Bubble Center Research Articles

Electron trapping and acceleration in plasma wake field produced by an evolving hollow electron beam

In this article, the electron trapping and acceleration in the wake field driven by an ultrarelativistic hollow electron beam is studied. When the hollow driver injects into plasma, there is a doughnut-shaped electron bubble formed because of the existence of a special ‘backflow’ beam in the centre of the electron bubble. At the same time, there is a transverse convergence of the hollow driver, which leads to the weakening of the backflow beam. This results in a local electron density transition at the rear of the bubble. During this process, there is an expansion of the longitudinal electron bubble size, and a bunch of background electrons is trapped by the wake field at the rear of the bubble. The tracks for the trapped electrons show that there are two sources: one is from the bubble sheath and the other is from the unique backflow beam. In the particle-in-cell simulation where the driving beam has initial energy of $1.0$ GeV per particle, the trapped beam can be accelerated to energy of more than $1.5$ GeV per particle and the corresponding transformer ratio is $1.5$ . With the increase of driving beam energy up to $40.0$ GeV, a transformer ratio of $1.4$ still can be achieved. By adjusting the hollow beam density, it is possible to control the trapped beam charge value and beam quality, such as its energy spread and transverse emittance.

The radiated acoustic pressure and time scales of a spherical bubble

Numerical simulations of violent bubble dynamics are often associated with numerical instabilities at the end of collapse, when a shock wave is emitted. Based on the Keller–Miksis equation, we show that this is caused by two time scales associated with the phenomenon. Nonsingular equations are thus formed based on asymptotic expansion theory and the time derivatives of the bubble radius are shown to have algebraic singularities in the Mach number. The period of oscillation is shown to divide into two asymptotic layers: a long and short time scale. The short time scale, on which significant acoustic radiation is emitted from the bubble, has been determined to be , where c is the speed of sound in the liquid, the maximum bubble radius, ρ the liquid density, the hydrostatic pressure of the liquid, the vapour pressure of the liquid and κ the polytropic index of the bubble gas. Using the scalings for this short time scale, the radiated acoustic pressure scale has been deduced to be , where is the radial distance from the bubble centre to the point of measurement. The results are validated by comparison with experimental results.

Dynamics of nonspherical bubble in compressible liquid under the coupling effect of ultrasound and electrostatic field

A model for a nonspherical bubble in a compressible liquid under the coupling effect of ultrasound and electrostatic field was developed in this study. The following assumptions are made: (1) the bubble undergoes adiabatic oscillation; (2) the gravity of the liquid is negligible; (3) the bubble is insulating. If the speed of sound approaches infinity (c→∞), the equation set is reduced to the equation set for an incompressible liquid. We found that, under ultrasonic irradiation coupled with electric stress, a nonspherical bubble cannot oscillate steadily in the liquid. The bubble is bound to collapse during several cycles. The presence of electric stress reduces the surface tension at the bubble wall, which produces a larger maximum bubble-radius during the rarefaction cycle and a smaller minimum bubble-radius during the compression cycle. Consequently, during the collapse, both the gas pressure and the temperature in the bubble center increase substantially, if the bubble is exposed to both ultrasound and electrostatic field instead of ultrasound alone. In addition, the cavitation threshold of the bubble within an electrostatic field decreases significantly, compared to the bubble without an electrostatic field. In general, bubble cavitation occurs more easily and violently in the liquid after the introduction of an electrostatic field.

Jet formation from bubbles near a solid boundary in a compressible liquid: Numerical study of distance dependence

A small, spherical bubble of high internal pressure is inserted into water at constant ambient pressure as a model of a laser-induced bubble. Its subsequent dynamics near a flat solid boundary is studied in dependence on the distance of the bubble to the boundary by numerically solving the Navier-Stokes equations with the help of the open source software environment OpenFOAM. Implemented is the finite volume method for discretization of the equations of motion and the volume of fluid method for capturing the interface between the bubble interior and exterior. The bubble contains a small amount of non-condensable gas that is treated as an ideal gas. The liquid is water obeying the Tait-equation. Surface tension is included where necessary. The evolution of the bubble shape and a selection of pressure and velocity fields are given for normalized distances $D^* = D/R_{\rm max}$ between 0 and 3 ($D$ = initial distance of the bubble centre to the boundary, $R_{\rm max}$ = maximum radius the bubble would attain without any boundary). $R_{\rm max} = 500 \mu$m is chosen for the study. Normal axial jet formation ($\sim 100$ m s$^{-1}$) by axial flow focusing is found for $0.24 \le D^* \le 3$ and the change to a different type of axial jet formation ($\sim 1000$ m s$^{-1}$) by annular-liquid-flow collision for bubbles very near to the solid boundary ($0 \le D^* \le 0.2$). The transition region ($0.2 < D^* < 0.24$) is characterized by additional inbound and outbound annular jets. Remarkably, the inclusion of the viscosity of the water is decisive to get the fast jets.

