Table of contents

It is our pleasure and privilege to welcome all the participants of the 9th International Symposium on Cavitation (CAV2015) to Lausanne.

Since its initiation in 1986 in Sendai, Japan, the CAV symposium has grown to become the world's foremost event dedicated to cavitation. Hosted by EPFL (Ecole Polytechnique Fédérale de Lausanne) and staged at the SwissTech Convention Center, CAV2015 is a unique opportunity to exchange with leading scientists and industry experts about the latest advances in theoretical modelling, numerical simulation and experimentation related to cavitation phenomena with a special emphasis on practical applications.

The topics covered by CAV2015 include cavitation in ¬fluid machinery and fuel systems, bubble dynamics, cavitation erosion, advanced numerical simulation, sonochemistery, biomedicine and experimental techniques.

CAV2015 will also host an exhibition of leading providers of state of the art measurement equipment, including high-speed imaging systems, non-intrusive velocimetry, pressure sensors, as well as numerical solvers.

We have accepted over 190 papers, which will be presented in four parallel sessions. The proceedings will appear in the open access Journal of Physics: Conference Series (JPCS), which is part of the IOP Conference Series. All published papers are fully citable and upon publication will be free to download in perpetuity. We would like to thank all the reviewers for their great help during the selection process.

We will also propose six plenary speakers to highlight cavitation issues in different fields.

Finally, we would like to warmly thank our sponsors for their valuable support and the local Organizing Committee for the efforts in setting up this important event.

We look forward to seeing you in Lausanne!

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

This paper is concerned with observations of the translation of a microbubble (80 μm or 137 μm in radius) in a viscoelastic medium (3 w% gelatin), which is induced by acoustic radiation force originating from 1 MHz focused ultrasound. An optical system using a high-speed camera was designed to visualize the bubble translation and deformation. If the bubble remains its spherical shape under the sonication, the bubble translation we observed can be described by theory based on the Voigt model for linear viscoelastic solids; mechanical properties of the gelatin are calculated from measurements of the terminal displacement under the sonication.

Numerical modelling of sound scattered by ultrasound contrast agent bubbles in arteries is presented. Nonlinear dynamics of an encapsulated microbubble coupled with transmission of sound through liquid-filled flexible tubing is developed. Based on the frequency response, a normal artery can be distinguished from that of a stenosed artery. Effects of parameters like incident pressure amplitude, driving frequency and degree of stenosis are studied. It is further found that the effect of variable pressure produced by blood flow does not have a significant effect on the observed sound pressure levels.

Sonoporation using low-frequency high-pressure ultrasound (US) is a non-viral approach for in vitro and in vivo gene delivery. We developed a new sonoporation device designed for spatial and temporal control of ultrasound cavitation. This device was evaluated for the in vitro transfection efficiency of a plasmid coding for Green Fluorescent Protein (peGFP- C1) in adherent and non-adherent cell lines. The frequency spectrum of the signal receive by a hydrophone is used to compute a cavitation index (CI) representative of the inertial cavitation activity. The influence of the CI on transfection efficiency, as well as reproducibility were determined. A real-time feedback loop control on CI was integrated in the process to regulate the cavitation level during sonoporation. In both adherent and non-adherent cell lines, the sonoporation device produced a highly efficient transfection of peGFP-C1 (40-80%), as determined by flow cytometry analysis of GFP expression, along with a low rate of mortality assessed by propidium iodide staining. Moreover, the sonoporation of non-adherent cell lines Jurkat and K562 was found to be equivalent to nucleofection in terms of efficiency and toxicity while these two cell lines were resistant to transfection with lipofection.

Laser lithotripsy is a medical procedure for fragmentation of urinary stones with a fiber guided laser pulse of several hundred microseconds long. Using high-speed photography, we present an in-vitro study of bubble dynamics and stone motion induced by Ho:YAG laser lithotripsy. The experiments reveal that detectable stone motion starts only after the bubble collapse, which we relate with the collapse-induced liquid flow. Additionally, we model the bubble formation and dynamics using a set of 2D Rayleigh-Plesset equations with the measured laser pulse profile as an input. The aim is to reduce stone motion through modification of the temporal laser pulse profile, which affects the collapse scenario and consequently the remnant liquid motion.

This study reports the technical breakthrough in generating intense ultrasonic cavitation in the confinement of a microfluidics channel [1], and applications that has been developed on this platform for the past few years [2,3,4,5]. Our system consists of circular disc transducers (10-20 mm in diameter), the microfluidics channels on PDMS (polydimethylsiloxane), and a driving circuitry. The cavitation bubbles are created at the gas- water interface due to strong capillary waves which are generated when the system is driven at its natural frequency (around 100 kHz) [1]. These bubbles oscillate and collapse within the channel. The bubbles are useful for sonochemistry and the generation of sonoluminescence [2]. When we add bacteria (Escherichia coli), and yeast cells (Pichia pastoris) into the microfluidics channels, the oscillating and collapsing bubbles stretch and lyse these cells [3]. Furthermore, the system is effective (DNA of the harvested intracellular content remains largely intact), and efficient (yield reaches saturation in less than 1 second). In another application, human red blood cells are added to a microchamber. Cell stretching and rapture are observed when a laser generated cavitation bubble expands and collapses next to the cell [4]. A numerical model of a liquid pocket surrounded by a membrane with surface tension which was placed next to an oscillating bubble was developed using the Boundary Element Method. The simulation results showed that the stretching of the liquid pocket occurs only when the surface tension is within a certain range.

Microbubbles are used as contrast agents in ultrasound medical imaging. Once the microbubbles are injected into the body, they flow through the vascular system, confined by viscoelastic boundaries. The proximity of the boundaries affects the dynamics of the bubbles in ultrasound, in a manner that depends on the boundary's viscoelastic properties. Experiments on violently collapsing bubbles have revealed the dynamics of deformation of blood vessel walls. However, the deformation field induced by a bubble undergoing small-amplitude oscillations, relevant for ultrasound imaging, is difficult to access in experiment, and has not been reported yet. We present an experimental method to measure the deformation field induced by a bubble oscillating inside a microchannel within a tissue phantom. We use high-speed video microscopy to track the displacement of tracer particles embedded in the phantom, along with the dynamics of the bubble.

In recent years, cavitation is increasingly utilized in a wide range of applications in biomedical field. Monitoring the spatial-temporal evolution of cavitation bubbles is of great significance for efficiency and safety in biomedical applications. In this paper, several acoustic methods for cavitation mapping proposed or modified on the basis of existing work will be presented. The proposed novel ultrasound line-by-line/plane-by-plane method can depict cavitation bubbles distribution with high spatial and temporal resolution and may be developed as a potential standard 2D/3D cavitation field mapping method. The modified ultrafast active cavitation mapping based upon plane wave transmission and reception as well as bubble wavelet and pulse inversion technique can apparently enhance the cavitation to tissue ratio in tissue and further assist in monitoring the cavitation mediated therapy with good spatial and temporal resolution. The methods presented in this paper will be a foundation to promote the research and development of cavitation imaging in non-transparent medium.

As an emerging cavitation technology, photoacoustic cavitation (PAC) means the formation of bubbles in liquids using focused laser and pre-established ultrasound synchronously. Its significant advantages include the decreased threshold of each modality and the precise location of cavitation determined by the focused laser. In this paper, a brief review of PAC is presented, including the physical mechanism description, the classic experimental technology, the representative results in variety of media, and its applications in biomedical imaging and therapy. Moreover, some preliminary results of PAC in perfluoropentane (PFP) liquid and PFP droplets investigated by passive cavitation detection (PCD) in our group are also presented.

In this study, the relationship between the efficiency of pulsed focused ultrasound (FUS)-induced thrombolysis and the size distribution of cavitation bubbles has been studied. Firstly, the thrombolysis efficiency, evaluated by degree of mechanical fragmentation was investigated with varying duty cycle. Secondly, the size distribution of cavitation bubbles after the 1st, 10³th and 10⁵th pulse during experiments for various duty cycles was studied. It was revealed that the thrombolysis efficiency was highest when the cavitation bubble size distribution was centred around linear resonance radius of the emission frequency of the FUS transducer. Therefore, in cavitation enhanced therapeutic applications, the essential of using a pulsed FUS may be controlling the size distribution of cavitation nuclei within an active size range so as to increase the treatment efficiency.

Single bubble dynamics in the vicinity of a solid boundary submerged in water were studied experimentally. Single bubble inside a water tank was generated by a spark discharge of capacitor into a couple of copper wires closing a simple circuit. A circular polycarbonate plate was placed horizontally above the bubble creation site. Polycarbonate plates with two different thicknesses were tested by changing the distance between the plate and the creation site. The effects of distance to the wall and wall thickness on the bubble motion is observed by considering the fluid-structure interaction. It is shown that motion of the two boundaries during the bubble generation differ from each other. Jetting behavior of two cases is also different.

A study is presented of the interaction of a shock wave with gas cavities cast in a hydrogel. Simulations are conducted using a front-tracking approach, whereby Lagrangian hypersurfaces are used to model the interface between materials. These 'fronts' are overlaid on an Eulerian grid which is used to model the bulk flow. Results are compared to an experimental investigation, in which a light gas gun is used to create ∼600 MPa shock waves in hydrogel blocks, within which air cavities have been cast. Experimental results are presented, including temporally resolved measurements of light emission. Comparison between experimental and simulated results shows good agreement.

