Pressure characteristics of bubble collapse near a rigid wall in compressible fluid

High speed liquid jet and shockwave can be produced when a bubble collapses near a rigid wall, which may cause severe damage to solid structures. A hybrid algorithm was adopted to simulate bubble motion and associated pressures near a wall combining Level Set-Modified Ghost Fluid-Discontinuous Galerkin (LS-MGF-DG) method and boundary element method (BEM). Numerical results were compared with experimental data to validate the presented algorithm. Jet formation was simulated by BEM and the induced pressure on the wall was calculated with auxiliary function. The pressure at the point on the wall where the jet points to reaches its peak value after the jet penetrates the bubble. Bubble collapse and rebounding were simulated by the LS-MGF-DG method. Shock-wave is induced when the bubble collapse toroidally to a minimum volume and the pressure at wall center reaches the maximum due to shockwave superposition. A third pressure peak is found associated with the bubble rebounds and bubble splitting. In the case studied, a higher pressure was found due to collapse shockwave than bubble jet and affects a larger area of the wall. In addition, the three pressure peaks due to jet impact, collapse impact as well as bubble rebounding and splitting decrease with the increase of the standoff distance.     

Motion Characteristics of Cavitation Bubble near the Rigid Wall with the Driving of Acoustic Wave

The dynamics of cavitation bubble is analyzed in the compressible fluid by use of the boundary integral equation considering the compressibility.After the vertical incidence of plane wave to the rigid wall,the motion characteristics of single cavitation bubble near the rigid wall with initial equilibrium state are researched with different parameters.The results show that after the driving of acoustic wave,the cavitation bubble near the rigid wall will expand or contract,and generate the jet pointing to the wall.Also,the existence of the wall will elongate time for one oscillation.With the compressible model,the oscillation amplitude is reduced,as well as the peak value of inner pressure and jet tip velocity.The effect of the wall on oscillation amplitude is limited.However with the increment of initial vertical distance,the effect of wall on the jet velocity is from acceleration to limitation,and finally to acceleration again.     

The dynamic behavior of a gas bubble near a wall

In this paper, a numerical model based on the potential flow theory is established to simulate the interaction of a gas bubble with a nearby wall. The time-integration boundary integral method is used to solve the dynamics of a gas bubble. With this method the numerical calculations show an excellent agreement with the experimental data. Employing the numerical code based on the presented algorithm, the dynamics of a gas bubble close to a rigid wall is investigated systematically, especially the relationship between various characteristic parameters and the Bjerknes effect due to the presence of a nearby wall. It is found that Blake's criterion, which is usually used to predict the direction of the bubble jet, has a great degree of accuracy for the bubble relatively far away from the wall and bubble near a wall, there is a significant error, attributed to its simplifications and assumptions. Further studies show that an oblique jet will be formed when a bubble close to an inclined wall collapses, direction and width of which have a close relationship with the characteristic parameters used to characterize the bubble. For the bubble near a horizontal wall, a liquid jet pointing directly to the wall is developed generally when the Bjerknes attraction and buoyancy are in the same direction; and at the same time, if the Bjerknes attraction is in the opposite direction of buoyancy, the direction of the jet will depend on a criterion. Then the interaction of gas bubble between complicated walls of some a submarine is also studied, which shows the most dangerous induced loading condition of structure in water, and the evidently effects of bubble jet on loading. The special phenomena mentioned above have a great significance for the further study on the interaction of the bubble with its boundaries.     

Experimental study on bubble pulse features under the combined action of horizontal and vertical walls

The pulse features of a bubble have a close connection with the boundary condition. When a bubble moves near a rigid wall, it will be attracted by the Bjerknes force of the wall, and a jet pointing at the wall will be generated. In real application, the bubble may move under the combined action of walls in different directions when it forms at the corner of a pipe or at the bottom of a dam. The motion of the bubble shows complex and nonlinear characteristics under these conditions. In order to investigate the bubble pulse features near complex walls, a horizontal wall and a vertical wall are put into the experimental water tank synchronously, and an electric circuit with 200 voltages is designed to generate discharge bubbles, and then experimental study on the bubble pulse features under the combined action of horizontal and vertical walls is carried out. The influences of the combined action of two walls on the bubble shape, pulse period, moving trace and inside jet are obtained by changing the distances from bubble center to the two walls. It aims at providing references for the relevant theoretical and numerical research.     

