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Numerical simulation for fluid flow over an attached rigid body with a deformable ring bubble is analyzed based on the velocity potential theory together with the boundary element method (BEM). The analysis is focused on the axisymmetric case. The bubble surface is treated as a well defined air-liquid interface and is tracked by a mixed Eulerian-Lagrangian method. The points of intersection between the bubble and body are treated, specially in the numerical procedure. The auxiliary function method is adopted to calculate the pressure on the body surface and in the flow field. The convergence study is undertaken to assess the developed numerical method and the computation code. Some case studies are undertaken in which the interactions between the bubble/body and the incoming flow field are simulated. The effects of various physical parameters on the interactions are investigated.

The motion of gas bubbles beneath a free surface will lead to a spike of fluid on the free surface. The distance of the bubbles to the free surface is the key factor to different phenomena. When the inception distance varies in some range, crown phenomenon would happen after the impact of weak buoyancy bubbles, so this kind of spike is defined as crown spike in the present paper. Based on potential flow theory, a three-dimensional numerical model is established to simulate the motion of the free-surface spike generated by one bubble or a horizontal line of two in-phase bubbles. After the downward jet formed near the end of the collapse phase, the simulation of the free surface is performed to study the crown spike without regard to the toroidal bubble's effect. Calculations about the interaction between one bubble and free surface agree well with the experimental results conducted with a high-speed camera, and relative error is within 15%. Crown spike in both single- and two-bubble cases are simulated numerically. Different features and laws of the motion of crown spike, depending on the bubble-boundary distances and the inter-bubble distances, have been investigated.

Some numerical studies were carried out on micrometer-sized rising bubble bouncing near a rigid boundary. Taking surface tension into consideration, the bubble motion could be solved using the potential flow theory. A correction should be made in Bernoulli equation because the pressure gradient was caused by the viscosity between the bubble and the wall. The numerical result agree well with the experimental data. Based on the fundamental phenomenon, we have studied the influence of characteristic parameter on bubble bouncing behavior, and the balanced shape due to the action of the wall. With the increase of the rising distance of the bubble, the distance of the bubble bouncing downward and the period of bouncing would increase. However, they would not change obviously when the rising distance is large enough. Surface tension has great effect on the dynamic behavior of the bubble. The bouncing period decreases when surface tension becomes large, but the bouncing distance will have an increase before it gradually decreases. Finally, the balanced shape of the bubble due to the wall effect can be mainly controlled by buoyance parameter and the Weber number.

The study of far-field pressure wavelet of air-gun bubble is the basic research of air-gun sources. In this paper, a boundary element bubble model is established to simulate the dynamics of bubble, and an energy equivalent method is put forward to solve the bottleneck of bubble jet. In our simplified model, the bubble model takes into consideration the thermodynamic factors such as heat transfer and gas release, and the numerical results agree with the data of Nucleus software well. Based on the established model, the influence of heat transfer coefficient, air-gun firing time, and specific heat at constant volume on the pressure wavelet are studied. Finally, the three-dimensional bubble merging numerical method is put forward, which is an expansion of the axisymmetric model. Thus, the preliminary study of coherent air-gun is conducted, especially the influence of the space between two bubbles on the wavelet. This paper provides a reference for the research of air-gun.

A gas-liquid-solid three-phase coupling dynamic model is established using lattice Boltzmann method (LBM). Interaction between rising bubble and complex solid walls at the same scale is studied. Firstly, based on the viscous fluid theory, a group of lattice Boltzmann equations are developed to describe the gas-liquid two-phase campaign by considering the viscosity, surface tension, and gravity in the form of a LB discrete body force. At the same time, combined with the finite difference scheme, the half-way bounce back model in LBM is adopted to deal with the solid boundary condition. Then, under the conditions of different feature size ratios, the coupling characteristics between bubbles and plane wall, taking into consideration the effect of boundaries and curved wall, are studied using the newly built model. Results show that both the solid wall condition and the feature size ratio have significant nonlinear effects on bubble movement and topology changes. Finally, the effect of fluid properties on the coupling regularity of bubbles and complex walls is researched.