In the present paper a diffuse interface approach [1] is used to address the collapse of a sub-micron vapor bubble near solid boundaries. This formulation enables an unprecedented description of interfacial flows that naturally takes into account topology modification and phase changes (both vapor/liquid and vapor/supercritical fluid transformations). Results from numerical simulations are exploited to discuss the complex sequence of events associated with the bubble collapse near a wall, encompassing shock-wave emissions in the liquid and reflections from the wall, their successive interaction with the expanding bubble, the ensuing asymmetry of the bubble and the eventual jetting phase.

The acting force mechanism of the water layer of the cavity on a body when it crosses the water surface is studied. A simplified mechanical model is proposed to explain the mechanism of the impact of the water layer onto the body. The estimating formula for the maximum pressure in the water layer and on the body surface impacted by the water layer is derived. It is proved that the maximum pressure is always in proportion to the square of the moving velocity of the maximum pressure position.

Cavitation associated with the impact of a sphere on a flat surface is investigated using high-speed photography. The sphere, of diameter 15 or 45 mm and made from Ertacetal^® or stainless steel, was fully submerged and accelerated using a spring-loaded mechanism to achieve Reynolds numbers based on impact velocity and sphere radius of up to 7.2×10⁴. The static pressure and impact velocity were varied to achieve cavitation numbers ranging from 8.9 to 120.9. High-speed photography of the impacting sphere and induced cavitation bubble was filmed at 105-140 kHz. A log law relationship was found between the non-dimensional maximum bubble radius and the cavitation number. The relationship was modulated by the material properties. Interaction between the sphere and the bubble was also noted.

The breakup of a millimetre size buoyantly rising bubble encountering a horizontal plane turbulent jet is experimentally investigated using high-speed shadowgraphy and acoustic techniques. The bubble diameter to jet height ratio is 0.75 and the jet height based Reynolds number is 4000. The high-speed imaging was recorded at 7 kHz simultaneous with hydrophone output at 100 kHz. Bubble breakup events were seen to produce simple binary divisions into products of similar size as well as three products where at least one was much smaller than the other products. Coalescence of products was also observed. In almost all cases time-frequency analysis of the acoustic emissions enabled the products to be identified and sized.

The thermal behaviour of a spherical gas bubble in a liquid driven by an acoustic pressure is investigated in the uniform pressure approximation by employing an iterative method to solve the energy balance equations between the gas bubble and the surrounding liquid for the temperature distribution and the gas pressure inside the bubble. It is shown that the first iterative solution leads to the first order law of the gas pressure as a polytropic power law of the bubble wall temperature and of the bubble radius, with the polytropic index given as an explicit function of the isentropic exponent of the gas. The resulting first order law of the gas pressure reduces to the classical isothermal and adiabatic laws in the appropriate limits. The first order gas pressure law is then applied to an acoustically driven cavitation bubble by solving the Rayleigh-Plesset equation. Results obtained show that the bubble wall temperature pulsations during collapse and rebound can become a few orders of magnitude higher than the bulk liquid temperature.

In this paper we investigate the initial sequence of events that lead to the fragmentation of a millimetre sized water droplets when interacting with a focused ns-laser pulse. The experimental results show complex processes that result from the reflection of an initial shock wave from plasma generation with the soft boundary of the levitating droplet; furthermore, when the reflected waves from the walls of the droplet refocus they leave behind a trail of microbubbles that later act as cavitation inception regions. Numerical simulations of a shock wave impacting and reflecting from a soft boundary are also reported; the simulated results show that the lowest pressure inside the droplet occurs at the equatorial plane. The results of the numerical model display good agreement with the experimental results both in time and in space.

The dynamics of micro-bubbles, which are typical in many industrial applications, is addressed by means the Direct Numerical Simulations (DNS) of two prototypal flows, namely a homogeneous shear flow and a fully developed pipe flows. This preliminary study has a two-fold purpose. The homogenous turbulent shear flow is useful to characterize the bubble dynamics in terms of their eventual clustering properties which is expected to be controlled by the Stokes number. The time history of the fluid pressure experienced by the bubbles during their evolution is recorded and successively employed to force the Rayleigh-Plesset equation [1]. The ensuing data are used to address a posteriori the bubble diameter statistics in view of bubble collapse induced by strong and intermittent turbulent pressure fluctuations. The turbulent pipe flow simulations serve to address the bubble dynamics in wall bounded flows. Here the bubbles are observed to accumulate in the near-wall region with different intensity depending on the bubble dimensions.

The oscillations of a single bubble excited with a dual frequency acoustic field are numerically investigated. Computations are made for an air bubble in water exposed to an acoustic field with a linearly varying amplitude. The bubble response to an excitation containing two frequencies f₁ = 500kHz and f₂ = 400kHz at the same amplitude is compared to the monofrequency case where only f₁ is present. Time-frequency representations show a sharp transition in the bifrequency case, for which the low frequency component f₂ becomes resonant while the high frequency component f₁ is strongly attenuated. The temporal evolution of the power spectra reveals that the resonance of the low frequency component is correlated with the time varying mean radius of the bubble. It is also observed that the total power of the bubble response in the bifrequency case can reach almost twice the power obtained in the monofrequency case, which indicates a strong enhancement of the cavitating behavior of the bubble for this specific frequency combination.

A specific physics called 'crown phenomenon' is discovered in the interaction between weak buoyancy bubbles and free surface. The 'crown phenomenon' is that a circle of the outer fluid appears to surround the middle spike of water after the jet impact of bubbles, and this kind of spike is defined as 'crown spike'. In this study, the crown spike due to the coupling effect between two bubbles and free surface is studied both experimentally and numerically. In the experiment, copper wires in series connection are used to generate two inphase bubbles and the bubble and free surface shapes are recorded by high-speed photography. In the numerical study, a three-dimensional model is established to simulate the bubble-free- surface interaction with a boundary integral method and then the motion of free surface is further simulated without regard to the effect of bubbles after the jet impact. The computation also traces the 'crown phenomenon', which is considered as a second spike related to a large high-pressure region formed after the impact. The large high-pressure region leads to a thick column of water on the free surface and then the column of water gradually increases to surround the first spike. Both oblique jets and crown spike are observed in the experimental and numerical results, and the favorable agreements of bubbles and free surface shapes validate the present model. The effect of the inter-bubble distance on crown spike is also investigated.

The ghost fluid method is improved to include heat and mass transfer across the gas- liquid interface during the bubble collapse in a compressible liquid. This transfer is due to both nonequilibrium phase transition at the interface and diffusion of the noncondensable gas across the interface. In the present method, the ghost fluids are defined with the intention of conserving the total mass, momentum, and energy, as well as the mass of each component while considering the heat and mass fluxes across the interface. The gas phase inside the bubble is a mixture of vapor and noncondensable gas, where binary diffusion between the mixture components is taken into account. The gas diffusion in the surrounding liquid is also considered. This method is applied to a simulation of a single spherical bubble collapse with heat and mass transfer across the interface in a compressible liquid. When noncondensable gas is present, it accumulates near the interface due to vapor condensation, thereby preventing further condensation. This results in a weaker bubble collapse than the case without noncondensable gas.

The oscillations of a single spherical bubble in a soft surrounding medium are investigated numerically. In particular, the combined effects of the viscoelasticity and compressibility of the surroundings, as well as subsequent heating, on the bubble dynamics are quantified for forced and free collapse. In a Keller-Miksis framework, a Kelvin-Voigt viscoelastic model with full thermal effects is considered, in which the elastic term is represented by a Neo-Hookean model to account for the finite strains. The history and spatial distribution of the stresses and temperatures produced in the surroundings are examined and related to potential cavitation damage mechanisms.

Pressure wave propagation in a liquid containing several bubbles is numerically investigated. We simulate liner plane wave propagation in a liquid containing 10 spherical bubbles in a rectangular duct with the equation of motion for N spherical bubbles. The sound pressures of the reflected waves from the rigid walls are calculated by using the method of images. The result shows that the phase velocity of the pressure wave propagating in the liquid containing 10 spherical bubbles in the duct agrees well with the low-frequency speed of sound in a homogeneous bubbly liquid.

The effect of the density of cavitation nuclei on the state and flow structure of the magma melt in the case of its explosive decompression is numerically studied within the framework of the gas-dynamic model of mechanics of multiphase media. It is demonstrated that a zone with anomalously high values of the basic characteristics of the magma state is formed in the vicinity of the free surface of the magma column as the density of cavitation nuclei increases. A drastic increase in the particle velocity up to 150 m/s on the lower boundary of this zone testifies to a high probability of its separation from the main flow. Within the framework of the numerical scheme, this separation is "realized," and the dynamic behavior of the magma column remaining in the conduit is analyzed. It is shown that the detected effects of anomalous zone formation and possibility of separation turn out to be fairly stable, which allows one to define them as a 'self-sustained regime of cyclic ejections."

The high speed liquid jet is an important mechanism of damage to hydraulic machinery by cavitation bubbles, as well as damage to vessels by underwater explosion bubble. In this study, the bubble motion near a wall and the pressure impulse are investigated through experimental and numerical methods. In the experiment, the bubble is generated by the electric discharge, and a high speed camera is used to capture the bubble motion. Numerical studies are conducted using the boundary element method, and the vortex ring model is adopted to deal with the discontinued potential of the toroidal bubble. Calculated results show excellent agreement with experimental observations. Meanwhile, the dynamic pressure caused by the bubble in the flow domain is calculated by an auxiliary function, which improves the accuracy of the results. A highly localized pressure region will be generated on the wall by the bubble jet. The optimal stand-off parameter (the ratio of the distance the bubble center at inception from the wall to the maximum bubble radius) for a most damaging jet formation is around 0.9.

