Bubble Model Research Articles

Study on the Dynamic Characteristics of Single Cavitation Bubble Motion near the Wall Based on the Keller–Miksis Model

The dynamic model of cavitation bubbles serves as the foundation for the study of all cavitation phenomena. Solving the cavitation bubble dynamics equation can better elucidate the physical principles of bubble dynamics, assisting with the design of hydraulic machinery and fluid control. This paper employs a fourth-order explicit Runge–Kutta numerical method to solve the translational Keller–Miksis model for cavitation bubbles. It analyzes the collapse time, velocity, as well as the motion and force characteristics of bubbles under different wall distances γ values. The results indicate that as the distance between the cavitation bubble and the wall decreases, the cavitation bubble collapse time increases, the displacement of the center of mass and the amplitude of translational velocity of the cavitation bubble increase, and the minimum radius of the cavitation bubble gradually decreases linearly. During the stage when the cavitation bubble collapses to its minimum radius, the Bjerknes force and resistance experienced by the bubble also increase as the distance to the wall decreases. Especially in the cases where γ = 1.3 and 1.5, during the rebound stage of the bubble, the Bjerknes force and resistance increase, causing the bubble to move away from the wall. Meanwhile, this study proposes a radiation pressure coefficient to characterize the radial vibration behavior of cavitation bubbles when analyzing the radiation sound pressure. It is found that the wall distance has a relatively minor effect on the radiation pressure coefficient, providing an important basis for future research on the effects of different scale bubbles and multiple bubbles. The overall idea of this paper is to numerically solve the bubble dynamics equation, explore the characteristics of bubble dynamics, and elucidate the specific manifestations of physical quantities that affect bubble motion. This provides theoretical references for further engineering applications and flow analysis.

Development of a simplified one-dimensional CDA bubble model

Sodium-cooled fast reactors (SFRs) have high safety with an extremely low probability of a core disruptive accident (CDA). However, from a defense-in-depth perspective, the CDA sequence is still worth studying. Severe accidents in SFRs, such as unprotected loss of flow, might lead to a CDA during which fuel and some fission products could be instantly released from a large CDA bubble through potential leak paths in the top shield structure. Therefore, a reasonable prediction of dynamic behavior of a large-scale bubble within the sodium pool is vital for accurately evaluating the migration of source terms. In this study, we propose a simplified one-dimensional CDA bubble model that can handle heat and mass transfer in two-phase multicomponent materials in different computational domains during the rising of bubbles through the sodium pool toward the cover-gas region. In this model, an entrainment model based on the Rayleigh–Taylor instability and Kelvin–Helmholtz instability was used to explain the coolant entrainment through the gas/liquid boundary and jet fragmentation. The model also addresses the mitigation effect of non-condensable gases on the condensation of fuel, steel and sodium vapor at bubble interface. We evaluated the model using a past experiment on the expansion of a two-phase, large bubble with high pressure in a stagnant liquid pool conducted by Purdue University in the late 1970 s using a 1/7-scale model of Clinch River Breeder Reactor. Good agreement with the experimental data demonstrates that the developed model can reasonably represent the essential characteristics of dynamic behavior of a large, high-pressure bubble with heat and mass transfer in two-phase multicomponent materials. This is valuable for evaluating the migration of the source terms, which will be carried out in future studies.

The effect of non-uniform inlet boundary conditions on the performance of the multiphase pump

Multiphase pump is an important equipment for oil and gas transportation. The gas-liquid distribution pattern at the inlet of a multiphase pump is crucial to its performance. We propose through an experiment that slug flow and annular flow are the main forms of gas-liquid distribution at the inlet of multiphase pumps. The effects of different flow patterns on the performance of multiphase pumps were investigated through numerical simulations and experimental tests. The results show that the multiphase pump is best adapted to the homogeneous bubble model, followed by the elastic flow and poorly by the annular flow. The energy conversion characteristic of annular flow is poor, and the higher the GVF is, the more obvious this characteristic is. The pressure distribution in the outlet region of the guide vane of the slug flow model is the most inhomogeneous, thus creating a larger vortex scale. The decrease in pressurization of the annular flow is most obvious with increasing GVF. At 30 % GVF, it decreased by 43 kPa compared to the uniform bubble flow model. The different flow patterns have a large effect on the impeller performance, but the distribution of the gas-liquid two-phase at the guide vane outlet tends to stabilize. The significance of this study is to further understand the performance of the first stage impeller of multiphase pumps under special working conditions, and then provide reference for the overall design of multistage pumps to broaden the scope of multiphase pump applications.

