captured by a high-speed camera and the near-field pressure signals measured by pressure sensors. The boundary integral simulations gain further insight into the high-speed liquid jet formation, jet impact, splash, fragmentation, and the associated flow field characteristics. Particularly, the numerical simulation reproduces the multiple splits of the coalesced bubble, which partly reveals the mechanism of the bubble cloud formation. These sub-bubbles collapse with different velocities and reach their minimum volumes at different times, leading to the emission of multiple bubble pulse pressures (shock waves) at the final collapse phase. Interestingly, we find that the last pressure peak is the largest one for non-axisymmetric configurations, which is attributed to the asymmetric collapse of the coalesced bubble about the centerline of the two bubbles at inception. More specifically, the lower bubble segments collapse earlier and generate large pressure waves, which further drives the remaining part of the bubble to collapse more violently. We also make quantitative comparisons of the pressure impulse between different configurations. • The coalescence of two underwater explosion bubbles is experimentally studied. • The numerical simulation reveals the mechanism of the bubble cloud formation. • Quantitative comparisons of the pressure impulse between different cases are made. • Multiple bubble pulse pressures are emitted and the last peak is the largest. [ABSTRACT FROM AUTHOR]

Abstract The bubble-sphere interaction beneath a free surface is investigated experimentally and numerically, which is associated with underwater explosion and cavitation. We use the electric discharge technique to generate an oscillating bubble that is set above a movable sphere and below a free surface. The transient fluid-structure interaction (FSI) is recorded by high-speed imaging. We identify three distinctive bubble jet impact patterns, i.e., (i) jet impacts on the sphere top with water layer between them; (ii) the bubble partly envelops the sphere at first and then the jet impacts on the sphere top without water layer; (iii) the jet impacts on an annular ring, splitting the bubble into a toroidal bubble and a new singly-connected bubble. Such transient FSI events are modeled by the boundary integral method and the foregoing bubble splitting is modeled by an improved vortex ring model. The bubble, free surface, and sphere dynamics in experiments are found to be captured extremely well by numerical simulations. The bubble dynamic behaviors are associated with three dimensionless parameters and a systematic study of these parameters are provided. Lastly, the two types of cavitation phenomena on sphere surface are discussed and the detailed physical mechanisms are analyzed. Highlights • The bubble-sphere interaction beneath a free surface is investigated experimentally and numerically. • We identify three distinctive bubble jet impact patterns, which are classified in a graph according to two parameters. • A full coupling model based on boundary integral method reproduces the experimental observations well. • An improved vortex ring model is established to study the splitting of a bubble into a torus and a singly-connected bubble. • Two types of cavitation phenomena on sphere surface during the rebounding phase of the bubble. [ABSTRACT FROM AUTHOR]

The underwater explosion (UNDEX) phenomenon involves hydrodynamic behaviors with a wide range of spatial scales, from macroscopic cavitation regions to refined areas with fluid-structure interactions around the shock wavefront. Correct description of the refined shock wavefront is important for determining the shock wave position and pressure peak. In this work, the local discontinuous Galerkin (LDG) method for the two-dimensional wave equation, which allows for the local triangular meshes refinement and merging during the shock wave propagation process, is presented to model the UNDEX shock hydrodynamics. This article is an extension of our previous work, where we discretize the UNDEX total wave formulation in the LDG framework and simulate the UNDEX shock wave and cavitation phenomenon. In order to save computational cost (including CPU time and computational storage) and capture the shock wavefront more accurately, the LDG method is extended to be in combination with the mesh adaption technique. The troubled-cell indicator, depending on the local jump of the pressure, is adopted to identify elements which require to be refined or coarsened. Typical numerical examples are tested to assess the capability of the present h -adaptive LDG method for capturing the UNDEX shock wave. The numerical results clearly demonstrate that the mesh adaption technique enables us to dynamically increase the mesh resolution in close proximity to the flow discontinuities with a large pressure jump. The local increase of the mesh resolution results in a substantial increase in the accuracy of the pressure peak. In terms of the computational efficiency, the h -adaptive LDG method can save nearly half of the calculation time in comparison to the non-adaptive LDG method on uniform meshes, whose mesh resolution is the same as that of the maximum level of refinement of the h -adaptive LDG method. • An h -adaptive LDG method is presented for simulating the UNDEX shock hydrodynamics. • The mesh resolution is adaptive with the evolution of the UNDEX shock wavefront. • The present h -adaptive LDG method can well capture the UNDEX pressure peak at a relative small computational cost. [ABSTRACT FROM AUTHOR]