In this paper, we perform a theoretical analysis on the translational motions ofgas and encapsulated bubbles undergoing deformation. We verify our theoretical model for the case of a gas bubble collapsing near a wall. By comparison, the encapsulated bubble near the wall is less unstable in shape. In the second case, the translations of two gas bubbles subjected to an oscillating driving pressure agree with Bjerknes' theory, that is, the two bubbles repel each other when the driving frequency is between the two natural frequencies ω₀₁ < ω_d < ω₀₂; while the two bubbles move towards each other at ω_d < ω₀₁ or ω_d > ω₀₂. For encapsulated bubbles, the translational displacements are smaller than those of gas bubbles. The encapsulating membrane and the deformation affect the translational direction. The encapsulated bubbles are prone to experience repulsive motion at resonance.

Cavitation bubbles initiated by focused ultrasound waves are investigated through experiments and modeling. Pulses of focused ultrasound with a frequency of 335 kHz and a peak negative pressure of 8 MPa is generated in a water tank by a piezoelectric transducer to initiate cavitation. The pressure field is modeled by solving the Euler equations and used to simulate single bubble oscillation. The characteristics of cavitation bubbles observed by highspeed photography qualitatively agree with the simulation results. Finally, bubble clouds are captured using acoustic B-mode imaging that works synchronized with high-speed photography.

A diffuse interface model is exploited to study in details the dynamics of a cavitation vapor bubble, by including phase change, transition to supercritical conditions, shock wave propagation and thermal conduction. The numerical experiments show that the actual dynamic is a sequence of collapses and rebounds demonstrating the importance of nonequilibrium phase changes. In particular the transition to supercritical conditions avoids the full condensation and leads to shockwave emission after the collapse and to successive bubble rebound.

Beer tapping is a well known prank where a bottle of beer is impacted from the top by a solid object, usually another bottle, leading to a sudden foam overflow. A description of the shock-driven bubble dynamics leading to foaming is presented based on an experimental and numerical study evoking the following physical picture. First, the solid impact produces a sudden downwards acceleration of the bottle creating a strong depression in the liquid bulk. The existing bubbles undergo a strong expansion and a sudden contraction ending in their collapse and fragmentation into a large amount of small bubbles. Second, the bubble clouds present a large surface area to volume ratio, enhancing the CO₂ diffusion from the supersaturated liquid, hence growing rapidly and depleting the CO₂. The clouds of bubbles migrate upwards in the form of plumes pulling the surrounding liquid with them and eventually resulting in the foam overflow. The sudden pressure drop that triggers the bubble dynamics with a collapse and oscillations is modelled by the Rayleigh-Plesset equation. The bubble dynamics from impact to collapse occurs over a time (t_b ≃ 800 μs) much larger than the acoustic time scale of the liquid bulk (t_ac = 2H/c ≃ 80 μs), for the experimental container of height H = 6 cm and a speed of sound around c ≃ 1500 m/s. This scale separation, together with the comparison of numerical and experimental results, suggests that the pressure drop is controlled by two parameters: the acceleration of the container and the distance from the bubble to the free surface.

A binary formulation of the classical nucleation theory (CNT) is developed for homogeneous bubble nucleation in systems composed of a liquid solvent and a dissolved gas. The CNT predictions coincide with experimental nucleation data from the literature for diethylether/N₂ and isobutane/CO₂ mixtures, while several inconsistencies are identified for propane/CO₂ and R22/CO₂ experimental datasets.

The collapsing behavior of a bubble generated at the center of the rigid walls and its effect on the wall are investigated experimentally and numerically. The bubble collapse drastically depends on the ratio of the gap width to the maximum bubble radius w*. In case of 2.66 < w* < 1.17, by the decrease in w* to 2.5, the splitting collapse occurs; the bubble splits into two at the center of the gap during collapse and each bubble collapses near the wall with the translation toward nearer wall. Further decrease in w* to 1.4 causes neutral collapse where the bubble collapses at the center of the gap without splitting and translation. These collapsing behaviors are successfully simulated by considering the bubble shape at the maximum bubble volume. The peak pressure on the wall decreases by the transition of the collapsing behavior from the splitting collapse to the neutral collapse due to the decrease in w*, which indicates the wall damage reduction due to the neutral bubble collapse in thinner gap.

We experimentally study a shock-bubble interaction problem in a viscoelastic solid, which is relevant to shock wave lithotripsy. A gas bubble is produced by focusing an infrared laser pulse into gelatin. A spherical shock is then created, through rapid expansion of plasma that results from the laser focusing, in the vicinity of the gas bubble. The shock-bubble interaction is recorded by a CCD camera with flash illumination of a nanosecond green laser pulse. The observation captures cavitation inception in the gelatin under tension that results from acoustic impedance mismatching at the bubble wall. Namely, the shock reflects at the bubble interface as a rarefaction wave, which induces the nucleation of cavitation bubbles as a result of rupturing the gelatin.

Cavitation bubble collapse is influenced by nearby surfaces or objects. A bubble near a rigid surface will move towards the surface and collapse with a high speed jet. When a hard particle is suspended near a bubble generated by electric spark, the bubble expands and collapses moving the particle. We found that within a limit of stand-off distance, the particle is propelled away from the bubble as it collapses. At a slightly larger stand-off distance, the bubble collapse causes the particle to move towards the bubble initially before moving away. The bubble does not move the particle if it is placed far away. This conclusion is important for applications such as drug delivery in which the particle is to be propelled away from the collapsing bubble.

The importance of nucleation from wall-bounded nuclei for cavitation and especially cavitation inception is undisputed. Although various theories and models found their way to standard literature, there is a lack of experiments allowing a closer look onto the process of nucleation. In the present paper we present a new experimental set-up that allows the investigation and analysis of nucleation from wall-bounded nuclei. The experimental findings support an extended understanding of nucleation as a self excited cyclic process. Impressive high-speed visualisations can be found in the supplementary material.

The problem of coalescence of two pulsating spherical bubbles is studied using Lagrangian formalism in assumptions that the acoustic field is weak, the frequency of the external impact is appreciably less than natural oscillation frequency and influence of viscosity on phase of radii pulsation is small. The obtained necessary condition for coalescence of the bubbles is determined by the dimensionless parameter, whose boundary value is nonlinearly depending on the quotient of the bubbles' radii.

Nanobubbles of less than 400 nm in diameter were formed by plasma in pure water. Pre-breakdown plasma termed streamer discharges, generated gas channels shaped like fine dendritic coral leading to the formation of small bubbles. Nanobubbles were visualized by an optical microscope and measured by dynamic laser scattering. However, it is necessary to verify that these nanobubbles are gas bubbles, not solid, because contamination such as platinum particles and organic compounds from electrode and residue in ultrapure water were also observed.

A homogeneous liquid system and a heterogeneous system with an impurity inserted inside it were used for investigation of bubble nucleation by molecular dynamics simulation. A constant particle number, volume, and temperature ensemble was used. The systems with the impurities showed an overall increase in bubble formation, which is consistent with previous studies. The shape of the impurities was changed to see if there was any direct influence on the bubble nucleation rate. With the limited number of systems investigated, the occurrence of a shape effect was inconclusive. As observed in previous heterogeneous nucleation studies with walls, the bubble initially forms remotely from the impurity and remains at some distance from the seed.

We present detailed visualizations of the micro-jet forming inside an aspherically collapsing cavitation bubble near a free surface. The high-quality visualizations of large and strongly deformed bubbles disclose so far unseen features of the dynamics inside the bubble, such as a mushroom-like flattened jet-tip, crown formation and micro-droplets. We also find that jetting near a free surface reduces the collapse time relative to the Rayleigh time.

For a validation of the application of conventional bubble dynamics to a nano-scale bubble behaviour, we simulated a nano-scale bubble collapsing or vibration by Molecular Dynamics (MD) method and compared the result with the solution of Rayleigh-Plesset (RP) equation and that of Confined RP (CRP) equation, whose boundary condition was corrected to be consistent with that of MD simulation. As a result, a good coincidence was obtained between MD, RP, and CRP in the case of one-component fluid. In addition, also a good correspondence was obtained particularly in the comparison between MD and CRP in the case of two-component fluid containing non-condensable gas. The present results indicate that conventional bubble dynamics equation can be applied even to a nano-scale tiny bubble.

We present a study of transient oscillating bubble-elastic membrane interaction by means of an experiment and a numerical simulation to study the dynamics of bubble's inertial collapse near an elastic interface. The bubble is generated very close to a thin elastic membrane using an electric spark, and their interaction is observed using high speed photography. The high pressure and temperature plasma from the dielectric breakdown precedes the bubble formation. The bubble then expands and creates a dimple on the membrane. After reaching its maximum size, the bubble begins to collapse. The membrane retracts back, transmitting a perturbation on the bubble surface. The coupling between bubble contraction and this perturbation strengthens the collapse and leads to the formation of a mushroom-shaped bubble, bubble pinching and splitting. Towards the end of the collapse, the water inertia surrounding the bubble pulls the membrane upwards forming a relatively sharp conical hump. The dynamics of this interaction is well predicted by the boundary element method (BEM) simulation.