Theoretical Optimization of Trapped-Bubble-Based Acoustic Metamaterial Performance

Acoustic metamaterials have proven to be a versatile tool for the precise control and manipulation of sound waves. One of the promising designs of acoustic metamaterials employ the arrays of bubbles and find applications for soundproofing, blast mitigation, and many others. An obvious advantage of bubble-based metamaterials is their ability to be relatively thin while absorbing low-frequency sound waves. The vast majority of theories developed to predict resonant behavior of bubble-based metamaterials capitalize on Minnaert frequency. Here, we propose a novel theoretical approach to characterize bubble-based metamaterials that are based on our previous findings for a single bubble trapped in circular cavity modeled as a thin clamped plate. We obtain analytical expressions for resonant frequencies of bubble metascreens using self-consistent approximation. Two geometry factors, distance between bubble centers and distance between bubble center and interface of acoustic impedance change, are taken into account. We demonstrate the existence of multiple bandgaps and possibility of switching between them via adjustment of geometry parameters and reflector properties.

Modeling capabilities of unsteady RANS for the simulation of turbulent swirling flow in an annular bluff-body combustor geometry

In this paper, we investigate the capabilities of the unsteady Reynolds-averaged Navier–Stokes (URANS) equations for capturing the helical structures found in a three-dimensional, incompressible and isothermal annular swirling jet undergoing vortex breakdown. The flow topology is representative of a bluff-body combustor operating at a Reynolds number Re = 8500 and swirl number S = 0.39. As a turbulence model, the SSG Reynolds stress model (RSM) was chosen. The numerical simulation is validated by means of tomographic particle image velocimetry measurements of the same flow configuration. To detect the coherent structures in the flow field, the recently introduced spectral proper orthogonal decomposition technique is adopted, which gives both temporal and spatial information on the large scale coherent structures. The spectral analysis of the sampled velocity signals identified a precessing vortex core with a frequency of 24.3 Hz. In particular, two different large-scale helical flow structures are identified: a single and a double helix. Both of them are wound in the counter-swirl direction and wrapped around the central breakdown bubble. Those findings are quite similar to recent experimental tomographic particle image velocimetry results (Vanierschot et al., Phys. Rev. Fluids (2018) & J. Fluid Mech. (2020)). This study demonstrates that the unsteady RANS approach with RSM is able to predict the coherent structures found in an annular swirling jet undergoing vortex breakdown both temporally and spatially with reasonable accuracy and this approach can hence be used in the design of bluff-body combustors, where a multi-dimensional parameter space may require many simulations to find the optimal design.

Theoretical and numerical studies on the collapse of single‐ and double‐bubble system in water

AbstractThe cavitation bubbles that collapse in the hydraulic machinery can cause damage to the structure and the internal wall. In order to find feasible preventive measures, the mechanism of cavitation bubble collapse needs to be thoroughly studied. However, the influence of the initial radius or the interaction between multi‐bubbles has not been studied in depth. In this paper, the collapse process of single‐ and double‐bubble system is studied by the volume of fluid (VOF) method. Three conditions are considered in this paper, single‐bubble (R0 = 0.3 mm, R0 = 0.4 mm) and double‐bubble system (R0,1 = 0.3 mm and R0,2 = 0.4 mm). The time evolution of pressure, bubble radius, radial velocity, and acceleration during the bubble collapse can be obtained. The bubble collapse time, pressure distribution, and radial velocity of single bubble are verified by theoretical values. It is found that with the increase of bubble initial radius, the collapse, and rebound time is delayed, the maximum pressure of the bubble center increases, the minimum radius of the bubble decreases, the maximum radial velocity increases. In double‐bubble system, during the first rebound of the small bubble, the central pressure, radius and radial velocity of the small bubble fluctuate with time. And the collapse time of each bubble is delayed, the maximum central pressure decreases and the minimum radius of the bubble increases.

