Morphological analysis for thermodynamics of cavitation collapse near fractal solid wall

A fractal geometric boundary with natural wall features is introduced into a hybrid lattice-Boltzmann-method(LBM)multiphase model. The physical model of cavitation bubble collapse near the irregular geometric wall is established to study the thermodynamic characteristics of the bubble collapse. Due to the lack of periodicity, symmetry, spatial uniformity and obvious correlation in the LBM simulation of the bubble collapse near the fractal wall, the morphological analysis based on Minkowski functional is introduced into the thermodynamic investigation of cavitation bubble so as to analyze and obtain the effective information. The results show that the Minkowski functional method can employed to study the temperature information in complex physical fields hierarchically and quantitatively. The high/low temperature region of the cavitation flow is explored, and thermal effect between irregular and fractal geometric wall and cavitation bubble can be revealed. It illustrates that LBM and morphological analysis complement each other, and morphological analysis can also be used as an optional and potential tool in research field of complex multiphase flows.

Study on shock wave-induced cavitation bubbles dissolution process

This study investigated dissolution processes of cavitation bubbles generated during in vivo shock wave（SW）-induced treatments. Both active cavitation detection（ACD） and the B-mode imaging technique were applied to measure the dissolution procedure of bi Spheres contrast agent bubbles by in vitro experiments. Besides, the simulation of SW-induced cavitation bubbles dissolution behaviors detected by the B-mode imaging system during in vivo SW treatments, including extracorporeal shock wave lithotripsy（ESWL） and extracorporeal shock wave therapy（ESWT）, were carried out based on calculating the integrated scattering cross-section of dissolving gas bubbles with employing gas bubble dissolution equations and Gaussian bubble size distribution. The results showed that（i） B-mode imaging technology is an effective tool to monitor the temporal evolution of cavitation bubbles dissolution procedures after the SW pulses ceased, which is important for evaluation and controlling the cavitation activity generated during subsequent SW treatments within a treatment period;（ii） the characteristics of the bubbles, such as the bubble size distribution and gas diffusion, can be estimated by simulating the experimental data properly.

Level set method for numerical simulation of a cavitation bubble,its growth, collapse and rebound near a rigid wall

A level set method of non-uniform grids is used to simulate the whole evolution of a cavitation bubble, including its growth, collapse and rebound near a rigid wall. Single-phase Navier-Stokes equation in the liquid region is solved by MAC projection algorithm combined with second-order ENO scheme for the advection terms. The moving inter-face is captured by the level set function, and the interface velocity is resolved by ＂one-side＂ velocity extension from the liquid region to the bubble region, complementing the second-order weighted least squares method across the interface and projection inside bubble. The use of non-uniform grid overcomes the difficulty caused by the large computational domain and very small bubble size. The computation is very stable without suffering from large flow-field gradients, and the results are in good agreements with other studies. The bubble interface kinematics, dynamics and its effect on the wall are highlighted, which shows that the code can effectively capture the ＂shock wave＂-like pressure and velocity at jet impact, toroidal bubble, and complicated pressure structure with peak, plateau and valley in the later stage of bubble oscillating.