Study on characteristics of gas–liquid two-phase flow in pump as turbine using multiple-size group model

The multi-size group (MUSIG) model is employed in this paper to simulate the gas–liquid two-phase flow in pump as turbine (PAT) since the traditional Eulerian–Eulerian two-fluid model is unable to take into account the phenomena of breakup and coalescence of bubbles. First, the simulation of gas–liquid two-phase flow in a square column is compared with the experiment to verify the accuracy of the MUSIG model. Then, the results of gas–liquid two-phase flow in PAT simulated by the MUSIG model are compared with those by the conventional uniform bubble (UB) model and find that the MUSIG model is more favorable to capture the flow pattern at high gas content compared to the UB model. Based on the MUSIG model, the internal flow characteristics, pressure fluctuation, and bubble size distribution of the PAT are analyzed. The rotation of the blades breaks a part of big bubbles into small bubbles in the volute, resulting in a smaller diameter of the bubbles entering the impeller. As the gas content increases, the number and size of vortices in the impeller flow channel increase. The vortex is formed at locations where the gas phase distribution in the impeller flow channel is concentrated. The outlet of the impeller is more prone to bubble consolidation under high gas content conditions. In conclusion, the MUSIG model can well predict the complex flow characteristics of gas–liquid two-phase inside the PAT and identify the key influencing factors of energy acquisition, which can provide support for improving the performance of the PAT design.

Effect of viscosity on bubble spreading on flat solid surfaces

The behavior and dynamics of bubble spreading has a great impact on interfacial contact area and time, which is significant for the heat/mass transfer or separation efficiency. In this work, the dynamical behavior of bubble spreading especially the three-phase contact line (TPL) on solid flat surfaces in low viscous liquids was investigated. The results show that the final length of TPL on homogeneous solid surfaces tend to decrease with the increasing liquid viscosity. For heterogenous solid surfaces, TPL motion on non-stick coal surface is basically the same as that on homogeneous solid surfaces, whereas that on anthracite surface shows an anomalous morphology. By applying the power-law model, the fast and slow spreading stages of bubble on homogeneous surfaces show the universal exponent of b = 1/2 and b = 1/10, respectively. While the exponent for bubble spreading on heterogeneous surface is complicated due to the special surface physico-chemical properties.

A lattice Boltzmann model for incompressible gas and liquid two-phase flows combined with free-surface method

A novel lattice Boltzmann (LB) model is proposed to study the gas and liquid two-phase flows with large density and viscosity ratios. In the model, both the gas and liquid phases are considered as viscous incompressible fluids, which are governed separately by the two-relaxation-time LB equations. They are coupled by a momentum exchange method at the interface. The interaction between the gas and liquid phases is explicitly described and naturally involved in the model. The interfacial conditions in the model are validated by the benchmarks of the layered Poiseuille flow and the Laplace law. The feasibility of combining this model with the bubble model and the wetting scheme is proven through transient flow problems of single bubble rising and capillary intrusion. The validity of this model is confirmed by more complex flows including solid–liquid–gas coupling and droplet breaking problems by simulating shearing a droplet on a substrate and a droplet falling on a liquid film. The results demonstrate that the present model can be used to describe both the gas and the liquid flows. This work provides a solution to model the simulation of the dynamical behaviors of multi-phase flows.

BIMBAMBUM: A potential flow solver for single cavitation bubble dynamics

In the absence of analytical solutions for the dynamics of non-spherical cavitation bubbles, we have implemented a numerical simulation solver based on the boundary integral method (BIM) that models the behavior of a single bubble near an interface between two fluids. The density ratio between the two media can be adjusted to represent different types of boundaries, such as a rigid boundary or a free surface. The solver allows not only the computation of the dynamics of the bubble and the fluid-fluid interface, but also, in a secondary processing phase, the computation of the surrounding flow field quantities. We present here the detailed implementation of this solver and validate its capabilities using theoretical solutions, experimental observations, and results from other simulation softwares. This solver is called BIMBAMBUM which stands for Boundary Integral Method for Bubble Analysis and Modeling in Bounded and Unbounded Media. Program summaryProgram Title: BIMBAMBUMCPC Library link to program files:https://doi.org/10.17632/89vv35pmhr.1Licensing provisions: GPLv3Programming language: C++ and PythonNature of problem: The code solves the axisymmetric dynamics of single cavitation bubble in the vicinity of different types of boundaries. The boundaries are treated as an interface between two fluids, where the fluids can have different density ratios. The two fluids are considered inviscid and incompressible and the associated flows irrotational so that Laplace's equation is valid everywhere.Solution method: A boundary integral method is used to calculate the velocities on the discretized bubble surface and the fluid-fluid interface. The position of these boundaries can then be updated in time using a Lagrangian approach. In the fluid domain surrounding the bubble, the velocities and pressure are estimated using a combination of the boundary integral method and finite differences.Additional comments including restrictions and unusual features: The code solves the bubble dynamics as long as its surface remains simply connected.