Hydrodynamic forces on a clean spherical bubble translating in a wall-bounded linear shear flow

The three-dimensional flow around a spherical clean bubble translating steadily in a wall-bounded linear shear flow is studied numerically. The present work is concerned with the drag and lift forces experienced by the bubble over a wide range of Reynolds number (0.1 ≤ Re ≤ 103, Re being based on the bubble diameter and relative velocity with respect to the ambient fluid), wall distance (1.5 ≤ LR ≤ 8, LR being the distance from the bubble center to the wall normalized by the bubble radius), and relative shear rate (−0.5 ≤ Sr ≤ 0.5, Sr being the ratio between the velocity difference across the bubble and the relative velocity). Based on the above range of parameters, situations where the bubble is repelled from or attracted to the wall are both covered. The flow structure and vorticity field are analyzed to obtain qualitative insight into the interaction mechanisms at work. The drag and lift forces are computed as well. Their variations agree well with theoretical predictions available in the limit of low-but-finite Reynolds number and, when the fluid is at rest, in the potential flow limit. Numerical results and analytical expressions are combined to provide accurate semi-empirical expressions for the drag and lift forces at arbitrary Reynolds number and separation distance.

Dynamics of interacting bubbles located in the center and vertices of regular polyhedra

The dynamics of spherical gas bubbles located in the center and vertices of regular polyhedra under a sharp pressure increase in liquid is studied. Before the pressure rise, the liquid and the bubbles are at rest, the liquid pressure is 1 bar, the radii of the bubbles are 0.25 mm. The liquid pressure rises by 3 bar. For comparison, the configurations with one bubble in the center of a sphere and the others stochastically distributed inside it are also considered. In all the cases, the initial minimum distance between the centers of the bubbles does not exceed 5 mm. A mathematical model is used, in which the dynamics of the bubbles is governed by second-order ordinary differential equations in the radii of the bubbles and the position-vectors of their centers. It is shown that in all the bubble configurations considered, the amplitude of the pressure oscillations in the central bubble decreases nonmonotonically. With a sufficiently large number of peripheral bubbles, the change in the amplitude begins with a phase of its significant increase. With a rise in the number of the peripheral bubbles, the oscillation frequency of all bubbles decreases.

Dynamics of Gas Bubbles Inside a Ball-like Area at the Nodes of a Uniform Cubic Mesh Under Sudden Liquid Pressure Rise

The influence of hydrodynamic interaction between spherical gas bubbles inside a ball-like area at the nodes of a uniform cubic mesh on their dynamics under sudden liquid pressure rise has been investigated. Main attention is payed to the dynamics of a bubble located in the center of such a cluster of cubic structure. Prior to the pressure rise, the liquid and the bubbles are at rest, the liquid pressure is 1 bar, the radii of the bubbles are 0.25 mm, the size of the cubic mesh cells is 5 mm. The increase in the liquid pressure is 3 bar. For the sake of comparison, ball-like clusters with spherical and stochastic structures are also considered, with similar position of the central bubble and with initial minimum distance between the centers of bubbles not exceeding 5 mm. In the clusters of spherical structure, the non-central bubbles are located on concentric spheres with radii of 5 and 10 mm at the nodes of equally-oriented regular polyhedra (icosahedra and dodecahedra). In the clusters of stochastic structure, the non-central bubbles are distributed stochastically in a sphere with radius of 10 mm. A mathematical model is applied, in which the dynamics of bubbles is governed by the ordinary differential equations in the radii of bubbles and the position-vectors of their centers. It is shown that in the case of a cluster with cubic structure, the interaction between the bubbles leads to strengthening the collapse rate of the central bubble and to non-monotonic decay of oscillations of their pressure. Similar features are characteristic of the clusters with spherical and stochastic structures.

Dynamics of bubbles in cavitation cloud based on lattice model

A lattice model is introduced to deal with the dynamics of bubbles in cavitation cloud driven by ultrasound, which makes it possible to extend the study of a finite number of bubbles to cloud with an infinite number of bubbles. In this model, the arrangement of bubbles in cloud is assumed to be a cubic lattice. The central bubble in one lattice cell is representative of all the bubbles in cloud. The numerical simulation shows that the bubble in cloud can be severely suppressed by other bubbles under a cubic lattice structure. An interesting phenomenon is found that the maximum radius of bubbles would be saturated when the driving amplitude exceeds a threshold in cavitation cloud, which makes it easy to understand that the sonoluminescence in a single bubble is always brighter than that in cloud.