Breakup of Cavitation Bubbles within the Diesel Droplet

Supercavitation in the diesel nozzle increases the instability of droplets in part due to the two-phase mixture, while the effect of cavitation bubbles on the instability of drops is still unclear. In order to investigate the breakup of cavitation bubbles within the diesel droplet, a new mathematical model describing the disturbance growth rate of the diesel bubble instability is developed. The new mathematical model is applied to predict the effects of fluids viscosity on the stability of cavitation bubbles. The predicted values reveal that the comprehensive effect of fluids viscosity makes cavitation bubbles more stable. Compared with the viscosities of air and cavitation bubble, the diesel droplet＇s viscosity plays a dominant role on the stability of cavitation bubbles. Furthermore, based on the modified bubble breakup criterion, the effects of bubble growth speed, sound speed, droplet viscosity, droplet density, and bubble-droplet radius ratio on the breakup time and the breakup radius of cavitation bubbles are studied respectively. It is found that a bubble with large bubble-droplet radius ratio has the initial condition for breaking easily. For a given bubble-droplet radius ratio （0.2）, as the bubble growth speed increases （from 2 m/s to 60 m/s）, the bubble breakup time decreases（from 3.59 gs to 0.17 ps） rapidly. Both the greater diesel droplet viscosity and the greater diesel droplet density result in the increase of the breakup time. With increasing initial bubble-droplet radius ratio （from 0.2 to 0.8）, the bubble breakup radius decreases （from 8.86 trn to 6.23 tm）. There is a limited breakup radius for a bubble with a certain initial bubble-droplet radius ratio. The mathematical model and the modified bubble breakup criterion are helpful to improve the study on the breakup mechanism of the secondary diesel droplet under the condition of supercavitation.

Instability and breakup of cavitation bubbles within diesel drops

A modified mathematical model is used to study the effects of various forces on the stability of cavitation bubbles within a diesel droplet. The principal finding of the work is that viscous forces of fluids stabilize the cavitation bubble, while inertial force destabilizes the cavitation bubble. The droplet viscosity plays a dominant role on the stability of cavitation bubbles compared with that of air and bubble. Bubble–droplet radius ratio is a key factor to control the bubble stability, especially in the high radius ratio range. Internal hydrodynamic and surface tension forces are found to stabilize the cavitation bubble, while bubble stability has little relationship with the external hydrodynamic force. Inertia makes bubble breakup easily, however, the breakup time is only slightly changed when bubble growth speed reaches a certain value(50 m·s-1). In contrast, viscous force makes bubble hard to break. With the increasing initial bubble–droplet radius ratio, the bubble growth rate increases, the bubble breakup radius decreases, and the bubble breakup time becomes shorter.

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.

Investigation of cavitation bubble collapse in hydrophobic concave using the pseudopotential multi-relaxation-time lattice Boltzmann method

The interaction between cavitation bubble and solid surface is a fundamental topic which is deeply concerned for the utilization or avoidance of cavitation effect.The complexity of this topic is that the cavitation bubble collapse includes many extreme physical phenomena and variability of different solid surface properties.In the present work,the cavitation bubble collapse in hydrophobic concave is studied using the pseudopotential multi-relaxation-time lattice Boltzmann model(MRT-LB).The model is modified by involving the piecewise linear equation of state and improved forcing scheme.The fluid-solid interaction in the model is employed to adjust the wettability of solid surface.Moreover,the validity of the model is verified by comparison with experimental results and grid-independence verification.Finally,the cavitation bubble collapse in a hydrophobic concave is studied by investigating density field,pressure field,collapse time,and jet velocity.The superimposed effect of the surface hydrophobicity and concave geometry is analyzed and explained in the framework of the pseudopotential LBM.The study shows that the hydrophobic concave can enhance cavitation effect by decreasing cavitation threshold,accelerating collapse and increasing jet velocity.

Cavitation Bubble Collapse near a Curved Wall by the Multiple-Relaxation-Time Shan-Chen Lattice Boltzmann Model

The cavitation bubble collapse near a cell can cause damage to the cell wall. This effect has received increasing attention in biomedical supersonics. Based on the lattice Boltzmann method, a multiple-relaxation-time Shan–Chen model is built to study the cavitation bubble collapse. Using this model, the cavitation phenomena induced by density perturbation are simulated to obtain the coexistence densities at certain temperature and to demonstrate the Young–Laplace equation. Then, the cavitation bubble collapse near a curved rigid wall and the consequent high-speed jet towards the wall are simulated. Moreover, the influences of initial pressure difference and bubble-wall distance on the cavitation bubble collapse are investigated.

