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The process of a damaged ship flooding is a complicated free surface flow problem. There is a complex coupling effect between the ship cabin and the flow inside and outside of the cabin. In this paper, a GPU (graphic processing unit)- δ + -SPH (smoothed particle hydrodynamics) numerical model for the cabin flooding in deep-water environments is developed based on GPU parallel acceleration technology and Nvidia's CUDA (compute unified device architecture). First, the computational accuracy and efficiency of this numerical model are verified by experiments results on the water flooding of a simple damaged cabin model. Furthermore, the flooding characteristics of a submarine cabin are analyzed, considering different numbers of damaged cabins, depths, and opening positions. Finally, the progressive flooding and the dynamic response characteristics of a full-scale submarine model are investigated. The results show that the process of progressive flooding in a submarine cabin is characterized by its rapidity and intensity. Different factors, for example, damaged cabin numbers, cabin depths, and opening positions, have great influences on the process of flooding and the motion of the submarine cabin. This study can offer valuable technical assistance in the post-damage remediation process. [ABSTRACT FROM AUTHOR]

High-speed water entry is a transient hydrodynamic process that is accompanied by strongly compressible flow, free surface splash, cavity evolution and other nonlinear hydrodynamic phenomena. To address these problems, a novel fluid–structure interaction (FSI) scheme based on the immersed boundary method is proposed which is suitable for strongly compressible multiphase flows. In this scheme, considering the multiphase interfaces at the immersed boundary, an improved immersed boundary method for effectively suppressing the non-physical force oscillation is proposed. Additionally, a quaternion-based six degrees of freedom motion system is used to describe rigid body motion, and the multiphase flow Eulerian finite element method is applied as the fluid solver. Using analytical solutions, experimental data and literature data, the accuracy and robustness of the FSI scheme are validated. Finally, the high-speed water entry of the slender body with different noses is investigated, and the hydrodynamic loads including the axial and normal drag forces and the bending moment are extensively discussed. The hydrodynamic load and motion trajectory are determined by the nose configuration. The tail slamming phenomenon is the primary focus, and it is revealed that its formation is primarily related to the pitch moment formed at the stage of crossing the free surface. Tail slamming also causes violent impact loads, especially bending moments, which may cause slender projectiles to break off. Finally, to combine the features of the flat and hemispherical noses, the water entry of the projectile with a truncated hemispherical nose is simulated and discussed. [ABSTRACT FROM AUTHOR]

High-pressure bubble dynamics often involves many complex issues, including large deformations and inhomogeneities, strong compression, moving interfaces, and large discontinuities, that bring challenges to numerical simulations. In this work, an axisymmetric Riemann–smoothed particle hydrodynamics (SPH) method is used to simulate high-pressure bubbles near different boundaries. This Riemann–SPH can adopt the real sound speed instead of the artificial one for the air phase in the bubble. Therefore, the real compressibility of the air phase can be considered, and the corresponding time step is significantly increased. To avoid unphysical interface penetration and maintain relatively homogeneous particle distribution, a new and simple particle shifting scheme for multiphase flows is proposed. Additionally, to minimize the influence of the unphysical boundary on the bubble, a large fluid domain with an optimized initial particle distribution is adopted to reduce the particle number. Several high-pressure bubbles under different boundary conditions are considered, including in a free field, near a free surface, near a solid boundary, and near a rigid sphere. Numerical results show that these bubble dynamic behaviors can be reproduced with satisfactory accuracy. [ABSTRACT FROM AUTHOR]

Solid object water entry is a common problem in various natural, industrial and military applications, which involves large deformation of free surfaces and violent fluid–structure interactions. In computational fluid dynamics (CFD), this is a type of problem that tests the robustness and capacity of any CFD numerical algorithm. In this work, the newly-developed updated Lagrangian particle hydrodynamics (ULPH) method, which is a fluid version of peridynamics, is enhanced and applied to simulate solid object water entry problems. ULPH method is Lagrangian meshfree particle method that can ensure the specific free surface conditions automatically satisfied. The density filter and artificial viscosity diffusion are adopted in the ULPH scheme to stabilize and smooth the pressure field. In the process of a rigid body entering water, it may induce negative pressure in some areas of impact region, which can cause spurious tensile instability in some meshfree particle simulations, such as SPH and ULPH. A tensile instability control technique based on the ULPH framework has been developed to overcome the numerical instability. To validate the stability and accuracy of the ULPH approach in simulating water entry problems, several 2D and 3D examples of water entry have been carried out in this work. The necking and cavity pinch-off phenomena are visible in the numerical results. The simulation results of the ULPH method are well compared with experimental data and other numerical solutions. The water crown, cavity shapes and stream pattern formed around the rigid body entering the water can be well captured. The computation results show that the ULPH method has the ability to simulate the complex solid object water entry precess accurately. [ABSTRACT FROM AUTHOR]

In this paper, we establish a fluid-structure interaction (FSI) model to investigate the dynamic interactions between the underwater explosion (UNDEX) shock wave and a movable sphere near the free surface. We utilize the local discontinuous Galerkin (LDG) method to capture the propagation of the shock wave in the fluid domain and employ the pressure cutoff model to calculate cavitation effects. The fluid elements at the fluid-structure interface are directly coupled to the structural dynamic model, and the structural transient dynamic responses are coupled with fluid acoustic pressure at the fluid-structure interface in the governing equation. The validity of the present FSI model is verified by comparing with the continuous Galerkin method. Due to the advantage of the LDG method in capturing the discontinuous wave, the present model shows better properties than the traditional coupled acoustic-structural model. With the present FSI model, we investigate the interaction between the UNDEX shock wave and a submerged and floated sphere. Under the combined effects of the free surface and structure, the UNDEX shock and cavitation loading characteristics are analyzed, and the influences of complicated cavitation effects on dynamic responses of the sphere are discussed. [ABSTRACT FROM AUTHOR]