Fully nonlinear 3D interaction of bubble dynamics and a submerged or floating structure

This paper is concerned with the interaction of bubbles, a submerged or floating structure, and free surface waves. A three-dimensional fully nonlinear model has been developed based on the coupling of the boundary integral method (BIM) for bubble dynamics and free surface waves and the finite element method for structure deformation. The present method is well validated by comparing the numerical results with the experimental data. Three structure characteristics, including fixed, rigidly moving and flexible, are investigated separately to determine their influence on bubble dynamics. For a free-floating structure, the free surface causes not only a larger reduction in peak pressure for a rigid structure compared with a fixed body but also the modification of the bubble period and structural response. The interaction between a bubble and a flexible structure, in the absence of a free surface, is simulated. Both the rigid motion and the deformation at the local structure appear in the simulation. The effect of the structural thickness on the reduction in peak pressure is also considered.     

Wave impacts on structures with rectangular geometries: Part 1. Seawalls

This paper considers steep wave impact on seawalls of various geometries. A simple analytical model for the pressure impulse due to a wave of idealized geometry and dynamics is developed and applied to the following geometries: (a) vertical seawall with a berm, (b) vertical seawall with a ditch at its base and (c) vertical seawall with a block missing (damaged condition).The method uses eigenfunction expansions in each of the rectangular regions that satisfy some of the rigid surface conditions and a simplified free-surface condition. Their unknown coefficients are determined from the impact boundary condition, rigid wall conditions and by matching the values and the horizontal derivatives of the solutions in each rectangular region at their mutual boundary. The method yields the pressure impulse throughout the entire region. The overall impulse and moment impulse on the seawall and a simple model for the uprush of the spray jet after the impact are also presented. The effects of different impact regions and different geometries can therefore be quickly estimated and used to show trends in the results. It is shown that berms generally have a beneficial effect on reducing the impulse, moment impulse and uprush, but not the maximum pressure impulse on the seawall, whereas ditches are generally and sometimes strongly detrimental for all effects except uprush. A missing block in the seawall gives an almost constant or linearly decreasing value inside the gap (depending on the boundary condition applied at the rear of the gap being hard or soft respectively); the soft case can affect the pressure impulse on the front face of the seawall, thereby affecting the impulse and moment impulse.     

Unsteady air bubble entrainment and detrainment at a plunging breaker: dominant time scales and similarity of water level variations

At plunging breakers, air bubbles are entrained at the impingement of the water jet, formed at the top of the wave, with the water free surface in front. During the present study, air bubble entrainment at a pseudo-plunging breaker was investigated at near full-scale and further experimental work studied the bubble detrainment process. Experimental observations included the generation and propagation of waves downstream of the plunge point. Experimental results highlighted a number of unsteady air–water flow patterns and emphasise high levels of aeration: i.e., depth-averaged void fraction of more than 10% next to jet impact in shallow waters. Unsteady bubble injection experiments showed a strong vortical motion induced by the rising bubbles. Altogether, the results suggest that a dominant time scale is the bubble rise time d₁/u_r, which cannot be scaled properly with an undistorted Froude model. The study contributes to a better understanding of unsteady bubble entrainment at a pseudo-plunging breaker and the associated vortical circulation.     

Far-Field Noise Induced by Bubble near Free Surface

The motion of a bubble near the free surface is solved by the boundary element method based on the linear wave equation, and the influence of fluid compressibility on bubble dynamics is analyzed. Based on the solution of the bubble motion, the far-field radiation noise induced by the bubble is calculated using Kirchhoff moving boundary integral equation, and the influence of free surface on far-field noise is researched. As the results, the oscillation amplitude of the bubble is weakened in compressible fluid compared with that in incompressible fluid, and the free surface amplifies the effect of fluid compressibility. When the distance between the bubble and an observer is much larger than that between the bubble and free surface, the sharp wave trough of the sound pressure at the observer occurs. With the increment of the distance between the bubble and free surface, the time of the wave trough appearing is delayed and the value of the wave trough increase. When the distance between the observer and the bubble is reduced, the sharp wave trough at the observer disappears.     

The effect of fluid compressibility on the simulation of sloshing impacts

Resonant and near-resonant sway-induced sloshing flow in a rectangular container is used to compare various combinations of compressibility models for air and water. The numerical model is implemented in a commercial RANS computational fluid dynamics (CFD) code. A criterion based on wave propagation is developed to assess the importance of including fluid compressibility. For sloshing flows with low levels of fluid impact, this can be simulated with incompressible fluid models for both air and water. When modelling sloshing at low-filling levels with a travelling wave, which generates large air bubble entrainment, the choice of fluid compressibility model is shown to have a significant influence on pressure magnitude and frequency of oscillation required for structural assessment. Further comparisons with theoretical models show that a full thermal energy compressibility model is also required.     