A numerical model for cloud cavitation based on bubble cluster

The cavitation cloud of different internal structures results in different collapse pressures owing to the interaction among bubbles. The internal structure of cloud cavitation is required to accurately predict collapse pressure. A cavitation model was developed through dimensional analysis and direct numerical simulation of collapse of bubble cluster. Bubble number density was included in proposed model to characterize the internal structure of bubble cloud. Implemented on flows over a projectile, the proposed model predicts a higher collapse pressure compared with Singhal model. Results indicate that the collapse pressure of detached cavitation cloud is affected by bubble number density.

Effect of non-condensable gas on a collapsing cavitation bubble near solid wall investigated by multicomponent thermal MRT-LBM

A multicomponent thermal multi-relaxation-time(MRT)lattice Boltzmann method(LBM)is presented to study collapsing cavitation bubble.The simulation results satisfy Laplace law and the adiabatic law,and are consistent with the numerical solution of the Rayleigh-Plesset equation.To study the effects of the non-condensable gas inside bubble on collapsing cavitation bubble,a numerical model of single spherical bubble near a solid wall is established.The temperature and pressure evolution of the two-component two-phase flow are well captured.In addition,the collapse process of the cavitation bubble is discussed elaborately by setting the volume fractions of the gas and vapor to be the only variables.The results show that the non-condensable gas in the bubble significantly affects the pressure field,temperature field evolution,collapse velocity,and profile of the bubble.The distinction of the pressure and temperature on the wall after the second collapse becomes more obvious as the non-condensable gas concentration increases.

Modeling and Simulation of a Gas-Liquid Coupling Excitation-Induced Cavitation Bubble

A gas-liquid coupling excitation mode is proposed and the gas-liquid excitation experimental system is developed. Air from pulse generator is mixed with liquid,through which the generated cavitation bubbles can strip contaminants adhered to the pipe inner wall rapidly. The kinematics equation of the bubble inside the hydraulic oil is established and the numerical simulations are carried out. The influential factors such as gas pressure, excitation frequency,initial bubble radius and fluid viscosity are analyzed.The results show that the cavitation will evolve from steady state to transient state with the increasing gas pressure and initial bubble radius. The pulse generator frequency has a slightly effect on the growth of the bubble radius,and the breakup time of the bubble is shortened with the rising frequency. Similarly, the increasing viscosity of liquid has minimal impact on cavitation effect,which can weaken the growth and the collapse of the bubble. Moreover,the temperature inside the cavitation bubble is investigated,indicating that the instantaneous temperature inside the bubble increases with the rising gas pressure. Once the gas pressure is raised to a certain value greater than the fluid static pressure, the instantaneous temperature inside the bubble will rise sharply. So, it can be concluded that the gas-liquid coupling excitation-induced cavitation process is controllable, and some theoretical basis of the new excitation mode is presented,which is expected to be applied in the online cleaning of the complex hydraulic system.

Effects of Sodium Dodecyl Sulfate on a Single Cavitation Bubble

Dynamics of a single cavitation bubble in sodium dodecyl sulfate（SDS） aqueous solutions is investigated experimentally and theoretically. The bubble pulsation is measured by a phase-locked integrated imaging technique,and the ambient radius is obtained by fitting the numerical calculation based on the Rayleigh–Plesset bubble dynamics model to the experimental data. The results show that, under the same driving condition, the ambient radius of the cavitation bubble decreases correspondingly with the increase of SDS concentration within the critical micelle concentration, while the compression ratio of the radius increases, which indicates that the addition of SDS decreases the internal molecular number of the cavitation bubble and increases the power capability of the cavitation bubble. In addition, bubble oscillation increases the concentration of the surfactant molecules on the bubble wall, so that the effect of SDS on a single cavitation bubble is reduced when the SDS concentration is greater than 0.8 m M.