The problem of a gas bubble break-up in liquid is considered in the conditions of the frequencies resonance of the radial and n^th axially symmetric deformational mode 2:1. The nonlinear energy transfer between the modes is described using an efficient Krylov-Bogolyubov averaging technique. It is shown that the deformational mode magnitude can be some orders larger than the radial mode magnitude which is damped by the thermal, viscous and acoustic dissipation. The estimative criterion of bubble break-up is obtained in the cases of slow and fast acoustic wave start. The obtained pressure magnitudes in the wave for break-up are very small and the mechanism can have strong medical and technical applications.

Bubble formation is involved in many engineering applications. It is important to understand the dynamics of bubble formation. This work reports experimental and numerical results of bubble formation on submerged orifice under constant gas flow rate. Compressible large eddy simulation combined volume of fluid (VOF) was adopted in simulation and results was validated by experiment. Bubble formation is divided into three stages in this paper, expansion stage, elongation stage and pinch-off stage. In expansion stage, The bubble grows radially due to the incoming gas flux, but the bubble base remains attached to the orifice. But as gas injected, the spherical bubble will go into the elongation stage when the downward resultant force is lager than upward resultant force. And when bubble neck's length is bigger than √2R_o the bubble will go into pinch-off stage. Cylindrical Rayleigh-Plesset equation can be used to describe the pinch-off stage. Uncertain parameter r in it is given reference value in this paper.

Following the collapse of a vapour bubble inside a rigid tube, various outcomes could be caused by the propagation and reflection of the shock wave. Using high-speed camera system and hydrophone, the secondary cavitation and acoustic pressure curve due to the collapse of single bubble in a rigid tube are studied experimentally. The secondary cavitation has a decisive effect on the pressure pulse sequence, which usually appears at a certain area symmetric to the first bubble. Two particular cases of first bubble generated near the midpoint and the endings of the tube are also investigated, where the strength, position and period of the secondary cavitation show different features. The mechanism behind these results are discussed briefly, which is related to the propagation and reflection of the shock wave.

The inertial collapse of cavitation bubbles is known to be capable of damaging its surroundings. While significant attention has been dedicated to investigating the pressures produced by this process, less is known about heating of the surrounding medium, which may be important when collapse occurs near objects whose mechanical properties strongly depend on temperature (e.g., polymers). Using a newly developed computational approach that prevents pressure and temperature errors generated by naively implemented shock- and interface-capturing schemes, we investigate the dynamics of shock-induced collapse of gas bubbles near rigid surfaces. We characterize the temperature fields based on the relevant nondimensional parameters entering the problem. In particular, we show that bubble collapse causes temperature rises in neighboring solid objects via two mechanisms: the shock produced at collapse and heat diffusion from the hot bubble close to the object.

Material pitting in a cavitating flow has been used for a long time as an indicator of the vague 'cavitation intensity' concept. Periodically, some researchers suggest pitting tests as a "simple" means to provide quantitative measurements of the amplitude of the impulsive pressures in the cavitation field, especially when combined with Tabor's formula or with simple finite element computations with static loads. This paper examines the viability of such a method using fully coupled bubble dynamics and material response, and strongly concludes that the commonly accepted idea is a myth, as different loading scenarios with the same amplitude of the cavitation impulsive pressure result in different pit aspect ratios.

Recently simultaneous observation of both cavitation structures and cavitation damage, has pointed to the fact that the small scale structures and the topology of the cavitation clouds play a significant role in cavitation erosive potential. Although this opened some new insights to the physics of cavitation damage, many new questions appeared. In the present study we attached a thin aluminium foil to the surface of a transparent Venturi section using two sided transparent adhesive tape. The surface was very soft - prone to be severely damaged by cavitation in a very short period of time. Using high speed cameras, which captured the images at 30000 frames per second, we simultaneously recorded cavitation structures (from several perspectives) and the surface of the foil. Analysis of the images revealed that five distinctive damage mechanisms exist - spherical cavitation cloud collapse, horseshoe cavitation cloud collapse, the "twister" cavitation cloud collapse and in addition it was found that pits also appear at the moment of cavitation cloud separation and near the stagnation point at the closure of the attached cavity.

The experimental works presented in here contribute to the clarification of erosive effects of hydrodynamic cavitation. Comprehensive cavitation erosion test series were conducted for transient cloud cavitation in the shear layer of prismatic bodies. The erosion pattern and erosion rates were determined with a mineral based volume loss technique and with a metal based pit count system competitively. The results clarified the underlying scale effects and revealed a strong non-linear material dependency, which indicated significantly different damage processes for both material types. Furthermore, the size and dynamics of the cavitation clouds have been assessed by optical detection. The fluctuations of the cloud sizes showed a maximum value for those cavitation numbers related to maximum erosive aggressiveness. The finding suggests the suitability of a model approach which relates the erosion process to cavitation cloud dynamics. An enhanced experimental setup is projected to further clarify these issues.

The relationship between mechanical properties and the erosion rate was examined for chloroprene rubber and a number of polyethylene materials produced by different methods. As electric power plants are in operation over long periods of time, the effect of aging was also examined by testing material intended for use in pipes in electric power plants. Cavitation erosion tests were carried out by using a flowing apparatus as specified in the American Society for Testing Materials G134-95 standard. A flow velocity of 150 m/s and a test time of 24hours, were the experimental conditions used for a cavitating liquid jet test on polyethylene. The maximum depth of erosion rate (MaxDER) of polyethylene was found to decrease with the increase in hardness. Among all the tested materials, the relatively high molecular weight polyethylene with low density (m-LLDPE-H), showed the best resistance to cavitation erosion in terms of MaxDER. The effect of aging on the erosion rate of polyethylene was limited.

Cavitation erosion tests for epoxy, unsaturated polyester, polycarbonate, and acrylic resin were conducted under various tensile stress conditions (Tensile-Cavitation test). A new testing device was designed to conduct the Tensile-Cavitation test and observe specimen surface during the experiment based on ASTM G32. When tensile stress of 1.31 MPa was loaded on epoxy resin, cracks occurred on the specimen after 0.5 hours during cavitation erosion. When no tensile stress was loaded on the epoxy resin, the damage was general cavitation erosion only. As well as the epoxy resin, unsaturated polyester resin applied tensile stress of 1.31 MPa and polycarbonate resin of 6.54 MPa indicated erosion damages and cracks. When tensile stress of 6.54 MPa was loaded on acrylic resin, the erosion damage was almost the same as the results without tensile stress. We confirmed that anti-cavitation property of epoxy resin was higher than those of acrylic and polycarbonate without tensile stress while the damage of epoxy resin was much serious than that of acrylic resins under tensile stress loadings.

The prediction of erosion under unsteady cavitation is crucial to prevent damage in hydraulic machinery. The present investigation deals with the numerical simulation of erosive partial cavitation around a NACA0015 hydrofoil. The study presents the calculation of the bubble collapse strength, Sb, based on the bubble potential energy to identify the surface areas with highest risk of damage. The results are obtained with a numerical scheme assuming homogeneous mixture flow, implicit LES and Zwart cavitation model. The 3D unsteady flow simulation has been solved using OpenFOAM. Python language and OpenFOAM calculator (foamCalcEx) have been used to obtain and represent Sb. The obtained results clearly show the instants of erosive bubble collapse and the affected surface areas.

A PVDF pressure sensor was used to measure the pressure peaks due to the collapse of cavitation bubbles in the high-speed tunnel of the LEGI laboratory. It was flush mounted on a stainless steel disk in the most erosive area of the test section. The recorded data were post- processed in order to get the impact load spectra for different velocities at constant cavitation number. The results are presented as cumulative histograms of peak rate and maximal impact load for different flow velocities of the high-speed tunnel.

A compressible inviscid flow solver with barotropic cavitation model is applied to two different ultrasonic horn set-ups and compared to hydrophone, shadowgraphy as well as erosion test data. The statistical analysis of single collapse events in wall-adjacent flow regions allows the determination of the flow aggressiveness via load collectives (cumulative event rate vs collapse pressure), which show an exponential decrease in agreement to studies on hydrodynamic cavitation [1]. A post-processing projection of event rate and collapse pressure on a reference grid reduces the grid dependency significantly. In order to evaluate the erosion-sensitive areas a statistical analysis of transient wall loads is utilised. Predicted erosion sensitive areas as well as temporal pressure and vapour volume evolution are in good agreement to the experimental data.

This paper is devoted to cavitation erosion modeling. It presents some recent numerical developments made in the code initially developed in collaboration with E.Johnsen and collaborators at University of Michigan [1] in order to account for fluid-structure interaction. The considered test case is that of a single air bubble collapsing near a wall due to an incident shock wave in the surrounding water. In our investigation, we focus on the code implementation and optimization and the bubble implosion mechanism. The paper is focused on the various events occurring during bubble collapse and the computation of the time evolution of the pressure distribution. The influence of the amplitude of the incident wave and the distance of the bubble to the wall are investigated.

The present work aims to predict cavitation erosion using a numerical flow solver together with a new developed erosion model. The erosion model is based on the hypothesis that collapses of single cavitation bubbles near solid boundaries form high velocity microjets, which cause sonic impacts with high pressure amplitudes damaging the surface. The erosion model uses information from a numerical Euler-Euler flow simulation to predict erosion sensitive areas and assess the erosion aggressiveness of the flow. The obtained numerical results were compared to experimental results from tests of an axisymmetric nozzle.