The strong bubble interactions and bursting behaviors near a free surface are studied numerically with a compressible two-phase flow solver. The interface is captured by the volume of fluid method. We investigate the effects of the dimensionless distance between the bubble and the free surface γf (scaled by the maximum bubble radius) ranging from 0.25 to 1.5. For the nonbursting cases, the essential evolution of the toroidal bubble is well captured, including the splitting, coalescence, and recollapse. Generally, a relatively thin spike is generated at the free surface during the first cycle of the bubble. Subsequently, a wider secondary spike at the base of the first spike is formed during the second bubble cycle, which leads to the formation of the crown-shaped spike. When γf is sufficiently small, the bubble bursts at the free surface and an opening cavity is generated. The pressure inside the cavity and the atmospheric pressure are not balanced immediately, and the pressure difference lasts for a while, causing the inward gas flow and the final closure of the cavity. The gas flow is found to play a vital role in the bubble bursting behaviors, which has not been well understood. By comparing with previous studies, three distinct bursting patterns are identified and discussed. [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]

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]

This paper presents an improved particle shifting technology (IPST) for smoothed particle hydrodynamics (SPH). It allows particles in the vicinity of the free-surface to be shifted in all the directions in case they are not uniformly distributed, rather than just shifted tangentially to the free-surface in some conventional particle shifting technologies. Therefore, with the new technique, the imprecise shifting due to the inaccurate evaluations of the local normal and tangential vectors of the free-surface can be avoided, and a more uniform particle distribution near the free-surface can be obtained even for long-term simulations, which improves the accuracy and stability of the SPH method. Besides, by combining the advantages of two existing free-surface detection methods, an optimized detection approach is provided. It is capable of detecting the free-surface particles accurately, and meanwhile, it is easier to implement and requires lower computational costs, especially for three-dimensional problems. Several numerical tests show that the proposed IPST and the optimized free-surface detection method are robust and accurate for the simulation of a variety of free-surface flows. • An improved particle shifting technology (IPST) in the SPH method is proposed. • An optimized free-surface detection method in SPH is introduced. • The accuracy and robustness of the proposed IPST is validated on several long-term simulations. [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]

The explosion near a free surface is a complex multiphase flow problem involving large deformation and even fragmentation of the fluid interface. Experiments and numerical simulations are presented to investigate the transient fluid dynamics of explosions approaching the free surface from the air and water sides. The numerical model is established based on the Eulerian finite element method and the Volume of Fluid method. The explosion experiments are conducted in a water tank. We classify the problem into cavities and bubbles according to whether the explosive is exposed to the air. Explosions above the free surface generate hemispherical cavities that evolve into W-shaped ones after an upward jet develops from the bottom. The hemispherical cavity will close if the explosion is close enough to the free surface. The simulations reveal that the distance parameter dominates the bubble's bursting and that the explosive equivalent and distance parameter compete to determine the cavity's closure. In addition, the impact pressure characteristics generated by the explosion near the free surface are also analyzed. • An axisymmetric Eulerian FEM model is presented to investigate the explosion near the free surface. • Explosion experiments with different standoff distances from the free surface are carried out. • The factors influencing cavity closure and bubble bursting are analyzed. • The impact pressure characteristics generated by the explosion near the free surface are analyzed. [ABSTRACT FROM AUTHOR]

In some sea areas, the rising storm of bubbles including the release of large-scale methane gas and eruption of submarine volcanoes will pose a potential threat to the safety of ships. In the former case, a large amount of rising methane gas may generate some large-scale bubbles which may cause sailing ships to capsize. When the size of the bubble is close to the characteristic length of the ship, one single bubble could sink a ship. For the latter, the initial radii of the bubbles formed by the eruption of shallow seafloor volcanoes maybe tens even hundreds of meters, which also largely increases the risk of maritime transportation. In this paper, a 2D smoothed particle hydrodynamics (SPH) model is used to investigate the interaction between a ship and large-scale bubbles. Firstly, the adopted SPH model is validated by comparing with other numerical results. Then, the coupling interaction between a bubble and free-surface is simulated. Finally, under different conditions of different bubble sizes, bubble depths and horizontal distances, interactions between a ship and one or two large-scale rising bubbles are simulated and discussed, aiming to provide a reference for the investigation of ship capsizing caused by large-scale rising bubbles. • The dynamics behaviors of a rising bubble near free surface are obtained. • The interactions of rising bubbles with a ship in different conditions are presented. • The responses of ship capsizing induced by large-scale rising bubbles are revealed. [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]

• A robust WCSPH model is applied to deal with the water entry of the bow-flare ship section. • The evolution laws of the free surface and spry jet are analyzed. • The water entry of a three dimensional ship hull is simulated. In the marine and ocean engineering area, the water-entry process is a typical problem of fluid-solid interaction, which involves complex phenomenon such as the large deformation of free surface and considerable structure movement. In this process, the predicting impact load and summarizing the evolution law of the free surface deformation have important reference significance for the hull structure design. To address this issue, numerical simulations are carried out using a robust Smoothed Particle Hydrodynamics (SPH) model. The accuracy of the present SPH model is firstly validated by simulating the water entry of bow-flare section in two and three dimensions, respectively. Then, we investigate the variation characteristics of impact load and the evolution of free surface during the entry of the bow-flare ship section with different roll angles (θ = 0 ∘ ∼ 20. 3 ∘ ). Attention is focused on the flow separating phenomenon and the spray jet on the free surface. Finally, the water entry of a three dimensional ship hull is simulated. The velocity and pressure of flow field are analyzed and some conclusions are drawn. [ABSTRACT FROM AUTHOR]