Experimental study on interaction, shock wave emission and ice breaking of two collapsing bubbles

In this work ice breaking caused by a pair of interacting collapsing bubbles was studied by an experimental approach. The bubbles were generated by an underwater electric discharge simultaneously, positioned either horizontally or vertically below a floating ice plate and observed via high-speed photography. The bubble-induced shock waves, which turn out to be crucial to the fracturing of the ice, were visualized using a shadowgraph method and also measured using pressure transduces. Unique bubble behaviour was observed, including bubble coalescence, bubble splitting, inclined counter-jets and asymmetric toroidal bubble collapse. Bubble dynamic properties, such as jet speed, jet energy and bubble centre displacement, were measured. Shock wave emission and ice breaking capability of the two bubbles were investigated over a range of inter-bubble and bubble–boundary distances. Regions where the damaging potential of the bubble pair are strengthened or weakened were summarized and possible reasons for the variation in the ice breaking capability were analysed based on bubble morphology, jet characteristics and shock wave pressure. The findings may contribute to more efficient ice breaking and also inspire new ways to manipulate cavitation bubble damage.

Numerical Solution of Single and Two Bubbles Moving in Quiescent Liquid Using Euler-Lagrange Approach

It is known that the bubbles dynamics are very important and dominant property in multiphase airlift systems. The major benefit came from understanding visually and numerically these dynamics that lead to improvement of bubbles distribution and a well-mixed mixture inside reactors. Hence, Euler-Lagrange approach has been used to study bubbles dynamics. By using the two-dimensional Reynolds-averaged Navier–Stokes equations that reinforces turbulence model the continuous phase velocity is calculated. The coupling between the phases was take into consideration through source terms of momentum and the source terms in the equations (ε and k), which include the effect of wake-generated turbulence by means consistent Lagrangian-similar terms. by utilizing the motion equations taking into account added mass, drag, pressure, gravity, wall, and the transverse lift force the Bubble motion was calculated. So as to determine the importance relative for the different physical phenomena’s included in the model., a modified particle source in cell (PIC) is introduced, where the effect of bubble is accounted not only where the center of bubble is located but also to all the cells that containing bubble.

Effect of particle size on the relative motion between particles and bubbles

Particle size plays a critical role in flotation. Experimental research on the effect of particle size on the relative motion between mineral particles and bubbles is far more inadequate. In this work, an experimental system is developed to track all particles and extra the parameters. Different sizes of coal particles are used to observe the evolution of the particle trajectory and velocity in the approaching process. The particle trajectory can be divided into two parts, and a bubble will affect the motion of the particle once the particle enters the near part. The distance between the turning point of the particle trajectory and the bubble center increases as the initial settling position expands outward, and the distance for coarse particles is shorter than that for fine particles. The distance to the bubble center when the decrease in the particle velocity reaches 10% is regarded as the boundary of the resistance layer, and the distance for coarse particles is longer than that for fine particles. The particle collision velocity is the final output of the resistance layer. The collision velocity increases as the collision angle increases, and the collision velocity of coarse particles is greater than that of fine particles.

To Split or Not to Split: Dynamics of an Air Disk Formed under a Drop Impacting on a Pool.

When a drop falls and impacts on a liquid pool, it entraps an air disk below the drop, which then contracts into a central bubble. Here, we use high-speed imaging and high-resolution numerical simulations to characterize the air-disk contraction dynamics for different liquid properties. We show that the air disk can contract into a single central bubble, form a toroidal bubble, or split vertically into two smaller bubbles. We demonstrate that the transitions between the different regimes can be separated by an Ohnesorge number, Oh_{e}, based on the air-disk thickness. For the lowest Oh_{e}, we find a new regime, where vortex shedding from the rim of the contracting air disk breaks the vertical symmetry and prevents the bubble from splitting in two.

Dynamic behavior of a single bubble between the free surface and rigid wall.