Dynamics of Vapor Bubble in a Variable Pressure Field

This paper presents analytical and numerical results of vapor bubble dynamics and acoustics in a variable pressure field.First,a classical model problem of bubble collapse due to sudden pressure increase is introduced.In this problem,the Rayleigh–Plesset equation is treated considering gas content,surface tension,and viscosity,displaying possible multiple expansion–compression cycles.Second,a similar investigation is conducted for the case when the bubble originates near the rounded leading edge of a thin and slightly curved foil at a small angle of attack.Mathematically the flow field around the foil is constructed using the method of matched asymptotic expansions.The outer flow past the hydrofoil is described by linear(small perturbations)theory,which furnishes closed-form solutions for any analytical foil.By stretching local coordinates inversely proportionally to the radius of curvature of the rounded leading edge,the inner flow problem is derived as that past a semi-infinite osculating parabola for any analytical foil with a rounded leading edge.Assuming that the pressure outside the bubble at any moment of time is equal to that at the corresponding point of the streamline,the dynamics problem of a vapor bubble is reduced to solving the Rayleigh-Plesset equation for the spherical bubble evolution in a time-dependent pressure field.For the case of bubble collapse in an adverse pressure field,the spectral parameters of the induced acoustic pressure impulses are determined similarly to equivalent triangular ones.The present analysis can be extended to 3D flows around wings and screw propellers.In this case,the outer expansion of the solution corresponds to a linear lifting surface theory,and the local inner flow remains quasi-2D in the planes normal to the planform contour of the leading edge of the wing(or screw propeller blade).Note that a typical bubble contraction time,ending up with its collapse,is very small compared to typical time of any variation in the flow.Therefore,the approach can also be applied to unsteady flow problems.

Cavitation Passive Control on Immersed Bodies

This paper introduces a new idea of controlling cavitation around a hydrofoil through a passive cavitation controller called artificial cavitation bubble generator （ACG）. Cyclic processes, namely, growth and implosion of bubbles around an immersed body, are the main reasons for the destruction and erosion of the said body. This paper aims to create a condition in which the cavitation bubbles reach a steady-state situation and prevent the occurrence of the cyclic processes. For this purpose, the ACG is placed on the surface of an immersed body, in particular, the suction surface of a 2D hydrofoil. A simulation was performed with an implicit finite volume scheme based on a SIMPLE algorithm associated with the multiphase and cavitation model. The modified k-ε RNG turbulence model equipped with a modification of the turbulent viscosity was applied to overcome the turbulence closure problem. Numerical simulation of water flow over the hydrofoil equipped with the ACG shows that a low-pressure recirculation area is produced behind the ACG and artificially generates stationary cavitation bubbles. The location, shape, and size of this ACG are the crucial parameters in creating a proper control. Results show that the cavitation bubble is controlled well with a well-designed ACG.

Numerical simulation of bubble chaotic motion in a cavitating water jet

A computational fluid dynamics (CFD) method is developed to investigate the radical motion of single cavitating bubble in the oscillating pressure field of a cavitating water jet. Regarding water as a compressible fluid, the simulation is performed at different oscillating frequencies. It is found that the bubble motion presents obvious nonlinear feature, and bifurcation and chaos appear on some conditions. The results manifest the indetermination of the cavitating bubble motion in the oscillating pressure field of the cavitating water jet.

Growth and collapse of laser-induced bubbles in glycerol-water mixtures

Comprehensive numerical and experimental analyses of the effect of viscosity on cavitation oscillations are performed. This numerical approach is based on the Rayleigh-Plesset equation. The model predictions are compared with experimental results obtained by using a fibre-optic diagnostic technique based on optical beam deflection （OBD）. The maximum and minimum bubble radii as well as the oscillation times for each oscillation cycle are determined according to the characteristic signals. It is observed that the increasing of viscosity decreases the maximum bubble radii but increases the minimum bubble radii and the oscillation time. These experimental results are consistent with numerical results.