Cavitation effects play a substantial role in the dynamic response of marine structures. In the previous numerical studies, it's assumed that the incident explosive loading is reflected by the horizontal free surface. But the cavitation phenomenon near the water wave has rarely been investigated. In this paper, we propose a novel 2D underwater explosion (UNDEX) model, which can be applied to study UNDEX cavitation characteristics near the water wave. On the basis of the local discontinuous Galerkin method, the 2D far-field UNDEX model is established to simulate the propagation of incident shock loading in fluid domain. In order to consider the water wave effects in the numerical model, the UNDEX model is combined with the nonlinear Stokes wave theory. The effects of Stokes wave pressure are introduced into the cavitation model, and the influences of the water wave profile on UNDEX loading characteristics are included in the present model. By comparing with an underwater explosion experiment, the present model is verified in simulating the shock wave propagation, and exhibits better properties than the acoustic finite element method. By means of the present model, the effects of the water wave phase angle and wave length on the cavitation characteristics are investigated. It's found that the cavitation duration of the region below wave crests is prolonged, while the cavitation duration of the region below wave troughs is shortened. The present model can be further extended to study the influence of irregular waves on the UNDEX loading characteristics. • Based on the LDG method and Stokes wave theory, the UNDEX cavitation characteristics near water wave are studied. • By comparing with the experimental result, the present LDG model is verified and exhibits better properties than the AFEM. • The curvature of the gravity wave surface is shown to play a profound role in UNDEX cavitation characteristics. • The cavitation phenomena near the gravity wave surface appear different scenarios with different wave lengths. [ABSTRACT FROM AUTHOR]

The damage effects of an underwater explosion have always been a crucial problem in the ship mechanics. Notably, the bubble evolution and the jet impact load are one of the most difficult parts in the shock-resistance design of ship structures due to the discontinuities and significant nonlinear deformation. In this paper, the Eulerian finite-element method is introduced to continuously simulate the shock wave and non-spherical bubble evolution stages near a horizontal solid wall with the volume of fluid method and pressure balance technique used to resolve the multi-medium flow. The numerical model is established in a cylindrical coordinate system and validated by comparing the results with a spark-generated bubble experiment. After that, based on the present model, the shock wave propagation and the bubble evolution are simulated to study the characteristics of the impact loads of an underwater explosion. Besides, the influences of the wall location (upside or downside) and the stand-off distance from the wall are also analyzed. The results show that the features of the jet impact load are much more complicated than those of the shock wave. Nearby a downside wall, the buoyancy and Bjerknes force compete to dominate the bubble motion with opposite influences. By contrast, They enhance the effect of each other to develop a liquid jet towards the upside wall. The pressure peak, impact range, and duration time nonlinearly depend on the combination of the case parameters and are not monotonic to a single one. Within a proper range of the parameter combination, the jet impact load can reach its maximum and be more destructive than the shock wave because of a comparable pressure peak and a much longer duration. [ABSTRACT FROM AUTHOR]

Understanding the dynamics of oscillating bubbles beneath a free surface is crucial to many practical applications including airgun-bubble clusters, underwater explosions, etc. In this paper, an experimental and numerical study of the dynamic behaviors of a coalesced bubble near a free surface is conducted, which shows quite different physical features from single bubble dynamics. Firstly, two similar sized underwater discharge bubbles are generated simultaneously beneath a free surface and their complex interactions are experimentally studied with high-speed photography imaging. A strong interaction between two bubbles and the subsequent coalescence are observed when the initial distance between two bubbles is smaller than the maximum equivalent bubble radius. Secondly, both axisymmetric and three-dimensional (3D) boundary integral models are used to simulate the pre-coalescence and post-coalescence of two bubbles. The results obtained by the two models agree well in axisymmetric conditions. The essential physical phenomena in representative experiments are well reproduced by the present 3D model. The pressure field is calculated by the auxiliary function method, which helps to reveal the underlying mechanisms of bubble collapse patterns and jetting behaviors. A parametric study reveals the dependence of the coalesced bubble dynamics and free surface motion on the governing dimensionless quantities. • The pre- and post-coalescence of two bubbles beneath a free surface are experimentally and numerically investigated. • The essential physical phenomena in several representative experiments are well reproduced by the present 3D BI model. • The dependence of the coalesced bubble dynamics and free surface motion on the governing dimensionless quantities is studied. • Compared with single bubble situations, a relatively weaker shock wave would be emitted by the collapsing coalesced bubble. [ABSTRACT FROM AUTHOR]

