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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]

How to effectively reduce the high-frequency output caused by excessively steep initial peak slope and enhance the low-frequency output generated by bubble oscillation has become present research interest in seismic source design. The most effective way to improve the low-frequency content of a seismic source is to increase its chamber volume. However, the size of air-gun bubbles generated by large-volume air-gun sources has increased by several hundred times compared to traditional high-pressure air guns, which has made the migration phenomenon of bubbles no longer negligible. The previous air-gun bubble dynamics models did not comprehensively account for the effects caused by bubble migration phenomenon. In this paper, we have developed an air-gun bubble dynamics model based on unified equation for bubble dynamics, and the newly established model demonstrates a closer alignment with experimental data compared to models based on the Gilmore and Keller equations. Based on this, the influence of the design parameters of air-gun seismic source on the bubble migration is studied. It explores the ramifications of migration on the dynamic properties of air-gun bubbles and the signatures of seismic sources. Additionally, we examine how incoming flow velocity magnitude and air-gun design parameters influence the signatures of air-gun seismic sources. Finally, we investigate the impact of both the spacing between dual guns and the horizontal movement of bubbles caused by mutual attraction on the signatures of dual-gun sources. [ABSTRACT FROM AUTHOR]

The multi-medium fluid flow around a supersonic sea-skimming flight is featured by the detached/attached shock wave, separation shock wave, and the reflected wave from the free surface. The complex wave structure and high nonlinearity pose a great challenge in accurate and stable numerical simulation. In this paper, a numerical model based on the high-order Runge–Kutta discontinuous Galerkin method is established to resolve the above problem. Based on the fact that the dimensionless vertical velocity is small, the air–water interface is linearized and a modified flux scheme is proposed to simplify the treatment of the multi-medium problem. A block-based adaptive mesh refinement scheme is adopted to capture the complex wave structure with the new nodes projected on the curved boundary. Finally, the numerical simulation of supersonic sea-skimming flight of the National Advisory Committee for Aeronautics 0012 airfoil is carried out by using the above-mentioned simplified numerical model based on the scheme of partition solution. The results show that the model can perform high-resolution simulations for the shock wave structure in various scenes. Meanwhile, the Mach number and distance between the airfoil and free surface are important factors affecting the structural characteristics of the shock wave systems and the airfoil loading characteristics. When the reflected shock wave acts on the airfoil's lower boundary, there will be a positive moment effect to make the airfoil dive, and the occurrence of this dangerous scene should be avoided. The relevant conclusions obtained can provide a reference for further research and engineering design. [ABSTRACT FROM AUTHOR]

This paper presents an experimental study focused on the annular secondary cavitation caused by the interaction between a high-voltage spark bubble and a cylinder. A 2000 V high-voltage underwater electric discharge was used to create the bubble, which reached a maximum diameter of approximately 31 mm. High-speed photography was employed to capture the behavior of the spark bubble and the induced secondary cavitation bubbles. The formation and evolution of the annular secondary cavitation bubbles near the cylinder's edge were captured and analyzed. The study classified the morphology of the annular secondary cavitation bubbles into three different types based on various bubble distances and cylinder diameters. Notably, unique bubble morphologies, such as the terraced bubble shape, were identified, resulting from the coupling between the spark bubble, the annular secondary cavitation bubble, and the cylinder. The interaction between the annular secondary cavitation bubble and the spark bubble, including coalescence, and the resulting effects on bubble shape and period were investigated. The changes of secondary cavitation bubbles are compared when the cylinder has different chamfer angles. Moreover, the study examined the dynamic characteristics of the bubbles, including their shape evolution, jetting behavior, period length, and pressure pulses upon collapse, at various distances from the top-surface of cylinders with different diameters. The experiment also introduced flow visualization with dye into spark bubble experiments for the first time to trace the vortex around the annular secondary bubble. Additionally, the transparency of bubbles in the images was improved through multi-source lighting techniques. [ABSTRACT FROM AUTHOR]