Pico–nano bubble column flotation using static mixer-venturi tube for Pittsburgh No.8 coal seam

The flotation process is a particle-hydrophobic surface-based separation technique. To improve the essential flotation steps of collision and attachment probabilities, and reduce the step of detachment probabilities between air bubbles and hydrophobic particles, a selectively designed cavitation venturi tube combined with a static mixer can be used to generate very high numbers of pico and nano bubbles in a flotation column. Fully embraced by those high numbers of tiny bubbles, hydrophobic particles readily attract the tiny bubbles to their surfaces. The results of column flotation of Pittsburgh No. 8 seam coal are obtained in a 5.08 cm ID and 162 cm height flotation column equipped with a static mixer and cavitation venturi tube, using kerosene as collector and MIBC as frother. Design of the experimental procedure is combined with a statistical two-stepwise analysis to determine the optimal operating conditions for maximum recovery at a specified grade. The effect of independent variables on the responses has been explained. Combustible material recovery of 85–90% at clean coal product of 10–11% ash is obtained from feed of 29.6% ash, with a much-reduced amount of frother and collector than that used in conventional column flotation. The column flotation process utilizing pico and nano bubbles can also be extended to the lower limit and upper limit of particle size ranges, minus 75 lm and 300–600 lm, respectively, for better recovery.

Experimental research of the cavitation bubble dynamics during the second oscillation period near a spherical particle

In this paper,the dynamic behaviors of the cavitation bubble near a fixed spherical particle during the second oscillation period are analyzed based on the high-speed photographic system.The deformation and motion of the bubble during the second period are investigated by changing the distance between the particle and the bubble and the maximum radius of the bubble.Meanwhile,the variation of the equivalent radius and the centroid motions are analyzed,and the dynamic behaviors of the bubble are categorized according to the bubble morphological characteristics during the second period.Through this research,it is found that(1)The dynamic behaviors of the bubble during the second oscillation period could be divided into three typical cases:For case 1,a bulge would exist on the bubble interface away from the particle,and for case 2,a bulge would appear on the bubble interface and evolve towards the particle,while for case 3,the bubble would be divided into two parts.(2)The larger the dimensionless distance between the particle and the bubble,the smaller the maximum bubble equivalent radius in the second period,and the shorter the second oscillation period.(3)When the bubble is close to the particle,a counter-jet appears at the bubble interface away from the particle during the rebound stage.

Recent progress on the jetting of single deformed cavitation bubbles near boundaries

Cavitation occurs widely in nature and engineering and is a complex problem with multiscale features in both time and space due to its associating violent oscillations. To understand the important but complicated phenomena and fluid mechanics behind cavitation, a great deal of effort has been invested in investigating the collapse of a single bubble near different boundaries. This review aims to cover recent developments in the collapse of single bubbles in the vicinity of complex boundaries, including single boundaries and two parallel boundaries, and open questions for future research are discussed. Microjets are the most prominent features of the non-spherical collapse of cavitation bubbles near boundaries and are directed toward rigid walls and away from free surfaces. Such a bubble generally splits, resulting in the formation of two axial jets directed opposite to each other under the constraints of an elastic boundary or two parallel boundaries. The liquid jet penetrates the bubble, impacts the boundary, and exerts a great deal of stress on any nearby boundary. This phenomenon can cause damage, such as the erosion of blades in hydraulic machinery, the rupture of human blood vessels, and underwater explosions, but can also be exploited for applications, such as needle-free injection, drug and gene delivery, surface cleaning, and printing. Many fascinating developments related to these topics are presented and summarized in this review. Finally, three directions are proposed that seem particularly fruitful for future research on the interaction of cavitation bubbles and boundaries.

Experimental study of the dynamics of a single cavitation bubble excited by a focused laser near the boundary of a rigid wall

Based on high-speed photographic experiments,this study presents a detailed qualitative and quantitative analysis of the dynamics of a single cavitation bubble near the boundary of a rigid wall in asymmetric settings.The main findings are reported as follows:(1)The non-sphericity of the bubble interface decreases with increasing spacing between the bubble and the boundary,and the asymmetry of the bubble becomes more significant with increasing asymmetry angle.(2)The motion mode of the bubble cluster in the second oscillation cycle can be divided into two typical modes depending on the direction of movement.(3)The angle between the oblique jet pointing towards the upper wall surface and the horizontal direction in the second oscillation cycle decreases as the dimensionless spacing decreases.