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.

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.

Dynamic behaviors of cavitation bubble for the steady cavitating flow

In this paper, by introducing the flow velocity item into the classical Rayleigh-Plesset dynamic equation, a newequation, which does not involve the time term and can describe the motion of cavitation bubble in the steadycavitating flow, has been obtained. By solving the new motion equation using Runge-Kutta fourth order methodwith adaptive step size control, the dynamic behaviors of cavitation bubble driven by the varying pressure fielddownstream of a venturi cavitation reactor are numerically simulated. The effects of liquid temperature (correspondingto the saturated vapor pressure of liquid), cavitation number and inlet pressure of venturi on radial motionof bubble and pressure pulse due to the radial motion are analyzed and discussed in detail. Some dynamicbehaviors of bubble different from those in previous papers are displayed. In addition, the internal relationshipbetween bubble dynamics and process intensification is also discussed. The simulation results reported in thiswork reveal the variation laws of cavitation intensity with the flow conditions of liquid, and will lay a foundationfor the practical application of hydrodynamic cavitation technology.

Experimental study of the interaction between the spark-induced cavitation bubble and the air bubble

Experiments are carried out by using high-speed photography to investigate the interaction between the spark-generated cavitation bubble and the air bubble in its surrounding fluid. Three problems are discussed in detail： the impact of the air bubble upon the development of the cavitation bubble, the evolution of the air bubble under the influence of the cavitation bubble, and the change of the fluid pressure during the development of a micro jet of the cavitation bubble. Based on the experimental results, under the condition of no air bubble present, the lifetime of the cavitation bubble from expansion to contraction increases with the increase of the maximum radius. On the other hand, when there is an air bubble present, different sized cavitation bubbles have similarity with one another generally in terms of the lifetime from expansion to contraction, which does not depend on the maximum radius. Also, with the presence of an air bubble, the lifetime of the smaller cavitation bubble is extended while that of the bigger ones reduced. Furthermore, it is shown in the experiment that the low pressure formed in the opposite direction to the cavitation bubble micro jet makes the air bubble in the low pressure area being stretched into a steplike shape.

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.

Cavitation bubbles collapse characteristics behind a convex body

Cavitation bubbles behind a convex body were experimentally studied by a high speed camera and a hydrophone synchronously. The experiments were conducted in a circulating water tunnel with five various contraction ratios： β = 0.497, β= 0.6, β= 0.697, β= 0.751, and β= 0.799. The distributions of the cavitation bubble collapse positions behind the five different convex bodies were obtained by combining the images taken by the high speed camera. According to the collapse positions, it was found that no cavitation bubble was collapsed in the region near the wall until the ratio of the water head loss over the convex body height was larger than 20, which can be used to predict if the cavitation damage would occur in the tunnel with orifice energy dissipaters.

High-speed photographic observation of collapse of two cavitation bubbles

Cavitation as a hydrodynamic phenomenon exists widely in water conservancy, shipbuilding, chemical and many other industries.Previous cavitation bubble dynamic studies mainly focused on single cavitation bubbles and their interaction with the wall. This paper studies the interaction between two cavitation bubbles under conditions with or without a wall. The results show that if the inception of two cavitation bubbles is not synchronized, the cavitation bubble of early inception collapse backwards the cavitation bubble of later inception; if the inception of two cavitation bubbles is synchronized, the two bubbles collapse towards each other; if a wall exists nearby, no matter whether the line connecting the centers of the two cavitation bubbles is vertical or parallel to the wall, the two cavitation bubbles collapse towards each other and then gradually merge, and the merged collapse body quickly moves to the wall. It is suggested that, as the number of cavitation bubbles increases, the cavitation erosion effect is not simply increased proportionally. Instead, mutual inhibitory effect may be demonstrated.

Collapse of cavitation bubbles near air bubbles

The cavitation erosion is one of the common damage modes in water engineering.The study of the interaction among cavitation bubbles,air bubbles and the wall is of great significance for understanding the mechanism of the air entrainment to alleviate the cavitation and to enhance the cavitation erosion mitigation effect of aeration.By using the high-speed camera,the regular patterns of the collapse of cavitation bubbles in the vicinity of the wall and the air bubbles are studied in this paper.It is shown that in the vicinity of air bubbles,the cavitation bubbles may only collapse towards or from air bubbles,while under the dual impacts of air bubbles and the wall,the direction of collapse of the cavitation bubbles depends on the combined vector of the impact forces of the air bubbles and the wall.When the air bubbles are very close to the cavitation bubbles,the air bubbles will be penetrated and stretched by the cavitation bubbles,when the distance between them is short enough,the cavitation bubbles and the air bubbles will connect to form gas-type cavitation bubbles,and the collapse strength will be significantly decreased,when there are two air bubbles near the cavitation bubbles,they may even be penetrated successively by the cavitation bubbles.Thus it can be concluded that during the air entrainment to alleviate the cavitation,the number of air bubbles is more important than the total air concentration.

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.

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.

Simulation of Heat Transfer with the Growth and Collapse of a Cavitation Bubble Near the Heated Wall

The growth and collapse behaviors of a single cavitation bubble near a heated wail and its effect on the heat transfer are numerically investigated. The present study is designed to reveal the mechanism of cavitation enhanced heat transfer from a microscopic perspective. In the simulation, the time-dependent Navier-Stokes equations are solved in an axisymmetric two-dimensional domain. The volume of fluid （VOF） method is employed to track the liquid-gas interface. It is assumed that the gas inside the bubble is compressible vapor, and the sur- rounding liquid is incompressible water. Mass transfer between two phases is ignored. The eaiculated bubble pro-files were compared to the available experimental data, and a good agreement was obtained. Then, the relationship among bubble motion, flow field and surface heat transfer coefficient was analyzed. On this basis, the effects of such factors as the initial distance between the bubble and the wall, the initial vapor pressure and the initial bubble nucleus size on the heat transfer enhancement are discussed. The present study is helpful to understand the heat transfer phenomenon in presence of cavitation bubble in liquid.