The underwater vehicle is subjected to complex hydrodynamic loads during water-exit process, which seriously affect the structural strength and water-exit stability of the vehicle. This paper investigates the effect of high-pressure venting conditions on the dynamic evolution characteristics of the cavity during the completely free water-exit of a vehicle based on self-designed experiments. Some novel phenomena are found in the experiment, and the hypothesis of constant acceleration is established to explain the formation mechanism. The results reveal that the reentrant jet is the main factor influencing the pattern of cavity development and causes great differences between the partial and supercavity states. The balance between the initial cavity volume increase and the gas leakage rate results in the fact that increasing the launch Froude number in the partial cavity state does not cause significant changes in the cavity size. There is a stable interval between 0.0038 and 0.03 for the effect of gas entrainment coefficient on the development of the cavity. The influence of the launch Froude number on the cavity morphology varies within different gas entrainment coefficient ranges. Besides, six patterns of cavity closure are found for free water-exit conditions. The coupling closure pattern of reentrant jet and interaction vortex tube is the most stable during the water-exit process. The stable development intervals of cavity closure pattern and cavity morphology are roughly the same. The present study aims to provide a reference for the active venting flow control of the vehicle during water-exit. [ABSTRACT FROM AUTHOR]

The dynamics of an oscillating bubble near a liquid–liquid interface is a complex multiphase flow problem due to the highly nonlinear interaction, such as interface fragmentation and bubble tearing. When one of the liquid mediums is non-Newtonian, its constitution would significantly influence both the bubble motion and the interface evolution. In this study, a numerical model is established based on the Eulerian finite element method with the non-Newtonian fluid described by the Herschel–Bulkley model. The numerical model is validated by comparing with experimental results for a non-spherical pulsating bubble at a water–oil interface and the analytical solution for the laminar flow of non-Newtonian fluids in a circular tube. According to the simulation and analysis with different case parameters, our findings suggest that the non-Newtonian fluid forms a crater when squeezed by the bubble, and the downward jet can penetrate the bubble and further deepen the crater. As the distance parameter increases, the crater gradually disappears or even bulges. Furthermore, the yield shear stress can give non-Newtonian fluid plastic properties similar to a solid, effectively reducing the bubble's pulsation and jet load. Additionally, the flow behavior index n comes from the power-law model for non-Newtonian fluids and significantly impacts the jet's impact process. When n ≤ 1 , the crater is likelier to become funnel-shaped, whereas when n > 1, it is likelier to become bullet-head-shaped. In addition to enhancing the bubble's nonsphericity, the reduction in Reynolds number also weakens the crimp deformation of the interface. When the distance parameter is zero, the larger the buoyancy parameter and the less deformable the non-Newtonian fluid, the easier the bubble to split by the annular jet. [ABSTRACT FROM AUTHOR]

In the rapid flooding process of a damaged ship, the air trapped in a damaged cabin will be compressed into an air cushion, which causes the air cushion effect (ACE). The ACE has a significant influence on the flooding process of an airtight cabin. In this paper, a three-cabin model is designed according to a parent ship, and a series of model experiments are carried out. First, the air-tightness ratio is defined by combining various air vents with different opening areas, and the flooding model experiments of different air-tightness ratios are carried out. The heeling and trimming angles of the model, the overpressure of the air cushion, and the water height inside the flooding cabin are recorded and analyzed, and the characteristics of ACE are summarized. Second, different forms of air vents with a same air-tightness ratio are designed, and the influence of the air vent distribution on the flooding process is analyzed. With the quasi-static method used for comparisons, the numerical results are compared with the experimental ones to check the effectiveness of the quasi-static method on the rapid flooding problems. The research on ACE can guide the design of ship subdivisions and provide a reference for the rescue of shipwreck accidents. [ABSTRACT FROM AUTHOR]

