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.

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.

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.

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.

Deflection of cavitation bubble near the rigid wall with a gas-containing hole

The presence of a rigid wall causes a microjet of the cavitation bubble to collapse to move toward the wall,while a free surface does the opposite.When a rigid wall surface is combined with a free surface,it may affect the direction of the microjet.The motive of this study is to find out the influence of the dynamic behavior of a laser-induced bubble near the rigid wall with a gas-containing hole.Evolutions of the bubble at different distances from the gas-containing hole in the horizontal and vertical directions were recorded by a high-speed camera(2.3×10^(5) fps).When the bubble collapse near the boundary,the bubble will produce two situations:away from or toward the boundary.It focuses on the direction of the bubble,the oscillation period of a bubble,and reflection angle,and quantitative analysis of the results.It was found that the boundary not only changes the morphologic of the bubble and the overall direction of movement but also affects the oscillation period.In addition,it can control the deflection of the bubble.

Effect of liquid viscoelasticity on the interactions between cavitation bubbles and free surfaces

The influence of liquid viscoelasticity on the interaction between cavitation bubbles and free surfaces is of great practical significance in understanding bubble dynamics in biological systems. A series of millimeter cavitation bubbles were induced by laser near the free surfaces of the water and viscoelastic polyacrylamide (PAM) solutions with different concentrations. The effects of liquid viscoelasticity on the interactions of cavitation bubbles with free surfaces are analyzed from the perspectives of the evolution of free surface and bubble dynamics. The experimental results show that as the dimensionless standoff distance increases, the evolutions of free surface behaviors in all experimental fluids can be divided into six types of water mounds, i.e., breaking wrinkles, spraying water film, crown, swallowed water spike, hillock, and slight bulge. All the critical values of the dimensionless distance dividing different types decrease with increasing concentration. The evolutions of first four types of water mounds in PAM solutions differ from those in the water. Water droplets splashing in different directions are produced around the breaking wrinkles in the water. Meanwhile, the breaking wrinkles in PAM solution move with the “liquid filaments” towards the central axis. The water spike in the pattern of spraying water film in PAM solution is more stable than that in the water. As the solution concentration increases, the water skirt in the pattern of crown contracts earlier and faster, and the rate of increase in the height of the water skirt decreases. For swallowed water spike in PAM solution, the upper part of the newly formed water spike is not significantly thicker than the middle part, and thus the water waist structure does not form. Liquid viscoelasticity inhibits the bubble growth and collapse, and the bubble migration as well, especially in the second period. Shorter and thicker cavities are formed in PAM solutions with higher concentration, while slender and stable cavities formed in the water at the same dimensionless distance. The velocity and displacement of the tip of bullet jet both decrease as the solution concentration increases.

Investigations of the dynamical behaviors of a millimeter-scale cavitation bubble near the rigid wall

The collapse of the cavitation bubble near the rigid wall emits shock waves and creates micro-jet,causing cavitation damage and operation instability of the hydraulic machinery.In this paper,the millimeter-scale bubble near the rigid wall was investigated experimentally and numerically with the help of a laser photogrammetry system with nanosecond-micron space-time resolution and the open source package OpenFOAM-2212.The morphological characteristics of the bubble during its growth phase,collapse phase and rebound phase were observed by experiment and numerical simulation,and characteristics of the accompanying phenomena including the shock wave propagation and micro-jet evolution were well elucidated.The numerical results agree well with the experimental data.The bubble starts from a tiny small size with high internal pressure and expands into a sphere with a radius of 1.07 mm forγ=d/R_(max)=1.78.The bubble collapses into a heart shape and moves towards to the rigid wall during its collapse phase,resulting in a higher pressure load for the rigid wall in the second collapse.The maximum pressure of the shock wave of the first bubble collapse phase reaches 5.4 MPa,and the velocity of the micro-jet reaches approximately 100 m/s.This study enriches the existing experimental and numerical results of the dynamics of the near-wall cavitation bubble.

Influence of bubble-particle distance on the dynamic behaviors of a cavitation bubble near a particle

Cavitation and silt-erosion often co-exist, causing severe damage on fluid machinery. In this paper, the dynamic behavior of a cavitation bubble near a fixed spherical particle is numerically studied, with the focus on the influence of the stand-off distance γ on the bubble collapse morphology, micro-jet velocities and pressure on the particle. With the increase in the value of γ, the bubble profile in the collapse stage exhibits three distinct characteristics: Mushroom-shaped, pear-shaped and spherical-shaped, and the corresponding micro-jets are identified as contact jet, non-contact jet, and long-distance jet. All studied distances can be categorized into three ranges, and the typical cases in each range are demonstrated. The maximum jet velocity Vmax and the maximum pressure difference between the upper and the bottom of the particle Δpmax show the highest peak at γ = 0.9, with Vmax up to 180 m/s and Δpmax up to 10.8 MPa.

Laser-induced cavitation bubble near boundaries

Laser-induced cavitation bubble has been widely used to investigate the mechanisms of hydraulic machinery cavitation erosion and to explore applications in atomization, alloy strengthening, ultrasonic chemistry, biomedicine, surface cleaning and materials processing. This paper consolidates existing research findings on the cavitation bubble dynamics near different boundaries and provides insights for future research work. Firstly, the dynamics of a single cavitation bubble in an infinite field is presented. Subsequently, the focus shifts to the dynamics of cavitation bubble near a rigid wall, angular walls, particles and hydrofoil. Lastly, the paper delves into the dynamics of cavitation bubble within a droplet, revealing the microscopic mechanism of droplet breakup induced by cavitation bubble.

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.

INTERACTION OF A CAVITATION BUBBLE AND AN AIR BUBBLE WITH A RIGID BOUNDARY

The motion of a spark-induced cavitation bubble and an air bubble near a rigid boundary is experimentally studied by using high-speed photography.Several dimensionless parameters are used to describe the geometrical configuration of the bubble-bubble-boundary interaction.The bubble-bubble interaction can be considered in two different conditions.The cavitation bubble will collapse towards the air bubble if the air bubble is relatively small,and away from the air bubble if the air bubble is relatively large.The two zones are identified in the bubble-boundary interaction,and they are the danger zone and the safety zone.The relative position,the bubble-boundary distance and the bubble-bubble distance play important roles in the bubble-bubble-boundary interaction,which can be considered in several conditions according to the responses of the bubbles.Air jets are found to penetrate into the cavitation bubbles.The cavitation bubble and the air bubble（air jet） move in their own way without mixing.The motion of a cavitation bubble may be influenced by an air bubble and/or a rigid boundary.The influence of the air bubble and the influence of the boundary may be combined,like some thing of a vector.