Laser forward and backward scattering characteristics and experimental study of bubbles in ship wake.

The detection and tracking of ships can be realized by using the laser forward and backward scattering characteristics of ship wake bubbles. In this paper, the detection ability of two kinds of scattering to wake bubbles is studied. Based on the distribution characteristics of ship wake and bubble targets, typical bubble targets are selected to study from both micro and macro aspects. The light scattering model of water is established from the microscopic aspect, and the forward and backward scattering light intensity equations of water are derived. The circumferential scattering characteristics of a single bubble are analyzed based on the Mie scattering theory. According to the transmission characteristics of light in wake bubbles, the secondary scattering model of wake bubbles is established, and the forward and backward scattering light intensity equations are derived. In the macroscopic aspect, the laser scattering simulation model of wake bubbles is established by Monte Carlo, and the forward and backward scattering characteristics of wake bubble clusters with different radii, densities, and thicknesses are analyzed emphatically. A laser forward scattering and backscattering detection system under typical bubble characteristics was built, and the composite scattering characteristics of wake bubbles with different parameter characteristics were experimentally analyzed. The theoretical and experimental results show that with the increase of bubble radius, density, and thickness, the amplitude of laser forward scattering signal of bubble groups decreases gradually, the amplitude of backward scattering signal increases gradually, the change rate of forward and backward scattering amplitude increases, and the change rate of backscattering is obviously larger than that of forward scattering. The detection of wake bubbles by backscattering has more characteristic changes than that by forward scattering, and the detection success rate is higher. The research results can provide theoretical and experimental support for the design of a ship wake laser detection system.

A Comptonized Fireball Bubble Fits the Second Extragalactic Magnetar Giant Flare GRB 231115A

Magnetar giant flares (MGFs), originating from noncatastrophic magnetars, share noteworthy similarities with some short gamma-ray bursts (GRBs). However, understanding their detailed origin and radiation mechanisms remains challenging due to limited observations. The discovery of MGF GRB 231115A, the second extragalactic MGF located in the Cigar galaxy at a luminosity distance of ∼3.5 Mpc, offers yet another significant opportunity for gaining insights into the aforementioned topics. This Letter explores its temporal properties and conducts a comprehensive analysis of both the time-integrated and time-resolved spectra through empirical and physical model fitting. Our results reveal certain properties of GRB 231115A that bear resemblances to GRB 200415A. We employ a Comptonized fireball bubble model, in which the Compton cloud, formed by the magnetar wind with high density e ±, undergoes Compton scattering and inverse Compton scattering, resulting in reshaped thermal spectra from the expanding fireball at the photosphere radius. This leads to dynamic shifts in dominant emission features over time. Our model successfully fits the observed data, providing a constrained physical picture, such as a trapped fireball with a radius of ∼1.95 × 105 cm and a high local magnetic field of 2.5 × 1016 G. The derived peak energy and isotropic energy of the event further confirm the burst’s MGF origin and its contribution to the MGF-GRB sample. We also discuss prospects for further gravitational wave detection associated with MGFs, given their high-event-rate density (∼8 × 105 Gpc−3 yr−1) and ultrahigh local magnetic field.

The dark bubbleography

We present the holographic construction of the dark bubble model of dark energy and highlight the pivotal role played by the non-normalizable modes. Following the route of holographic renormalization, we show that the non-normalizable modes are essential for having a vanishing mass for the induced graviton in any braneworld model. We then apply this idea in the computation of the propagator on the wall of the dark bubble introduced in [1].

Quasar outflow deceleration or acceleration: predictions and a search

ABSTRACT Quasar winds can shock and sweep up ambient interstellar medium (ISM) gas, contributing to galactic quenching. We combine and extend past models of energy-conserving shock bubbles around quasars, investigate model implications from an observational standpoint, and test model predictions using new high-resolution spectroscopic observations of the broad absorption-line quasar SDSS J030000.56+004828.0 (J0300). Even with constant energy input from the wind, a bubble’s expansion decelerates over time as more ISM gas is swept up. Our new observations enable a direct search for this deceleration. We obtain the tightest reported 3σ limit on the average rest-frame deceleration (or acceleration) of a quasar outflow: |a| < 0.1 km s−1 yr−1 (<3 × 10−4 cm s−2) in the relatively low-velocity Ca ii outflow of J0300 over 9.65 rest-frame years. We can satisfy these limits with certain parameter choices in our model, but the large velocity range of the Ca ii absorption in J0300 rules out the hypothesis that such gas shares the velocity of the swept-up ISM gas in a self-similar shock bubble. We investigate the possibility of ram-pressure acceleration of preexisting ISM clouds and conclude that the velocity range seen in Ca ii in J0300 is potentially consistent with such an explanation. The Ca ii-absorbing gas clouds in J0300 have been inferred to have high densities by Choi et al., in which case they can only have been accelerated to their current speeds if they were originally at least an order of magnitude less dense than they are today.