Lloyd's Register Technical Investigation Department (LR TID) have developed numerical functions for the prediction of cavitation erosion aggressiveness within Computational Fluid Dynamics (CFD) simulations. These functions were previously validated for a model scale hydrofoil and ship scale rudder [1]. For the current study the functions were applied to a cargo ship's full scale propeller, on which the severe cavitation erosion was reported. The performed Detach Eddy Simulation (DES) required a fine computational mesh (approximately 22 million cells), together with a very small time step (2.0E-4 s). As the cavitation for this type of vessel is primarily caused by a highly non-uniform wake, the hull was also included in the simulation. The applied method under predicted the cavitation extent and did not fully resolve the tip vortex; however, the areas of cavitation collapse were captured successfully. Consequently, the developed functions showed a very good prediction of erosion areas, as confirmed by comparison with underwater propeller inspection results.

The prediction of pressure fluctuations amplitudes on Francis turbine prototype is a challenge for hydro-equipment industry since it is subjected to guarantees to ensure smooth and reliable operation of the hydro units. The European FP7 research project Hyperbole aims to setup a methodology to transpose the pressure fluctuations measured on the reduced scale model to the prototype generating units. This paper presents this methodology which relies on an advanced modelling of the draft tube cavitation flow, and focuses on the transposition to the prototype of the draft tube model parameters identified on the reduced scale model. Different modelling assumptions of the draft tube are considered and their influence on the eigenmodes and the forced response of the system are presented.

The 1D modelling of cavitation vortex rope dynamics in Francis turbine draft tube is decisive for prediction of pressure fluctuations in the system. However, models are defined with parameters which values must be quantified either experimentally or numerically. In this paper a methodology based on CFD simulations is setup to identify these parameters by exciting the flow through outlet boundary condition. A simplified test case is considered to assess if 1D cavitation model parameters can be identified from CFD simulations. It is shown that a low wave speed and a second viscosity due to the cavitating flow can be identified.

Estimations of scale effects on blade cavitation require consideration of multiple models for both water flows and cavities. In particular, distinction of laminar and turbulent boundary layers is very important. A qualitative impact of selection of models is manifested for blade sheet cavitation. Its quantitative impact is shown for vortex cavitation inception.

The cavitation on the lip of a flushed water-jet inlet has been simulated with a transient RANS model and the results has been validated against experiments. The k-ω SST turbulence model has been adopted together with the cavitation correction proposed by Reboud. The defined setup shows promising results and the vortex shedding has been qualitatively predicted. Moreover, the importance of the sufficient spatial resolution to capture the cavity closure and its extension has been studied and proved to be crucial.

1D hydro-electric models are useful to predict dynamic behaviour of hydro-power plants. Regarding vortex rope and cavitation surge in Francis turbines, the 1D models require some inputs that can be provided by numerical simulations. In this paper, a 2D cavitating Venturi is considered. URANS computations are performed to investigate the dynamic behaviour of the cavitation sheet depending on the frequency variation of the outlet pressure. The results are used to calibrate and to assess the reliability of the 1D models.

The cavitation helical vortex rope arising at Francis turbine partial load induces pressure fluctuations at the rope precession frequency, which can be decomposed into two components; the convective one and the synchronous one. The latter acts as an excitation source for the hydraulic system and is amplified in case of resonance. The present paper aims to highlight the impact of both components on the mechanical behaviour of the runner by performing on-board measurements. It is shown that the use of on-board pressure sensors enables to naturally separate the components of the pressure fluctuations. In addition, the synchronous component has little impact on the mechanical behaviour of the runner, even for the case in which hydro-acoustic resonance occurs.

The size of axial flow pumps used in drainage pump stations has recently decreased, and their rotation speeds have increased, causing an increase in the risk of cavitation. Therefore, to provide highly reliable pumps, it is important to understand the internal flow of pumps under cavitating conditions. In this study, high-speed camera measurements and computational fluid dynamics analysis were performed to understand the cavitation performance of an axial flow pump. The mechanism that causes the head to change as a result of cavitation under low net positive suction head values is shown to be the balance between the increasing angular momentum and the loss indicated by the changing streamlines.

The backflow-vortex cavitation on a rotating inducer was experimentally observed in both liquid nitrogen and water. The cavitation appeared "foggy" in nitrogen and "foamy" in water. This is explained by the critical Weber number theory. The number of backflow-vortex cavitation columns decreased as the head coefficient increased. This tendency is explained by a theoretical analysis in which backflow vortices are regarded as an array of vortex filaments rotating along the casing around the inducer center. The number of backflow-vortex cavitation columns is determined by the fluid dynamics and is independent of thermodynamic properties.

A progress made in numerical simulation of turbulent cavitating flow in an axial waterjet pump (ONR AxWJ-2) is presented. The computational approach is designed to resolve the interaction between the rotor and the stator both in time and in space comprising the full 360° sector of the pump, using a scalable finite-volume-based Navier-Stokes solver. Unsteady Reynold-Averaged Navier-Stokes (URANS) and a hybrid of URANS and Large Eddy Simulation (LES) are employed for turbulence modeling and also for directly capturing some of large-scale coherent structures in the flow. A continuum mixture approach based on phasic volume-fraction is adopted along with a finite-rate mass-transfer model. It is shown that both the major quantities of interest (QOI) of waterjet pumps and the salient features of the flow such as tip-leakage vortex (TLV) cavitation can be predicted with a commendable accuracy.

Commonly, for the simulation of cavitation in centrifugal pumps incompressible flow solvers with VOF kind cavitation models are applied. Since the source/sink terms of the void fraction transport equation are based on simplified bubble dynamics, empirical parameters may need to be adjusted to the particular pump operating point. In the present study a barotropic cavitation model, which is based solely on thermodynamic fluid properties and does not include any empirical parameters, is applied on a single flow channel of a pump impeller in combination with a time-explicit viscous compressible flow solver. The suction head curves (head drop) are compared to the results of an incompressible implicit standard industrial CFD tool and are predicted qualitatively correct by the barotropic model.

The numerical predictions of cavitating flow around a marine propeller working in non-uniform inflow and an axial turbine are presented. The cavitating flow is modelled using the homogeneous (mixture) model. Time-dependent simulations are performed for the marine propeller case using OpenFOAM. Three calibrated mass transfer models are alternatively used to model the mass transfer rate due to cavitation and the two-equation SST (Shear Stress Transport) turbulence model is employed to close the system of the governing equations. The predictions of the cavitating flow in an axial turbine are carried out with ANSYS-CFX, where only the native mass transfer model with tuned parameters is used. Steady-state simulations are performed in combination with the SST turbulence model, while time-dependent results are obtained with the more advanced SAS (Scale Adaptive Simulation) SST model. The numerical results agree well with the available experimental measurements, and the simulations performed with the three different calibrated mass transfer models are close to each other for the propeller flow. Regarding the axial turbine the effect of the cavitation on the machine efficiency is well reproduced only by the time dependent simulations.

Spool valves play an important role in fluid power system. Cavitation phenomena happen frequently inside the spool valves, which cause structure damages, noise and lower down hydrodynamic performance. A numerical tools incorporating the cavitation model, are developed to predict the flow structure and cavitation pattern in the spool valve. Two major flow states in the spool valve chamber, i.e. flow-in and flow-out, are studies. The pressure distributions along the spool wall are first investigated, and the results agree well with the experimental data. For the flow-in cases, the local pressure at the throttling area drops much deeper than the pressure in flow-out cases. Meanwhile, the bubbles are more stable in flow-in cases than those in flow-out cases, which are ruptured and shed into the downstream.

An axial flow impeller and a mixed flow impeller with same specific speed were experimentally investigated, and the suction performance was studied with the help of CFD simulations. The results show that the axial impeller is roughly better than the mixed flow one. Especially under the design condition and a low flow rate condition range near the designed one, the axial flow impeller is more stable and therefore more suitable to be used in a water jet propulsion, while under these conditions the mixed flow impeller displays significant discrepancies. On the other hand, though its efficiency at the best efficiency point is lower than that of the axial flow one, the mixed flow impeller has a larger range of high efficiency conditions and is more convenient to be controlled to satisfy the irrigation and drainage systems that ought to be adjusted to varied flow rate conditions under a fixed head. In addition, the numerical investigation at the rated point shows that the axial impeller has a much better suction performance than the mixed flow impeller, which contradicts with the experience knowledge and therefore details need to be further studied.

Tip leakage vortex cavitation in axial hydro-turbines may cause erosion, noise and vibration. Damage due to cavitation can be found at the tip of the runner blades on the low pressure side and the discharge ring. In some cases, the erosion follows an oscillatory pattern that is related to the number of guide vanes. That might suggest that a relationship exists between the flow through the guide vanes and the tip vortex cavitating core that induces this kind of erosion.

On the other hand, it is known that air injection has a beneficial effect on reducing the damage by cavitation. In this paper, a methodology to identify the interaction between guide vanes and tip vortex cavitation is presented and the effect of air injection in reducing this particular kind of erosion was studied over a range of operating conditions on a Kaplan scale model.

It was found that air injection, at the expense of slightly reducing the efficiency of the turbine, mitigates the erosive potential of tip leakage cavitation, attenuates the interaction between the flow through the guide vanes and the tip vortex and decreases the level of vibration of the structural components.