When an underwater collision or explosion happens to a ship, the water will rush into the cabin through the broken opening. The water spike induced by hydrostatic pressure has the potential to destroy the facilities and structures inside the cabin, and the water flooding may threat the vitality of ship. Dynamic characteristics of this water spike during early flooding process is studied by a three-dimensional fast multipole boundary element method (FMBEM) based on the potential theory, in this article. The edge swap operation is elaborated and adopted, to eliminate the slender elements at the air-water interface, which helps us study the evolution of the inrush water and maintains the computational efficiency. The numerical model is validated by experimental data and the result from the finite volume method. The flooding process can be divided into the developing flow stage and the stable flow stage. The flow rate increases gradually during the former stage and reaches a constant value in the latter one. Through parametric study, we find that the water flooded through the opening earlier is subjected to the gravity for longer time and achieves larger velocity, which results in a slender water spike. When the opening gets deeper, the developing flow stage becomes shorter and the flow rate increases; whilst the increasing speed slows down with the growing depth. It is the area of the opening rather than the shape, that influences the flow rate and flooding velocity, and the maximum velocity in the horizontal direction appears at the transition time between the two stages. This study reveals that the water flooding spike has complex and non-linear dynamic behaviour, and helps lay the foundation of studying the interaction between high-speed water jet and the structures. It also shows that the FMBEM is suitable for dealing with the large scale moving boundary problems efficiently and accurately. • The early stage of water spike flooding through an opening is studied by the FMBEM. • The edge swap operation is used to improve the mesh quality of air-water interface. • Dynamics of the water spike in developing and stable flow stages has been studied. [ABSTRACT FROM AUTHOR]

Dynamics of the underwater explosion (UNDEX) bubble in a free field is numerically investigated in the present paper using a compressible two-phase flow solver. The finite volume method (FVM) is adopted for discretization of the Navier-Stokes equations. The volume of fluid (VOF) method is utilized to capture the bubble-water interface. Validation is carried out against the Gilmore model for a spherical bubble and an experiment for the aspherical UNDEX bubble subjected to buoyancy. The bubble expansion, collapse, high-speed liquid jet and the rebounding are well predicted. Meanwhile, the propagating pressure waves can be clearly captured. The pressure and velocity fields within and surrounding the bubble are described in detail. For the UNDEX bubble subjected to strong buoyancy effect, the jet impacts on the opposite side in a small region rather than at a single point. Splitting of some tiny bubbles can be observed in the jet impact area. The toroidal bubble undergoes splitting and coalescence subsequently. Additionally, non-uniform distribution of the velocity of the gas in the bubble could be observed almost in the entire bubble life while the pressure field inside the bubble is quite uniform. Lastly, the jet dynamics as well as the migrating behaviors of the bubble under the effect of buoyancy is carefully investigated. [ABSTRACT FROM AUTHOR]

The present work develops an accurate and robust axisymmetric SPH method by introducing the Riemann solver into the framework of axisymmetric SPH. To reduce numerical dissipations caused by the intrinsic numerical viscosity of the Riemann solver, PVRS Riemann solver with MUSCL reconstruction is embedded into the scheme of the axisymmetric Riemann SPH. In addition, in order to maintain the uniformity of particle distributions, the volume adaptive scheme and the particle shifting technique are applied in this work. The advantage of the present axisymmetric Riemann SPH method is that it can consider the real compressibility of the air, which allows a larger stable time step in the simulation of the strongly-compressible flows. Through the three benchmark tests, including the Sod shock tube test, the Sedov point explosion test and the blast wave problem test, the accuracy of the present axisymmetric Riemann SPH method is verified. Then this method is applied to the simulations of some practical issues in ocean engineering, including the shockwave propagation of the underwater explosion, the water entry of the sphere and the coalescence of an oscillating bubble pair. • An accurate and robust axisymmetric Riemann-SPH method is developed by introducing the Riemann solver into the axisymmetric SPH. • Through the three basic cases, the accuracy and convergence of the present axisymmetric Riemann SPH method are verified. • The proposed SPH is used to simulate the underwater explosion, the water entry of a sphere and the coalescence of a bubble pair. [ABSTRACT FROM AUTHOR]

Abstract: In order to evaluate the strength and comparability of impulsive environment of model and practical structure in the water when subjected to underwater explosion, a new shock factor based on energy acting on the structure is presented to describe the loading of underwater explosion. To test the validity of this new factor, numerical experiments of double stiffened cylindrical shells are carried out a series of cases designed by the new factor and two other standard shock factors respectively. The results of the cases designed by the new factor indicate that the kinetic energy, potential energy and shock response spectrums of the structures agree well with each other in different cases designed by the equal new shock factor. However, the results of the cases designed by the two other standard shock factors are rather diverse. The analysis considers that the old shock factors do not take the spherical characteristics of shock wave front and relative position between detonation and structure into account, which can hardly reflect the similarity of underwater explosion loadings. The new shock factor can make up for such limitations. [Copyright &y& Elsevier]

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]