Fluid impact onto a corrugated panel with trapped gas cavity

Initial stage of incompressible liquid impact onto a corrugated elastic panel with account for compressible gas trapping between the corrugations is studied. The liquid free surface is flat and parallel to the panel before impact. The impact velocity is constant in this study. The corrugations are modelled as identical rigid short structures on the surface of the flat panel. The panel is either of infinite or finite length. There are only two corrugations which are placed symmetrically on the panel. Only a part of the panel between these two corrugations is elastic. The liquid free surface closes the gas cavity between the two corrugations at the initial instant of impact and compresses the gas before the fluid comes in contact with the elastic part of the panel. The elastic deflections of the panel are caused by gas pressure in the cavity. The elastic deflections modify both the pressure in the cavity and the hydrodynamic pressure distribution along the wetted part of the panel. The hydroelastic problem is solved within the Wagner approach. The effect of gas compressibility on the elastic behaviour of the corrugated elastic panel is investigated. It is shown that the pressure in the gas cavity and elastic deflections grow beyond all bounds for the panel of infinite length and are finite if the panel is of finite length. The present model is relevant for the strength assessment of the cargo containment system (CCS) in the tanks of LNG carriers.     

薄片炸药作用于波纹板防爆墙时的流场压力分析

在薄片炸药冲击试验中,所产生的均布流场压力会对波纹板防爆墙造成中拱效果,但该作用机理尚未明确。在该试验的比较基础上,通过流固耦合法对薄片炸药所产生的流场压力变化开展研究。在分析波纹面板及空气的压力分布变化后,发现并揭示了波纹面板上出现第二次压力峰值和自由边压力耗散现象的机理。在此基础上定量分析了薄片炸药量和槽型深度对流场压力和波纹面板变形的变化规律。研究发现,随着炸药量增加,二次压力峰值将使波纹面板中拱现象愈加明显,而槽型深度会加大压力峰值。文中机理和定量分析可为海洋平台防爆结构的设计分析提供补充参考。     

深海浮球内部气压对水下内爆波的抑制机理

深海潜器常携带中空浮球来为其提供浮力。陶瓷因其高强度、低密度等优点成为浮球的理想材料。然而,中空结构在外部高压环境下易发生内爆,产生的内爆波会对周围结构产生毁灭性损害。为了探索浮球内部初始气压对内爆波的影响,首先,利用气泡动力学对其不考虑球壳影响时进行理论分析,得到内爆波压力脉冲沿径向以指数?1 衰减,并指出其物理意义和隐含假设,进而从能量分析得到增加内压使压缩空气消耗的能量增加,从而减弱释放到水中的压力波能量;其次,采用三相流固耦合有限元模型进行计算,考虑水的可压缩性和球壳因挤压引起的脆性破裂的影响,得到更为接近实际的内爆压力的分布。由于两侧挤压球壳,外部的水在不断扩大的缺口处产生向内的射流,造成内部气体非球形塌缩,后续压力波呈现出与球壳碎裂方式有关的方向性差异。通过有限元模型对内部初始气压的研究表明,增加初始内部气体压力到 1 MPa 时,压力脉冲在球壳表面处下降了 15. 6%~24. 8%。这一结果表明,在几乎不增加浮球质量的条件下,增加内部初始气压具有很好地抑制近端内爆波强度的效果。     

Experimental investigation of bubble dynamics near the bilge with a circular opening

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.     

楔形物体在静水与波浪中自由入水砰击试验研究

通过自由落体的入水方式,分别在静水和规则波中开展了两种不同横剖面的曲面楔形体入水砰击问题试验研究。使用高速摄像系统记录楔形体入水过程流场演变和运动特性,采用加速度传感器和压力传感器进行数据的动态采集。试验结果表明,在静水中入水时,外凸剖面楔形体入水砰击后模型两侧的射流飞溅比反曲剖面更剧烈,而在楔形体前端的水面以下部分形成的气腔更小;在规则波中入水时,对于相同模型,在波峰和上跨零点相位下模型入水砰击后两侧的射流飞溅比在波谷相位更剧烈。相同工况时,反曲剖面模型所受砰击的加速度峰值和压力峰值更小;在相同的入水速度下,对于相同模型,波浪载荷和砰击载荷的共同作用会使模型所受砰击压力显著增大。     

Numerical predictions of water–air wave slam using incompressible–compressible smoothed particle hydrodynamics

The high-speed impact between a body and water is an important practical problem, whether due to wave impact on a structural deck or wall, or due to a moving body such as a ship or aircraft hitting water. The very high pressures exerted are difficult to predict and the role of air may be significant. In this paper, numerical simulations are undertaken to investigate the impact of a rigid horizontal plate onto a wave crest and, in the limit, onto a flat water surface. A two-phase incompressible–compressible smoothed particle hydrodynamics (SPH) method for water and air, respectively, is applied where the water phase imposes kinematics on the air phase at the air–water interface and the air phase imposes pressures on the water at the interface. Results are compared with experimental measurements undertaken using a drop rig positioned over a wave flume so that a horizontal plate impacts the water surface in free flight. Numerical predictions of impact pressure are quite accurate; air is shown to have a significant cushioning effect for impact on to flat water and this reduces for waves as the ratio of wave height to wavelength increases.     