Modeling of vapor bubble dynamics considering the metastable fluid state

This study investigates the dynamic modeling of a spherical vapor bubble in an infinite liquid. Initially, the liquid is in a state of saturation, but then, there is a change in ambient pressure. Unlike previous studies that assumed vapor saturation, our model fully considers the metastable fluid state of subcooled vapor and superheated liquid. The theoretical model is based on the state equation of vapor and the kinetic theory of gases, allowing the visualization of the effects of superheating and subcooling on the bubble pressure and the phase transition rate. The accuracy of the numerical solutions for the bubble collapse and growth is confirmed by experimental results using water as the working fluid. Two approaches of heat transfer simplification are validated in the numerical solution, and an adhesion coefficient within the range of 0.1–1 is recommended for the calculation. Additionally, this study provides insights into how the metastable fluid state affects the bubble pressure and phase transition, especially in the early stages of bubble collapse. Furthermore, the conservation of vapor mass inside the bubble is also demonstrated.

Primary resonance characteristics of a cylindrical bubble based on the multi-scale method

This paper describes a primary resonance theoretical model for a cylindrical bubble under acoustic excitation. Based on the multi-scale method, an analytical solution of the bubble–wall equation with second-order accuracy is obtained and numerically verified. The oscillation characteristics in the time domain and the frequency response characteristics of the oscillations under primary resonance are analyzed with different amplitudes and frequencies of acoustic excitation and the equilibrium radius of the bubble. This study yields the following primary findings: (1) For the cylindrical bubbles, the primary resonance of the bubble exists in unstable regions. Nonlinear behaviors such as jumps, hysteresis, and multivalued solutions may be widely present. (2) As the amplitude of the acoustic excitation and the bubble equilibrium radius increase, the backbone of the amplitude–frequency response curve bends to the left and the unstable region gradually expands. (3) When the dimensionless amplitude of the acoustic excitation is less than 0.005 and the bubble equilibrium radius is less than 1.0 × 10−5 m, the unstable region of resonance disappears.

Numerical investigation of partial cavitation in a Venturi tube by Eulerian-Lagrangian multiscale modelling

The cavitating flow in a Venturi tube has a complex flow structure. In this paper, the partial cavitation in an axisymmetric Venturi tube, dominated by bubbly shock, is investigated by utilizing Eulerian-Lagrangian multiscale modelling. The unsteady partial cavitation is simulated by Large Eddy Simulation coupled with the Volume of Fluid and the Discrete Bubble Model. The numerical results show a well agreement with the high-speed photography. Through a comprehensive analysis of the development and transportation of macro cavities and micro bubbles, a detailed explanation of the cavity shedding process triggered by bubbly shock is provided. The results highlight the precise capability of the multi-scale method in elucidating the intricate flow field induced by partial cavitation. The findings may pave the way for the further investigations on the underlying mechanisms of partial cavitation, fostering a deeper understanding of bubbly shock dominated cavitating flow.

Numerical erosion prediction of aluminum induced by cavitating jet using an Eulerian–Lagrangian method

Cavitation-induced erosion in pump machinery is a significant issue that leads to material loss and increased operating costs. This study develops a numerical method based on an energy balance approach to address the risk of cavitation erosion. Compared with other published methods, three improvements are made. Firstly, it assumes that the local instantaneous pressure is the driving force behind cavity collapse, rather than the far-away ambient pressure field. Secondly, it counts erosion only at the moment that the released shock wave is strong enough to cause surface damage. Thirdly, an Eulerian–Lagrangian method is introduced to simulate multiscale cavitation, in which the volume of fluid (VOF) method and a discrete bubble model (DBM) are combined to reproduce resolvable water-vapor interfaces and unresolvable discrete bubbles, respectively. The developed numerical modeling framework is validated by predicting the erosion of pure aluminum surface caused by a cavitating jet, and it is shown that the simulated erosion region fits well against the experimental results. Additionally, appropriate model coefficients of the erosion prediction method are introduced to achieve quantitative prediction of material mass loss, and the detailed erosion behavior is discussed.