Bubble pulsation is a characteristic multiphase compressible flow, which involves periodic oscillation and strong pressure wave and is vulnerable to boundary conditions. The smoothed particle hydrodynamics (SPH) has limitations in imposing the fluid boundary suitable for such problems, which have been verified first with the state-of-the-art SPH boundaries. It brings challenges to the three-dimensional modeling. Then, we propose to combine SPH with the finite volume method via the spatial coupling to deal with this problem. The accuracy of the coupled method has been validated by comparisons with other numerical methods and the theoretical equation from the spherical pulsation to the more complex bubble oscillations. Good agreements are obtained in terms of the bubble radius and the pulse pressure peak. The conclusions drawn in this work and the computational framework lay the foundation for the further complicated study on the bubble dynamics, the complete process of underwater explosion, and the related fluid–structure interaction problems. [ABSTRACT FROM AUTHOR]

Particle propulsion by an attached acoustic cavitation bubble under strong ultrasonic wave excitation occupies the core of many applications, including ultrasonic cleaning, ultrasonography, targeted therapy, and microbubble motors. However, the driving capacity and mode of bubbles in the field of ultrasonics are far from being well understood, which severely limits its applicability in a variety of fields. In this study, a fluid–structure interaction model based on the boundary integral method is proposed to simulate complex interactions between a suspended spherical particle and an attached cavitation bubble. A one-to-one comparison between the numerical results and experimental data demonstrates the distinct advantage of our model over conventional approaches. Thereafter, we systematically investigate the dependence of bubble–particle interactions on the governing parameters, including the amplitude and phase of the ultrasonic wave, particle density, and particle-to-bubble size ratio. We also document different types of bubble dynamic behaviors under various governing parameters. Finally, we obtain scaling laws for the maximum displacement of the particle with respect to the governing parameters. [ABSTRACT FROM AUTHOR]

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 paper aims at presenting a general-purpose-oriented and fully parallelized meshless framework to simulate complex Fluid–Structure Interaction (FSI) problems in ocean engineering. In this framework, a Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) solver is combined with several advanced pre- and post-processing techniques. Based on the framework, we have been developing our in-house WCSPH-FSI package named SPHydro for solving hydrodynamic problems involving complex FSI processes in an accurate, efficient, and convenient manner. Three benchmarks are performed to qualitatively and quantitatively validate the accuracy and convergence of SPHydro. In addition, several practical applications are also provided to further highlight the generality and applicability of SPHydro in ocean engineering simulations. It is demonstrated that SPHydro holds satisfactory performance in solving complex FSI problems in ocean engineering and that the present framework can be further developed to tackle more complex FSI problems for general engineering applications due to its high flexibility and extensibility. [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]

We report on an experimental study of the trajectories of truncated cone projectiles on water entry. The water entry trajectory stability is of great significance to the motion control of projectile. In this paper, the truncated cone nose shape can be described by the area of the leading plane and the cone angle α. Two high-speed cameras are used to capture the trajectories of the projectiles and the initial stage of cavity dynamics. We reveal that the trajectory stability of a projectile is highly dependent on the wetted surface of the nose, which is determined by the location of the separation line between the surfaces of the cavity and body. The increase in the leading plane area is beneficial to the formation of a stable trajectory, in which only the leading plane is wetted. In an unstable trajectory case, the large hydrodynamic moment from the wetted surface on the side of the nose causes a significant rotation of the projectile. However, for the projectile with the cone angle α ≳ 60 ° , though the side of the nose is fully wetted, the trajectory of the projectile turns into stable again. Results show that the attitude deflection of the projectile is determined by the cone angle of the nose. It is also found that the attitude deflection results in an irregular cavity, which further aggravates the rotation of the projectile. We quantify the relationship between the trajectory stability and two nose parameters systematically, and a phase diagram is obtained for a large parameter space. The findings in this work can be used as a reference for future designs to ensure stable trajectories on water entry. [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]