In this paper cavitation around 3D hemispherical head-form body as well as disk and conical cavitators were studied numerically with particular emphasis on detailed comparisons of the various turbulence and mass transfer models. Dynamic and unsteady behaviors of cavitation were simulated using the large eddy simulation (LES) and k-ω SST turbulence models together with Kunz, Sauer and Zwart mass transfer models. In addition, the compressive volume of fluid (VOF) method is used to track the cavity interface. Simulation is performed under the framework of the OpenFOAM package. Discussions on the boundary layer separation, re-entrant jet, cavity cloud, vortices and pressure/volume fraction contours over a broad range of cavitation numbers, especially in very low cavitation numbers, are provided. Our numerical results compared fairly well with experimental data and a wide set of analytical relations. Our results indicate that the most accurate solutions will be obtained with the LES/ Kunz approach. Moreover, for the first time, we present a correlation between the cavity length and diameter for hemispherical head-form bodies.

When a hydraulic turbine is operated at off-design conditions, cavitation on the runner and other machine parts can occur. Vibration, noise and erosion caused by cavitation can damage the turbine and lead to a limitation of the operational range. To avoid damage of the turbine, it is fundamental to get knowledge of the presence of cavitation. In this paper, the acoustic emissions at a pump-turbine model at different operating conditions with and without the presence of cavitation were recorded and analysed. High speed video recordings were carried out simultaneously to validate the acoustic measurements. The main goal of the investigation was to compare the acoustic emissions with the visual observations at operating conditions with cavitation on the leading edge of the turbine runner. The analysis of the recorded signals and the visual observations are in good accordance for the investigated operating points.

In the 'universe' of the general cavitation phenomena the issue of cavitation in bearings, due to its particular application and the mostly non-homogeneous working fluids associated with it, has presented a rather specialized challenge. The present paper models the phenomenon of pseudo-cavitation in fluid film bearings and offers a physics-based approach that conserves mass while solving the Reynolds (RE) and Rayleigh-Plesset (RP) equations in a coupled, fully transient environment. The RP solution calculates a time dependent void fraction synchronized with the RE transient solution, where density and viscosity are (re)calculated at every grid point of this homogeneous two-phase fluid. The growth and evolution of the cavitation zone expanse is physics-based and thus can accommodate evaporation, diffusion, or pseudocavitation as separate processes. This is a step beyond the present available cavitation models both for the RE and the Navier-Stokes equations.

A cavitating propeller subject to an oblique inflow in a cavitating tunnel is simulated using potential flow methods coupled with a Reynolds-averaged Navier-Stokes (RANS) solver. The propeller is mainly modelled using a panel method, while the inflow to the propeller is evaluated by coupling a Vortex-Lattice Method (VLM) with the RANS solver. The effects of the tunnel wall are incorporated into the calculated effective inflow to the propeller. The predicted propeller forces and cavity pattern are correlated with experiment. The fully wetted open water characteristics of the propeller predicted by the panel method are presented as well.

In recent years, the operating range of hydraulic machines has been more and more extended. As a consequence, the turbines are facing off-design conditions with highly complex flow phenomena like cavitation. In the present study, the occurrences of cavitating inter blade vortices at deep part load conditions in a Francis turbine are investigated using two-phase flow simulations. The numerical simulations require small time steps and fine meshes to reproduce the required flow characteristics and resolve the minimum pressure in the vortex core. Furthermore, the treatment of the outlet boundary condition is important, as this operating point is facing severe backflow in one diffusor channel in the draft tube. The simulation results indicate that the inter blade vortices can be reproduced.

Cavitation in hydraulic machine is undesired due to its negative effects on performances. To improve cavitation performance of a Francis turbine without the change of the best efficiency point, a model runner geometry optimization was carried out. Firstly, the runner outlet diameter was appropriately increased to reduce the flow velocity at runner outlet region. Then, to avoid the change of the flow rate at the best efficiency point, the blade shapes were carefully adjusted by decreasing the blade outlet angles and increasing the blade wrap angles. A large number of the modified runners were tested by computational fluid dynamic (CFD) method. Finally the most appropriate one was selected, which has the runner outlet diameter 10% larger, the blade outlet angles 3 degrees smaller and the blade wrap angles 5 degrees larger. The results showed that the critical cavitation coefficient of the model runner decreased at every unit rotational speed after the optimization, and the effect was much remarkable at relative high flow rate. Besides, by analysing the internal flow field, it was found that the zone of the low pressure on pressure surface of the optimized turbine blades was reduced, the backflow and vortex rope in draft tube were reduced, and the cavitation zone was reduced obviously.

The spiral cavitating vortex rope developed in the draft tube of Francis turbine under part load condition maybe causes serious pressure fluctuations and power swings, which threatens the safety and stability of the power plant operations. Many works have been performed to explore the mechanisms of it. In this paper, the runner cavitation and spiral vortex rope under part load conditions were studied to investigate the relations of runner cavitation and the spiral vortex rope. The results proved the existence of obvious interaction between them. The swirl flow at the runner outlet plays an important role in the formation of vortex rope. And the periodic procession of vortex rope in turn intensifies the uneven pressure distribution near the runner outlet and causes the asymmetric cavitation on the runner blades, which then give rise to the modification of swirl flow at the runner blades and thereby affects the characteristics of vortex rope.

Inception cavitation is a crucial indicator for reversible pump-turbines especially in pump mode. In actual applications, it is difficult to use CFD for the inception cavitation character. In this study, CFD simulation is conducted to find a proper way to evaluate the inception cavitation, different levels of vapor volume fraction in the impeller is predicted based on the tested results. Results show that the prediction of the location and scale of cavitation is accurate. The predicted cavitation number also matches the experimental data well. The vapor volume fraction levels from 0.0001% to 0.001% are recommended as the criterion of inception cavitation.

To minimize cavitation induced pressure fluctuations by marine propellers with minimum efficiency loss, the paper presents a new design and optimization method using a blade section design method. The sheet cavity volume variation on a two-dimensional blade section in quasi-steady condition has been simplified to a relation with only a limited number of non-dimensional parameters. This results in a fast prediction method of the cavity volume of a blade section passing a wake peak, using a pre-calculated database. This makes optimization feasible. The optimization method was applied to the propeller of a container ship. Extensive tests in a towing tank and a cavitation channel validated the reduction of pressure fluctuations: 33% reduction in the first blade frequency amplitude and 18% reduction in the second blade frequency amplitude, with the same open water efficiency.

The current investigation presents numerical simulations of cavitating flows in a simplified model of a mushroom valve chamber of a piezo common rail injection system. Two discharge throttles with different step diameters are investigated. The developed models are able to predict relevant features of cavitating flow in fuel injectors. Special attention is put on the investigation of wave dynamics and related instationary mechanisms in the discharge throttle and the valve chamber. To this respect, a compressible flow solver with a homogeneous mixture model and barotropic description of the diesel-like-fluid is utilized. Highly unsteady phenomena are observed in both investigated designs. The structure of the cavitating flow is further analyzed with an emphasis on the interaction between collapsing vapor clouds in the throttle step and reentrant motion in the discharge throttle. Furthermore, numerical simulations reveal significant influence of the throttle step diameter on the cavity dynamics.

A combination of simulation and special experimental techniques has been used to investigate the transient flow and cavitation phenomena of a control device inside a high performance diesel injector. Dynamic cavitation behaviour was captured on a large scale transparent model, which was then used to develop and validate an advanced turbulence CFD model with Large Eddy Simulation. These techniques are used within Delphi to gain insight and optimise injector performance at real-size.

This paper presents a numerical method for modelling a compressible multiphase flow that involves phase transition between liquid and vapour in the context of gasoline injection. A discontinuous compressible two fluid mixture based on the Volume of Fluid (VOF) implementation is employed to represent the phases of liquid, vapour and air. The mass transfer between phases is modelled by standard models such as Kunz or Schnerr-Sauer but including the presence of air in the gas phase. Turbulence is modelled using a Large Eddy Simulation (LES) approach to catch instationnarities and coherent structures. Eventually the modelling approach matches favourably experimental data concerning the effect of cavitation on atomisation process.

Nozzle-orifice flow and cavitation have an important effect on primary breakup of sprays. For this reason, a number of studies in recent years have used injectors with optically transparent nozzles so that orifice flow cavitation can be examined directly. Many of these studies use injection pressures scaled down from realistic injection pressures used in modern fuel injectors, and so the geometry must be scaled up so that the Reynolds number can be matched with the industrial applications of interest. A relatively small number of studies have shown results at or near the injection pressures used in real systems. Unfortunately, neither the specifics of the design of the optical nozzle nor the design methodology used is explained in detail in these papers. Here, a methodology demonstrating how to prevent failure of a finished design made from commonly used optically transparent materials will be explained in detail, and a description of a new design for transparent nozzles which minimizes size and cost will be shown. The design methodology combines Finite Element Analysis with relevant materials science to evaluate the potential for failure of the finished assembly. Finally, test results imaging a cavitating flow at elevated pressures are presented.

Variation of fuel properties occurring during extreme fuel pressurisation in Diesel fuel injectors relative to those under atmospheric pressure and room temperature conditions may affect significantly fuel delivery, fuel injection temperature, injector durability and thus engine performance. Indicative results of flow simulations during the full injection event of a Diesel injector are presented. In addition to the Navier-Stokes equations, the enthalpy conservation equation is considered for predicting the fuel temperature. Cavitation is simulated using an Eulerian-Lagrangian cavitation model fully coupled with the flow equations. Compressible bubble dynamics based on the R-P equation also consider thermal effects. Variable fuel properties function of the local pressure and temperature are taken from literature and correspond to a reference so-called summer Diesel fuel. Fuel pressurisation up to 3000bar pressure is considered while various wall temperature boundary conditions are tested in order to compare their effect relative to those of the fuel heating caused during the depressurisation of the fuel as it passes through the injection orifices. The results indicate formation of strong temperature gradients inside the fuel injector while heating resulting from the extreme friction may result to local temperatures above the fuel's boiling point. Predictions indicate bulk fuel temperature increase of more than 100°C during the opening phase of the needle valve. Overall, it is concluded that such effects are significant for the injector performance and should be considered in relevant simulation tools.