The objective of this paper is to apply high-speed photography and schlieren method to investigate the bubble dynamics between the free surface and a rigid wall. The temporal evolution of the bubble shape and the free surface motion are recorded by two synchronous high-speed cameras. Experiments are carried out for a single bubble generated at various normalized stand-off distances from bubble center to the free surface and to the rigid wall. The results show that (1) three distinctive patterns are identified with the morphology of the bubble and free surface, namely single toroidal bubble without spike (STB), single toroidal bubble with a spike (STBS) and double toroidal bubbles with a spike (DTBS). (2) The dynamic characteristics of the bubble at collapse and rebound stage vary evidently at different patterns, including the bubble shape variations and free surface motion. In detail, the schlieren images show the formation and propagation of shock waves, which explains the radiative process of bubble collapse energy. (3) Qualitative comparisons are carried out for the bubble and free surface at the same pattern. And quantitative analyses are conducted for the jet velocity, bubble collapse position, bubble collapse time and spike height, etc. for different values of bubble-rigid wall distance.

Shock-Wave/Boundary-Layer Interactions in Transitional Rectangular Duct Flows

Shock-wave/boundary-layer interactions (SBLI) are an important feature of high-speed gas dynamics. In many numerical studies of SBLI span-periodicity is assumed to reduce computational complexity. However, span-periodicity is not a valid assumption for aeronautical applications such as supersonic engine intakes where lateral confinement leads to highly three-dimensional behaviour. In this work transitional oblique SBLI are simulated for a rectangular duct with a theta _{sg} = 5^{circ } shock generator ramp at Mach 2. The baseline configuration is a duct with an aspect ratio of 0.5. Time-dependent disturbances are added to the base laminar flow via wall localised blowing/suction strips to obtain intermittent transition upstream of the SBLI. Two forcing configurations are evaluated to assess the response of the SBLI to different tripping locations. The transition is observed to develop first in the low-momentum corners of the duct and spread out in a wedge shape. The central separation bubble is seen to react dynamically to oncoming turbulent spots, shifting laterally across the span. While instantaneous corner separations do occur, the time-averaged corner flow remains attached. Comparisons to a one-to-one aspect ratio duct show that the SBLI is heavily dependent on aspect ratio; the wider duct exhibited significantly larger regions of flow-reversal due to a strengthened interaction.

Concentration profiles around and chemical composition within growing multicomponent bubble in presence of curvature and viscous effects

Abstract The regularities of changing chemical composition and size of a ultra-small multicomponent gas bubble growing in a viscous solution have been analyzed. The full-scale effects of solution viscosity and bubble curvature at non-stationary diffusion of arbitrary number of dissolved gases with any value of gas supersaturations and solubilities in the surrounding liquid solution have been taken into account. The nonuniform concentration profiles of gas species in supersaturated solution around the growing bubble with changing composition have been found as a function of time and distance from the bubble center. Equations describing transition to stationary concentrations of gases in the bubble with increasing radius have been obtained. Analytic asymptotic solutions of these equations for a ternary system have been presented.

Deciphering the 3D Orion Nebula-I: Expanding Shells in the Huygens Region

Abstract Based on imaging and spectroscopic data, we develop a 3D model for the Huygens Region of the Orion Nebula. Ori C, the hottest star in the Trapezium, is surrounded by a wind-blown Central Bubble that opens SW into the Extended Orion Nebula. Outside of this feature lies a layer of ionized gas at about 0.4 pc from Ori C. Both of these features are moving rapidly away from Ori C with an expansion age for the Central Bubble of only 15,000 yr.

Phase-Field Modeling of Microstructure Evolution in the Presence of Bubble During Solidification

Simulation of the solid–liquid–gas interaction during solidification is challenging due to the presence of complex phase interfaces, bubble deformation, and high liquid/gas density ratio. In this work, a hybrid phase-field lattice-Boltzmann (PFLB) approach, together with a parallel and adaptive-mesh-refinement (Para-AMR) algorithm, is developed to model interactions between the gas bubble and solid growth front during solidification. The solid growth and bubble evolution are solved by the phase-field method. Both melt flow and bubble movement are determined by a kinetic-based lattice-Boltzmann model. Bubble dynamics during alloy solidification is modeled and compared with experiments, and a good agreement is achieved for various solid/liquid interfaces including planar, cellular, and dendritic interfaces. Results show that the effect of the bubble on solid array is dependent on the solid/liquid interface morphology, bubble size, and relative position between the bubble center and dendritic tip. Two interaction mechanisms, including engulfment and entrapment, are compared, and the difference is caused mainly by the redistribution of solute. The interaction mechanism between the rising multibubbles with large deformation and the dendritic array is also discussed.