The dynamics of a buoyant pulsating bubble near two crossed perpendicular rigid boundaries (a horizontal and a vertical wall) are studied using the boundary element method combined with the method of mirror images. The Kelvin impulse and the elastic mesh velocity method are used to calculate the direction and volume of the liquid jet generated during bubble collapse. The numerical results show good agreement with experiments. An increase in buoyancy causes a local high-pressure zone at the root of the jet to move toward the bottom of the bubble, causing the jet to rotate upward toward the vertical wall. At a certain position, with the change in buoyancy, the dimensionless bubble volume at the instant of jet impact reaches a minimum when the jet direction is horizontal, with a peak in the dimensionless jet velocity occurring. A comprehensive parametric study of jet characteristics, including jet direction, velocity, and relative volume (the volume ratio of the jet to the bubble at the instant of jet impact), is carried out in terms of buoyancy and the standoff distances to the two walls. The Blake criterion can be used to judge whether a bubble jet is pointing obliquely upward or downward, provided that it deviates significantly from the horizontal direction. Depending on the buoyancy, the jet characteristics at different standoff distances are found to exhibit three distinct patterns of behavior. Finally, we discuss the changes in the jet velocity and relative volume as the buoyancy is varied. [ABSTRACT FROM AUTHOR]

Interaction between a two-phase fluid and a structure involving contact line dynamics is a common phenomenon. In this paper, we aim to develop a fluid–solid coupling model that can study contact line dynamics in the case of a high density ratio between the two fluids. The fluids are treated using a multiphase lattice Boltzmann flux solver (MLBFS) that uses the cell-centered finite volume method to obtain macroscopic flow variables, and the interface fluxes are reconstructed locally by the standard lattice Boltzmann method (LBM) solutions. This approach retains the advantages of the original LBM while being more flexible in handling nonuniform grids and external force terms. The immersed boundary method (IBM) is an effective method for processing structural information, and here, the implicit boundary-condition-enforced IBM is used to accurately satisfy the Dirichlet boundary condition (no-slip boundary). Moreover, the Neumann boundary condition is deemed to represent the contribution from the structure boundary flux and is incorporated into the IB-MLBFS. The developed IB-MLBFS is verified by several test cases, including contact line motion of a two-phase fluid along a circular cylinder and droplet spreading on a flat plate, where both equilibrium results and dynamic process are correctly reproduced for different density ratios and wettability conditions. Furthermore, based on the IB-MLBFS established here, the contact line dynamics of a two-phase fluid between two square cylinders or two circular cylinders is studied. The effects of distance, structure size, and wettability on the interface state and the contact angle are studied in detail. The robustness of the proposed model is verified. [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]

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]

During the process of wave slamming on a structure with sharp corners, the wave receding after wave impingement can induce strong negative pressure (relative to the atmospheric pressure) at the bottom of the structure, which is called the suction effect. From the practical point of view, the suction force induced by the negative pressure, coinciding with the gravity force, pulls the structure down and hence increases the risk of structural damage. In this work, the smoothed particle hydrodynamics (SPH) method, more specifically the δ+SPH model, is adopted to simulate the freak wave slamming on a fixed platform with the consideration of the suction effect, i.e., negative pressure, which is a challenging issue because it can cause the so-called tensile instability in SPH simulations. The key to overcome the numerical issue is to use a numerical technique named tensile instability control (TIC). Comparative studies using SPH models with and without TIC will show the importance of this technique in capturing the negative pressure. It is also found that using a two-phase simulation that takes the air phase into account is essential for an SPH model to accurately predict the impact pressure during the initial slamming stage. The freak wave impacts with different water depths are studied. All the multiphase SPH results are validated by our experimental data. The wave kinematics/dynamics and wave impact features in the wave-structure interacting process are discussed, and the mechanism of the suction effect characterized by the negative pressure is carefully analyzed. [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]

Nonlinear interaction and coalescence features of oscillating bubble pairs are investigated experimentally and numerically. The spark technique is used to generate in-phase bubble pairs with similar size and the simulation is performed with the compressible volume of fluid (VOF) solver in OpenFOAM. The initial conditions for the simulation are determined from the reference case, where the interbubble distance is sufficiently large and the spherical shape is maintained at the moment of maximum volume. Although the microscopic details of the coalescing behaviors are not focused, the compressible VOF solver reproduces the important features of the experiment and shows good grid convergence. We systematically investigate the effects of the dimensionless interbubble distance γ (scaled by the maximum bubble radius) and define three different coalescing patterns, namely, coalescence due to the expansion in the first cycle for γ < 1.1 (Pattern I), bubble breaking up and collapsing together with coalescence at the initial rebounding stage for 1.1 < γ < 2.0 (Pattern II), and coalescence of the rebounding toroidal bubbles for 2.0 < γ < 3.65 (Pattern III). For Pattern I, prominent gas flow and velocity fluctuation can be observed in the coalescing region, which may induce the annular protrusion in the middle of the coalesced bubble. For Patterns II and III, migration of the bubbles toward each other during the collapsing and rebounding stages greatly facilitates the bubble coalescence. [ABSTRACT FROM AUTHOR]