In this paper, a comprehensive two-fluid model is suggested in order to compute the in-nozzle cavitating flow and the primary atomization of liquid jets, simultaneously. This model has been applied to the computation of a typical large marine Diesel injector. The numerical results have shown a strong correlation between the in-nozzle cavitating flow and the ensuing spray orientation and atomization. Indeed, the results have confirmed the existence of an off-axis liquid core. This asymmetry is likely to be at the origin of the spray deviation observed experimentally. In addition, the primary atomization begins very close to the orifice exit as in the experiments, and the smallest droplets are generated due to cavitation pocket shape oscillations located at the same side, inside the orifice.

For over twenty years, DME has shown itself to be a most promising fuel for diesel combustion. DME is produced by simple synthesis of such common sources as coal, natural gas, biomass, and waste feedstock. DME is a flammable, thermally-stable liquid similar to liquefied petroleum gas (LPG) and can be handled like LPG. However, the physical properties of DME such as its low viscosity, lubricity and bulk modulus have negative effects for the fuel injection system, which have both limited the achievable injection pressures to about 500 bar and DME's introduction into the market. To overcome some of these effects, a common rail fuel injection system was adapted to operate with DME and produce injection pressures of up to 1000 bar. To understand the effect of the high injection pressure, tests were carried out using 2D optically accessed nozzles. This allowed the impact of the high vapour pressure of DME on the onset of cavitation in the nozzle hole to be assessed and improve the flow characteristics.

This paper aims to compare the results of two commonly used methods for the simulation of cavitating flows; one is the two phase mass transfer approach and the other is a homogenous equilibrium model. Both methodologies are compared in a shock tube and a throttle flow, which resembles the constrictions in Diesel injector passages. The mass transfer rate in the two phase model plays the fundamental role in affecting how close to equilibrium the model is; by increasing the mass transfer the two phase model comes close to the homogenous equilibrium model.

This paper discusses the implementation of an explicit density-based solver, based on the central-upwind schemes originally suggested by Kurganov, for the simulation of cavitating bubble dynamic flows. Explicit density based solvers are suited for highly dynamic, violent flows, involving large density ratios, as is rather common in cavitating flows. Moreover, the central-upwind schemes have the advantage of avoiding direct evaluation of the Jacobian matrix or estimation of the wave pattern emerging from Euler equations. Second order accuracy can be achieved with TVD MUSCL schemes. Basic comparison with the predicted wave pattern of the central-upwind schemes is performed with the exact solution of the Riemann problem showing an excellent agreement. Then several different bubble configurations were tested, similar to the work of Lauer et al. (2012). The central-upwind schemes prove to be able to handle the large pressure and density ratios appearing in cavitating flows, giving similar predictions in the evolution of the bubble shape.

In the current paper, indicative results of the flow simulation during the opening phase of a Diesel injector are presented. In order to capture the complex flow field and cavitation structures forming in the injector, Large Eddy Simulation has been employed, whereas compressibility of the liquid was included. For taking into account cavitation effects, a two phase homogenous mixture model was employed. The mass transfer rate of the mixture model was adjusted to limit as much as possible the occurrence of negative pressures. During the simulation, pressure peaks have been found in areas of vapour collapse, with magnitude beyond 4000bar, which is higher that the yield stress of common materials. The locations of such pressure peaks corresponds well with the actual erosion location as found from X ray scans.

The injection process of diesel engines influences the pollutant emissions. The spray formation is significantly influenced by the internal flow of the injector. One of the key parameters here is the generation of cavitation caused by the geometry and the needle lift.

In modern diesel engines the injection pressure is established up to 3000 bar. The details of the flow and phase change processes inside the injector are of increasing importance for such injectors. With these experimental measurements the validation of multiphase and cavitation models is possible for the high pressure range. Here, for instance, cavitation effects can occur. Cavitation effects in the injection port area destabilize the emergent fuel jet and improve the jet break-up.

The design of the injection system in direct-injection diesel engines is an important challenge, as the jet breakup, the atomization and the mixture formation in the combustion chamber are closely linked. These factors have a direct impact on emissions, fuel consumption and performance of an engine. The shape of the spray at the outlet is determined by the internal flow of the nozzle. Here, geometrical parameters, the injection pressure, the injection duration and the cavitation phenomena play a major role.

In this work, the flow dependency in the nozzles are analysed with the Neutron-Imaging. The great advantage of this method is the penetrability of the steel structure while a high contrast to the fuel is given due to the interaction of the neutrons with the hydrogen amount. Compared to other methods (optical with glass structures) we can apply real components under highest pressure conditions. During the steady state phase of the injection various cavitation phenomena are visible in the injector, being influenced by the nozzle geometry and the fuel pressure. Different characteristics of cavitation in the sac and spray hole can be detected, and the spray formation in the primary breakup zone is influenced.

Cavitation inception occurring in immersed jets was investigated in a purpose-built mechanical flow rig. The rig utilized custom-built cylindrical and conical nozzles to direct high-velocity jets of variable concentration n-octane-hexadecane mixtures into a fused silica optically accessible receiver. The fluid pressure upstream and down-stream of the nozzles were manually controlled. The study employed a variety of acrylic and metal nozzles. The results show that the critical upstream pressure to downstream pressure ratio for incipient cavitation decreases with increasing n-octane concentration for the cylindrical nozzles, and increases with increasing n-octane concentration for the conical nozzle.

A conventional diesel and paraffinic-rich model diesel fuel were subjected to sustained cavitation in a custom-built high-pressure recirculation flow rig. Changes to the spectral extinction coefficient at 405 nm were measured using a simple optical arrangement. The spectral extinction coefficient at 405 nm for the conventional diesel sample was observed to increase to a maximum value and then asymptotically decrease to a steady-state value, while that for the paraffinic-rich model diesel was observed to progressively decrease. It is suggested that this is caused by the sonochemical pyrolysis of mono-aromatics to form primary soot-like carbonaceous particles, which then coagulate to form larger particles, which are then trapped by the filter, leading to a steady-state spectral absorbance.

Cavitation and its effect on spray formation and its dispersion play a crucial role in proper engine combustion and controlled emission. This study focuses on these effects in a typical common rail 6-hole diesel injector accounting for 3D needle movement and flow compressibility effects. Coupled numerical simulations using 1D and 3D CFD codes are used for this investigation. Previous studies in this direction have already presented a detailed structure of the adopted methodology. Compared to the previous analysis, the present study investigates the effect of 3D needle movement and cavitation on the spray formation for pilot and main injection events for a typical diesel engine operating point. The present setup performs a 3D compressible multiphase simulation coupled with a standalone 1D high pressure flow simulation. The simulation proceeds by the mutual communication between 1D and 3D solvers. In this work a typical common rail injector with a mini-sac nozzle is studied. The lateral and radial movement of the needle and its effect on the cavitation generation and the subsequent spray penetration are analyzed. The result indicates the effect of compressibility of the liquid on damping the needle forces, and also the difference in the spray penetration levels due to the asymmetrical flow field. Therefore, this work intends to provide an efficient and user-friendly engineering tool for simulating a complete fuel injector including spray propagation.

The importance of cavitation inside multi-hole injectors for direct injection internal combustion (IC) engineshas been addressed in many previous investigations. Still, the effect of cavitation on jet spray, its stability and liquid breakup and atomisation is not yet fully understood. The current experimental work aims to address some of these issues. It focuses on the initiation and development of cavitation inside a 7× enlarged transparent model of a symmetric 6-hole spark ignition direct injection (SIDI) injector and quantifies the effect of cavitation on near-nozzle spray cone angle and stability utilising high speed Mie scattering visualisation. The regions studied include the full length of the nozzle and its exitjet spray wherethe primary breakup takes place.

X-ray computed tomography (CT) is well-known and widely used in the medical sector for diagnosis of various illnesses. The technique is based on the absorption (i.e. attenuation) of the ionising electromagnetic radiation by the object. The amount of energy to be absorbed depends on the density and its thickness; the transmitted radiation through the object is then compared to the incident radiation that leads to a reconstruction of attenuation coefficients versus spatial position in the object. Thus, the resulting three-dimensional slices of the object are used (a) to identify internal geometric features of objects, and (b) to distinguish between media of different densities, i.e. liquid and air/vapour. In this study, the geometry extraction capability has been applied on time-averaged cavitation pocket shapes, as well as, the capability of density differentiation measurements on Diesel fuel flows. Results appear promising and pose a challenge in providing quantitative measurements of cavitation vapour fraction inside an injection hole.

Predictive capability of RANS and LES models to calculate incipient cavitation of water in a step nozzle is assessed. The RANS models namely, Realizable k-ε, SST k-ω and Reynolds Stress Model did not predict any cavitation, due to the limitation of RANS models to predict the low pressure vortex cores. LES WALE model was able to predict the cavitation by capturing the shear layer instability and vortex shedding. The performance of a barotropic cavitation model and Rayleigh-Plesset-based cavitation models was compared using WALE model. Although the phase change formulation is different in these models, the predicted cavitation and flow field were not significantly different.