Hot bubbles of planetary nebulae with hydrogen-deficient winds. III. Formation and evolution in comparison with hydrogen-rich bubbles

We seek to understand the evolution of Wolf-Rayet central stars by comparing the diffuse X-ray emission from their wind-blown bubbles with that from their hydrogen-rich counterparts with predictions from hydrodynamical models. We simulate the dynamical evolution of heat-conducting wind-blown bubbles using our 1D radiation-hydrodynamics code NEBEL/CORONA . We use a post-AGB-model of 0.595 but allow for variations of its evolutionary timescale and wind power. We follow the evolution of the circumstellar structures for different post-AGB wind prescriptions: for O-type central stars and for Wolf-Rayet central stars where the wind is hydrogen-poor, more dense, and slower. We use the CHIANTI software to compute the X-ray properties of bubble models along the evolutionary paths. We explicitly allow for non-equilibrium ionisation of key chemical elements. A sample of 12 planetary nebulae with diffuse X-ray emission ---seven harbouring an O-type and five a Wolf-Rayet nucleus--- is used to test the bubble models. The properties of most hydrogen-rich bubbles (X-ray temperature, X-ray luminosity, size) and their central stars (photon and wind luminosity) are fairly well represented by bubble models of our 0.595 AGB remnant. The bubble evolution of Wolf-Rayet objects is different, thanks to the high radiation cooling of their carbon- and oxygen-rich winds. The bubble formation is delayed, and the early evolution is dominated by condensation instead of evaporation. Eventually, evaporation begins and leads to chemically stratified bubbles. The bubbles of the youngest Wolf-Rayet objects appear chemically uniform, and their X-ray properties can be explained by faster-evolving nuclei. The bubbles of the evolved Wolf-rayet objects have excessively low characteristic temperatures that cannot be explained by our modelling. The formation of nebulae with O-type nuclei follows mainly a single path, but the formation pathways leading to the Wolf-Rayet-type objects appear diverse. Bubbles with a pure Wolf-Rayet composition can exist for some time after their formation despite the presence of heat conduction.

Experimental tests of dark bubble cosmology

In this paper we use α′2 corrections to the D3-brane action to obtain a nonzero and positive cosmological constant in the induced cosmology living on the dark bubble. Its measured value together with the value of the fine structure constant correspond to a dark dimension of size 5×10−5 m and a string scale at 11 TeV. We conclude that the dark bubble model predicts deviations of Newtonian gravity and stringy excitations of known particles within reach of future experiments. Published by the American Physical Society 2024

An Agent-Based Model of the Housing Market Bubble in Metropolitan Washington D.C.

An Agent-Based Model of the Housing Market Bubble in Metropolitan Washington D.C.

Pressure waves from air gun bubbles: A numerical analysis based on the finite volume method

Pressure waves emitted from the air gun contain many frequencies, among which low-frequency waves are desirable for exploration and imaging, while high-frequency waves need to be suppressed as they are harmful to marine species. The high-frequency waves originate from the fast oscillations of the flow during the release of the air, such as the impingement of the gas jet into the liquid, the expansion of the air gun bubble, and the interaction between the air gun body and the bubble. However, those dynamic and the emitted waves are adjustable by the special design of the air guns. To analyze the underlying relations, we present a numerical study with a compressible air gun bubble model using the volume of fluid (VOF) approach combined with the finite volume method (FVM) implemented in STAR-CCM+. The venting process of an air gun is investigated to reveal the influence of the air gun body. The results show that air gun pressure for the far field is mainly proportional to the expansion acceleration of the whole gas. Our results also indicate that the opening and chamber shape of the air gun affects the gas expansion acceleration, which influences the first peak of the pressure wave significantly. The larger the opening is, the faster the gas is released, the greater the amplitude of the first peak is. The larger the chamber length/diameter ratio, the slower the gas is released and the lower the amplitude of the first peak.

A bubble model for the gating of Kv channels

Abstract Voltage-gated K$_{\mathrm{v}}$ channels play fundamental roles in many biological processes, such as the generation of the action potential. The gating mechanism of K$_{\mathrm{v}}$ channels is characterized experimentally by single-channel recordings and ensemble properties of the channel currents. In this work, we propose a bubble model coupled with a Poisson–Nernst–Planck (PNP) system to capture the key characteristics, particularly the delay in the opening of channels. The coupled PNP system is solved numerically by a finite-difference method and the solution is compared with an analytical approximation. We hypothesize that the stochastic behaviour of the gating phenomenon is due to randomness of the bubble and channel sizes. The predicted ensemble average of the currents under various applied voltage across the channels is consistent with experimental observations, and the Cole–Moore delay is captured by varying the holding potential.