The dynamics of a bubble bypassing or passing between spherical obstacles, which is associated with many industrial applications, is investigated numerically. A gas–liquid–solid interaction model is established by combining the lattice Boltzmann method and the immersed boundary method. The deformation and the surface velocity of the bubble, as well as the streamlines of the flow field, are studied as the bubble bypasses a single spherical obstacle or passes between a pair of such obstacles. It is found that for the case of a single sphere, the rise velocity reaches a minimum value at the moment at which an annular bubble forms and the whole sphere is enveloped by the bubble. The initial distance between the bubble and the sphere, as well as the ratio of their sizes, has distinct influences on bubble shape and rise velocity. For a pair of spherical obstacles, the rise velocity of the bubble reaches a minimum value twice as the bubble rises between the obstacles. The distance between the two obstacles has a stronger influence on bubble motion than does their size, although when the two obstacles are of different sizes, the bubble will deviate toward the smaller one. [ABSTRACT FROM AUTHOR]

The Boundary Integral Method (BIM) has been widely and successfully applied to cavitation bubble dynamics; however, the physical complexities involved in the coalescence of multiple bubbles are still challenging for numerical modeling. In this study, an improved three-dimensional (3D) BIM model is developed to simulate the coalescence of multiple cavitation bubbles near a rigid wall, including an extreme situation when cavitation bubbles are in contact with the rigid wall. As the first highlight of the present model, a universal topological treatment for arbitrary coalescence is proposed for 3D cases, combined with a density potential method and an adaptive remesh scheme to maintain a stable and high-accuracy calculation. Modeling for the multiple bubbles attached to the rigid boundary is the second challenging task of the present study. The effects of the rigid wall are modeled using the method of image; thus, the boundary value problem is transformed to the coalescence of real bubbles and their images across the boundary. Additionally, the numerical difficulties associated with the splitting of a toroidal bubble and self-coalescence due to the self-film-thinning process of a coalesced bubble are successfully overcome. The present 3D model is verified through convergence studies and further validated by the purposely conducted experiments. Finally, representative simulations are carried out to elucidate the main features of a coalesced bubble near a rigid boundary and the flow fields are provided to reveal the underlying physical mechanisms. [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]

The growth and departure of bubbles from an orifice and their interactions is a common phenomenon. In this paper, a multiphase flow model based on the lattice Boltzmann method is constructed to study this process, with an improved interface capture method being adopted to deal with the high density ratio between liquid and gas. A virtual layer is added outside the computational domain to handle the boundary condition at the orifice. The processes of bubble formation and interaction are well simulated by the model, and the results agree well with those of theoretical calculations for single-bubble formation and departure diameter and period. Bubble formation is controlled by the inertial force of the gas, buoyancy, surface tension, and the viscous force of the liquid. The inertial force of the gas and buoyancy promote bubble growth and departure, respectively, while the surface tension controls bubble deformation and the viscous force affects the necking process. Increases in both the orifice size and the gas outflow velocity can enlarge the departure diameter of the bubble, but the orifice size plays a more important role here. Both of these two parameters have obvious effects on the departure period. For the interaction of bubbles growing from orifices with the same or different sizes, different coalescence categories are distinguished according to the stage of coalescence, and the characteristics of the coalescence process are considered in terms of their dependence on surface tension, viscous force, and buoyancy. Finally, the departure diameter and departure period of coalesced bubbles are studied under the different coalescence conditions. [ABSTRACT FROM AUTHOR]