This study focuses on the dynamic behavior of rising bubble in water with taking surface tension and viscous effect into consideration. The Young-Laplace equation is adopted to obtain the viscous component of the normal stress, and the tangential component is evaluated by viscous correction pressure, which is based on viscous dissipation energy equivalence principle. Firstly, both axi-symmetric and three-dimensional model is established by employing boundary integral method. The validation of our model is confirmed by comparing the analytical results with the experimental results, and they are in good agreement with each other. Secondly, the shape and balanced velocity of millimetre-sized bubble are studied, and the influences of initial condition, surface tension and viscosity on the dynamic behaviour of the bubble are also discussed. Finally a numerical technic is put forward to handle the coalescence of two rising bubbles, which can show some detailed information about the coalescence process.

Strong interaction between bubble and free-surface will cause complex phenomena, producing many different types of spike. Based on potential flow theory, a numerical model was established to simulate the crown spike. A downward jet was formed during the bubble’s collapsing, and simulation of the free-surface was continued regard less of the ring bubble’s effect on it. Simulation results show good agreement with the experiment conducted with a high speed camera and a spark-generated device, and the relative error was less than 10%. Some special phenomena were found through numerical calculation, such as apron-shrink and peak-dropped. Finally, the effects of initial condition and Weber number on crown-type water column were studied.

Traditional studies on bubble dynamics near solid boundaries mainly focus on its pulsation and jet features near a full plate. A hole will be formed when a warship is attacked by an underwater weapon and it may be subjected to a subsequent attack generated by charge explosion. And the hole on the plate would affect the blow effect of the underwater explosion bubble nearby. To study the bubble pulsation and jet features near a plate with a hole in the middle, a series of experiments is carried out using a spark bubble generator and high-speed camera. We find that when a bubble is generated homocentricly near the hole, cavity-attraction effect of the bubble will be formed due to the effect of the hole, and the opposite-jets can then be formed. Then the influences of dimensionless standoff distance and hole size are analyzed. Finally, the dynamic behavior of a bubble which is generated decenteredly near the hole is studied to show that the blow effect of a bubble increases with decentered position increasing.

In this work the bubble dynamics near a plate with circular hole is investigated. Numerical model for bubble dynamics is established based on incompressible potential theory. To overcome the numerical limitation of traditional boundary element method for the case with small initial distance between bubble and the edge of hole, the fluid domain is divided into two semi-infinite domains which are solved separately by fusing the bubble wall and the plate wall together, by which numerical simulation in various parameter ranges is implemented. The numerical results match the experimental ones well. Through the analysis of bubble dynamics near circular hole, we find that the influence of hole is opposite to that of solid wall. During the expansion phase, cavity-attraction effect is exerted on the bubble, while the bubble is pushed away during the collapsing phase. In some specific cases, opposite-jets are formed under the conjunction of solid plate and circular hole. Finally, the case where bubble wall and solid wall are fused together is analyzed to study the bubble dynamics after the separation of fluid domain and the influences of no-dimensional parameters.

Study on the interaction between bubble and free surface near an inclined vertical wall is carried out in this paper. Firstly, boundary element model for bubble dynamics based on incompressible potential flow is established, and the solid wall is modeled using the images of bubble and free surface. Then, through the numerical model, bubble dynamics near the walls with various inclination angles are studied respectively. We find that the inclination would lead discontinuity of the boundary condition of intersection between free surface and solid wall, which can affect its motion nonlinearly. Finally, the influence of the inclination angle on the bubble and spike dynamics is analyzed.

Under potential flow assumption, a numerical method is established to simulate the nonlinear movement of the free surface after the breakup of a bubble, with taking the surface tension and viscous into consideration. A method to handle the splitting of the jet or drop is put forward. Besides, an experiment of rising bubble bursting at the free surface is conducted, and the numerical result is in good agreement with the experimental result. In order to study the mechanism and law of the free surface movement after bubble breakup, the dynamic behavior of different sizes of bubble breakup is studied with the program developed, including the jet from the bottom of the bubble, the splitting of the jet or drop and so on. The variation law of the size and time of the first splitting drop, and the maximum velocity of the jet is studied and summarized. Finally, the influences of Reynolds number and Weber number on the free surface after bubble breakup are also analyzed.