The jet (pulse) model of mushroom-like flow formation

A barotropic model on the -plane is used to consider the problem of mushroom-like flow formation. The method of contour dynamics is applied to investigate the evolution of a bounded jet flow whose linear axi is identified with a rigid wall. The quasi-stationary form of the flow's head part and the velocity of its propagation have been found. The stability of the stationary solution has been studied.Translated by V. Puchkin.     

Impact pressure of breaking waves on vertical and sloping walls

Laboratory tests are conducted to measure the impact pressures of breaking waves on vertical, 5° forward, and 5, 10, 20, 30, and 45° backward sloping walls. The base structure of the wall has a foreshore slope of . Regular waves are used throughout the experiments for all wall angles. The maximum impact pressures on the wall are shown to satisfy the log-normal probability distribution. It is found from the present experiments that the impact pressures and resulting forces on sloping walls can be greater than those on a vertical wall. On the seven different walls tested, the maximum impact pressures occur most frequently slightly below the still-water level. The pattern of the impact pressure history does not change with the slope of the wall, and as the probability of maximum impact pressure decreases, the pressures around the peak pressure region of the impact pressure histories remain longer.     

Fully Coupled Fluid-Structure Interaction Model Based on Distributed Lagrange Multiplier/Fictitious Domain Method

This paper,with a finite element method,studies the interaction of a coupled incompressible fluid-rigid structure system with a free surface subjected to external wave excitations.With this fully coupled model,the rigid structure is taken as "fictitious" fluid with zero strain rate.Both fluid and structure are described by velocity and pressure.The whole domain,including fluid region and structure region,is modeled by the incompressible Navier-Stokes equations which are discretized with fixed Eulerian mesh.However,to keep the structure's rigid body shape and behavior,a rigid body constraint is enforced on the "fictitious" fluid domain by use of the Distributed Lagrange Multiplier/Fictitious Domain(DLM/FD) method which is originally introduced to solve particulate flow problems by Glowinski et al.For the verification of the model presented herein,a 2D numerical wave tank is established to simulate small amplitude wave propagations,and then numerical results are compared with analytical solutions.Finally,a 2D example of fluid-structure interaction under wave dynamic forces provides convincing evidences for the method excellent solution quality and fidelity.     

Integral bubble and jet models with pressure forces

Modifications of integral bubble and jet models including the pressure force are proposed. Exact solutions are found for the modified model of a stationary convective jet from a point source of buoyancy and momentum. The exact solutions are compared against analytical solutions of the integral models for a stationary jet that are based on the approximation of the vertical boundary layer. It is found that the modified integral models of convective jets retain the power-law dependences on the altitude for the vertical velocity and buoyancy obtained in classical models. For a buoyant jet in a neutrally stratified atmosphere, the inclusion of the pressure force increases the amplitude of buoyancy and decreases the amplitude of vertical velocity. The total amplitude change is about 10%. It is shown that in this model there is a dynamic invariant expressing the law of a uniform distribution of the potential and kinetic energy along the jet axis. For a spontaneous jet rising in an unstably stratified atmosphere, the inclusion of the pressure force retains the amplitude of buoyancy and increases the amplitude of vertical velocity by about 15%. It is shown that in the model of a spontaneous jet there is a dynamic invariant expressing the law of a uniform distribution of the available potential and kinetic energy along the jet axis. The results are of interest for the problems of anthropogenic pollution diffusion in the air and water environments and the formulation of models for statistical and stochastic ensembles of thermals in a mass-flux parameterization of turbulent moments.     

海堤坡角变化对海啸波传播过程影响数值分析

针对近岸海域极端海况的防灾减灾问题,准确模拟追踪海啸波传播过程,再现液面局部射流、崩破波等波面湍动现象。建立SPH数值水槽,边界条件基于固壁粒子法,减少海堤坡角改变对计算域精度的影响,讨论粒子间距设置对模拟精度的影响。模拟7种不同海堤坡角下波浪的爬高与衰减情况,讨论了海堤坡角变化对消波系数的影响。当粒子间距设置为0.002 m时,模型能准确地捕捉海啸波的强非线性现象。随着海堤坡角增大,海啸波峰值爬升率增大,波浪越堤后因崩破波的产生,波能衰减进一步加剧。当坡角较小时,消波系数随坡角的增大提升明显,而后趋于缓慢增长。