A high-speed liquid jet is commonly observed during the collapse phase of a cavitation bubble. In this letter, we present a surprising counter-jet (directed away from the nearby boundary) that forms in the early expansion phase of the bubble near a curved elastic boundary, which has not been reported before. The boundary integral simulation reveals the most possible mechanism as follows: First, the expansion of the bubble causes a local concave deformation on the boundary. Thereafter, the bubble partly envelops the curved elastic boundary, leading to the confinement of some liquid in a local dent. During the deformation recovery, a localised high pressure region is built up within the narrow dent, which drives a thin liquid jet away from the boundary. [ABSTRACT FROM AUTHOR]

This paper is concerned with the surface stability of a bubble in a liquid, fully covered by an elastic solid, which is common in natural and engineering applications. A theoretical model is described for the phenomenon, assuming that the bubble gas undergoes a polytropic process, the flow is irrotational, and the variation of the liquid volume is proportionally related to the liquid pressure. The boundary valued problem is modeled using the perturbation method via the Legendre polynomials, and the evolution equations for radial and shape oscillations of a confined bubble are formulated. We derive an explicit analytical expression for the natural frequency of shape modes for a confined bubble. The analyses lead to interesting conclusions including: the natural frequency of shape mode increases due to the confinement only if the cavity dimension is within 2-3 bubble radii, for which the shape oscillation of a bubble is always stable and damps with time; as the cavity dimension is 10 times larger than the bubble radius, the natural frequency for radial oscillation is significantly larger, while the natural frequency for shape mode remains the same as that for an unconfined bubble. An unconfined bubble experiences shape mode oscillation under the Mathieu relation. By contrast, shape mode resonance of confined bubbles occurs only when both the radial resonance condition and the Mathieu relation are satisfied, which is associated with a much larger driving frequency of ultrasound. [ABSTRACT FROM AUTHOR]

This study aims to elucidate the complex interaction between a suspended particle and an attached bubble, which is associated with cavitation in silt-laden flow. Systematic experiments are performed with high-speed photography, in which bubbles are generated by underwater electric discharge means. The bubble-particle interactions are found to be strongly dependent on two dimensionless parameters, i.e., the particle-bubble size ratio λL and the particle-liquid density ratio λρ. When λρ equals 2.61, the bubble split phenomenon is universally observed and the particle shooting effect (the particle acceleration during bubble expansion and after bubble-particle detachment) becomes more obvious as λL decreases. If λL < ∼0.34, the particle velocity keeps positive (away from the bubble), otherwise the particle velocity drops below zero (toward the bubble) during the bubble collapse phase. As λρ increases, the particle achieves a lower velocity but a higher impulse, and the bubble necking phenomenon is more pronounced. Our boundary integral simulations reproduce the experiments extremely well, including the particle dynamics, the bubble wrapping the particle, the bubble necking and detachment, and the mushroom-shaped bubble. After the bubble-particle detachment, the liquid around the detachment location is drawn inward and collides on the axis of symmetry, leading to the formation of a localized high pressure region between the bubble and the particle, which accelerates the particle for the second time even in the bubble collapse phase. [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]

Using molecular dynamics simulations, the effects of gas concentration and species on the coalescence and growth of nanobubbles were systematically investigated. With increasing gas concentration, not only surface nanobubbles but also bulk nanobubbles are formed. The bulk nanobubble in water is less explored so far. Here, its coalescence, stability, movement trajectory and velocity are discussed. A comparison of the motion and coalescence of the bulk nanobubble to the surface nanobubble, directly demonstrates that the three-phase contact line plays a crucial role for surface nanobubble stability. Compared with the bubble size, the distance between surface nanobubbles is a more important factor to decide the merging order among three nanobubbles. The study also shows that three factors including the oversaturated gas concentration, the distance between surface nanobubbles, and the stronger solid-gas interactions influence the formation of the gas-enrichment layer at the solid-liquid interface. The result has an important significance to enhancing the boundary slip due to the presence of nanobubbles. [ABSTRACT FROM AUTHOR]