The interactions between a spark generated bubble and sand particles with different diameters are studied in this paper using a high speed camera. And distance between the bubble and sand particle is varied. The experimental results show that there are two distinct phenomena during the interaction between the bubble and sand particle. On the one hand, the jet formed is much like that near a rigid wall; on the other hand, a mushroom-shape bubble will form, which will split into two bubbles and two jets with opposite directions along the axes will be generated afterwards. Thus, it is found that the sand particle has the characteristics of a rigid wall and an elastic material. In addition, as the distance d between the bubble and sand particle increases, the pulsating period of the bubble will rise to a peak before it reduces. For different sand particles, the distance corresponding to the peak decreases as the diameter of sand particle increases.

As a bubble moves near different boundaries, the motion characteristic will change largely compared with the condition of free field, especially near the free surface: there will appear a complex phenomenon because of the interaction. This paper aims to investigate experimentally the phenomenon and the regularity of the interaction between bubble and free surface. Using a spark-generated device and a high-speed camera, the influences of free surface on the maximal radius, period, jet time and width of the bubble are discussed. The relation between the voltage and the maximal radius is obtained. Different typical phenomena near the free surface are observed. The factors inducing different plume phenomena are obtained. Then the regurality of maximal height of the water column varying with dimensionless distance under the same initial condition is obtained, which provides a reference to the research on the interaction between bubble and free surface.

In order to study the interaction between underwater explosion bubble and surface waves, numerical and analytical methods are combined in this paper to solve the singular problem of the opened free surface and to consider the influence of far field. Then we decompose the velocity potential into incident potential due to the waves and the disturbing potential due to the bubble to consider the influence of waves. With the numerical model, interaction between the underwater explosion bubble and surface waves and the influence of wavelength and initial phase on the bubble dynamics are analyzed in this paper. Through the analysis of the numerical results, following conclusions are reached. During the collapsing phase of the bubble, the existence of the waves would budge the upside bubble and the downward liquid jet, while for the spike of the free surface, the influences on its height and width are considerable besides its migration. These magnitudes of influence are changed with the initial phase periodically, and decrease with the increase of wavelength in the range considered in this paper.

The fluid is assumed to be inviscid and incompressible and the flow irrotational. The three_dimensional numerical model is established to simulate the interaction of multiple bubbles and the fast Fourier transform on multipoles (FFTM) method is combined with the higher order boundary method (BEM) to study the physics of multiple bubble dynamics. FFTM method is employed to speedup the solution of the boundary integral equation while achieving the same order of accuracy, enabling to simulate the dynamics of multiple bubbles in a reasonable time. Elastic mesh technique (EMT), which is a new mesh regulation technique, is applied to maintain the regularity of the triangular element mesh used to discretize the dynamic boundary surface during the evolution of bubbles. All these measures make the present approach viable and robust, which is validated by computations of several bubble dynamics problems. Numerical analysi was carried out for the interaction of multiple bubbles and the bubble dynamics. Some physical behaviors of the multiple bubbles are presented in this work. The factors affecting the expansion, collapse, moving of multiple bubbles and the jet formation are also discussed.

The numerical model of underwater explosion bubble coupling with free surface is created based on boundary integral method and the corresponding program is exploited to get the calculated result which presents satisfactory precision with experiment data. From the basic phenomenon of the interaction between bubble and free surface, the dynamic behavior of bubble near free surface is studied systematically employing the exploited program including the ring rebound of bubble near free surface and spike of free surface as well as the relation between distance parameter buoyancy parameter strength parameter and Bjerknes effect near free surface to summarize relative laws that the dynamic behavior near free surface has close relation with these characteristic parameters. In the process of study, scope of applicability of Blake rule on the basis of Kelvin_impulse theory is discussed and the reason for inactivation of Blake rule is interpreted to present references to research on dynamic behavior of underwater explosion bubble near free surface.

Based on the assumption of potential flow, the coupled numerical model of the bubble and the wall is created and it is calculated with boundary integral method and a three-dimensional computing program is developed. The calculated result agrees with the experimental result well. Starting with the basic phenomenon of the interaction between the bubble and the wall, the dynamics of the bubble near a rigid wall is studied systematically with the program developed in this paper, including both cases of the parallel wall and the oblique wall. The relation between Bjerknes effect of the wall and the characteristic parameters is studied and the calculated results of various cases are compared and discussed with the Blake criterion based on the Kelvin-impulse theory. The analysis shows that the jet direction and the pressure on the rigid wall have close relationship with the bubble's characteristic parameters. Besides, the application range of Blake criterion is given. This paper aims to provide reference for the relevant researches on the dynamics of bubble near the wall.