We present implicit large-eddy simulations (LES) to study the primary breakup of cavitating liquid jets. The considered configuration, which consists of a rectangular nozzle geometry, adopts the setup of a reference experiment for validation. The setup is a generic reproduction of a scaled-up automotive fuel injector. Modelling of all components (i.e. gas, liquid, and vapor) is based on a barotropic two-fluid two-phase model and employs a homogenous mixture approach. The cavitating liquid model assumes thermodynamic- equilibrium. Compressibility of all phases is considered in order to capture pressure wave dynamics of collapse events. Since development of cavitation significantly affects jet break-up characteristics, we study three different operating points. We identify three main mechanisms which induce primary jet break-up: amplification of turbulent fluctuations, gas entrainment, and collapse events near the liquid-gas interface.

We perform large-eddy simulations (LES) of the turbulent, cavitating flow inside a 9-hole solenoid common-rail injector including jet injection into gas during a full injection cycle. The liquid fuel, vapor, and gas phases are modelled by a homogeneous mixture approach. The cavitation model is based on a thermodynamic equilibrium assumption. The geometry of the injector is represented on a Cartesian grid by a conservative cut-element immersed boundary method. The strategy allows for the simulation of complex, moving geometries with sub-cell resolution. We evaluate the effects of needle movement on the cavitation characteristics in the needle seat and tip region during opening and closing of the injector. Moreover, we study the effect of cavitation inside the injector nozzles on primary jet break-up.

This paper evaluates the solution effects of different Rayleigh-Plesset models (R-P) for simulating the growth/collapse dynamics and thermal behaviour of homogeneous gas bubbles. The flow inputs used for the discrete cavitation bubble calculations are obtained from Reynolds-averaged Navier-Stokes simulations (RANS), performed in high-pressure nozzle holes. Parametric 1-D results are presented for the classical thermal R-P equation [1] as well as for refined models which incorporated compressibility corrections and thermal effects [2, 3]. The thermal bubble model is coupled with the energy equation, which provides the temperature of the bubble as a function of conduction/convection and radiation heat-transfer mechanisms. For approximating gas pressure variations a high-order virial equation of state (EOS) was used, based on Helmholtz free energy principle [4]. The coded thermal R-P model was validated against experimental measurements [5] and model predictions [6] reported in single-bubble sonoluminescence (SBSL).

The formation of vortex or 'string' cavitation has been visualised at pressures up to 2000 bar in an automotive-sized optical diesel fuel injector nozzle. The multi-hole nozzle geometry studied allowed observation of the hole-to-hole vortex interaction and, in particular, that of a bridging vortex in the sac region between the holes. Above a threshold Reynolds number, their formation and appearance during a 2 ms injection event was repeatable and independent of upstream pressure and cavitation number. In addition, two different hole layouts and threedimensional flow simulations have been employed to describe how, the relative positions of adjacent holes influenced the formation and hole-to-hole interaction of the observed string cavitation vortices, with good agreement between the experimental and simulation results being achieved.

A numerical study of two-phase flow inside the nozzle holes and the issuing spray jets for a multi-hole direct injection gasoline injector has been presented in this work. The injector geometry is representative of the Spray G nozzle, an eight-hole counterbore injector, from, the Engine Combustion Network (ECN). Simulations have been carried out for the fixed needle lift. Effects of turbulence, compressibility and, non-condensable gases have been considered in this work. Standard k—ɛ turbulence model has been used to model the turbulence. Homogeneous Relaxation Model (HRM) coupled with Volume of Fluid (VOF) approach has been utilized to capture the phase change phenomena inside and outside the injector nozzle. Three different boundary conditions for the outlet domain have been imposed to examine non-flashing and evaporative, non-flashing and non-evaporative, and flashing conditions. Inside the nozzle holes mild cavitation-like and in the near-nozzle region flash boiling phenomena have been predicted in this study when liquid fuel is subjected to superheated ambiance. Noticeable hole to hole variation has been also observed in terms of mass flow rates for all the holes under both flashing and non-flashing conditions.

Cavitating propellers generate pressure fluctuations on the hull of the ship. These pressure fluctuations are usually analyzed in the frequency domain using FFTs and the spectrum is composed of tonals at multiples of the blade passage frequency and a broadband part. The two are often considered separately but a relation between the two exists which has been investigated by theoretical signal analysis. It will be shown that the broadband part is related to the variability of the signal between blade passages and a simple procedure is proposed to quantify the variability in terms of amplitude and phase angle. The procedure has been applied to a data set obtained at sea trials.

An experimental investigation has been carried out to research the noise induced by cavitation under the asymmetric cavitation (AC) condition in a centrifugal pump. The acoustic pressure signals at the pump inlet and outlet were measured respectively during the development of cavitation in a closed hydraulic test rig. It could be found that both the pump inlet and outlet acoustic pressures changed obviously with the development of cavitation. The time domain and the power spectrum density of the pump inlet and outlet acoustic pressure pulsations were analyzed. The broadband pulses of the acoustic pressure pulsations were found and the reasons for the phenomenon were given.

Dynamics and acoustics generated in a cavitating Venturi tube are followed up as a function of the input power of a centrifugal pump. The pump of 5 hp with a modified impeller to produce uniform bubbly flow, pumps 70 liters of propylene glycol in a closed loop (with a water cooling system), in which the Venturi is arranged. The goal was to obtain correlations among acoustical emission, dynamics of the shock waves and the light emission from cavitation bubbles. The instrumentation includes: two piezoelectric transducers, a digital camera, a high-speed video camera, and photomultipliers. As results, we show the cavitation patterns as function of the pump power, and a graphical template of the distribution of the Venturi conditions as a function of the cavitation parameter. Our observations show for the first time the sudden formation of bubble clouds in the straight portion of the pipe after the diverging section of the Venturi. We assume that this is due to pre-existing of nuclei-cloud structures which suddenly grow up by the tensile tails of propagating shock waves (producing a sudden drop in pressure).

In order to clarify the mechanism of noise generation in a hydraulic relief valve, oil cavitating flows in a half cut model of the valve were observed by means of a high-speed camera and were simulated numerically. As the result of image analysis, the fluctuation of cavitation volume is corresponding to the pressure fluctuation of downstream, and the both fluctuations take peaks at frequencies from 1.5 to 2.5 kHz depending on the back pressure. In addition, as the back pressure increases, the frequency of the pressure fluctuation increases and the peak value decreases. These phenomena were also qualitatively reproduced in the numerical simulation.

The objective of this paper is to investigate the correlation between fluid induced vibration and unsteady cavitation behaviours. Experimental results are presented for a modified NACA66 hydrofoil, which is fixed at α=8°. The high-speed camera is synchronized with a single point Laser Doppler Vibrometer to analyze the transient cavitating flow structures and the corresponding structural vibration characteristics. The results showed that, with the decreasing of the cavitation number, the cavitating flows in a water tunnel display several types of cavitation patterns, such as incipient cavitation, sheet cavitation and cloud cavitation. The cavity shedding frequency reduces with the decrease of the cavitation number. As for the cloud cavitation regime, the trend of the vibration velocity goes up with the growth of the attached cavity, accompanied with small amplitude fluctuations. Then the collapse and shedding of the large-scale cloud cavities leads to substantial increase of the vibration velocity fluctuations.

The method to predict underwater radiated noise from tip vortex cavitation was studied. The growth of a single cavitation bubble in tip vortex was estimated by substituting the tip vortex to Rankine combined vortex. The ideal spectrum function for the sound pressure generated by a single cavitation bubble was used, also the empirical factor for the number of collapsed bubbles per unit time was introduced. The estimated noise data were compared with measured ship's ones and it was found out that this method can estimate noise data within 3dB difference.

The main impurities in coal are sulphur, ash and alkali. On combustion, the volatile forms of these impurities are either condensed on the boilers, or emitted in the form of potentially hazardous gases. The alkali elements present in coal help the fly ash particles adhere to boiler surfaces by providing a wet surface on which collection of these particles can take place. Use of ultrasonic techniques in cleaning of coal has stirred interest among researchers in recent times. Extraction of alkali elements by cavitation effect using low-frequency ultrasound, in the presence of reagents (HNO₃ and H₂O₂) is reported in this paper. Powdered coal was dissolved with the reagent and exposed to ultrasonic fields of various frequencies at different time intervals. The treated solution is filtered and tested for alkali levels.

Surface of duralumin plate can be treated by not only laser abrasion but also bubble induced by pulse laser. The pulse laser produced two kinds of shock waves related to laser abrasion and bubble collapse. In the case of laser peening, the shock wave induced by abrasion was normally used. In the present paper, the behaviour of bubble was observed and noise was detected by the hydrophone. It was revealed that the impact induced by the bubble collapse produced by the pulse laser was stronger than that of the laser abrasion. A numerical simulation was also carried out to investigate phenomenon of bubble collapse.

Cavitation can cause considerable erosion to adjacent materials. Erosion is accompanied by acoustic emissions, related to crack formation and propagation inside the material. In this study a piezoelectric acoustic sensor mounted on the back of a grade DH36 steel plate is used to identify the acoustic signatures of cavitation. Cavitation is induced near the plate by means of an ultrasonic transducer (sonotrode). Various 'non-erosive' and erosive test rig configurations are examined and an acoustic threshold value for the onset of cavitation erosion is identified and presented. The use of a fibre Bragg grating (FBG)-based acoustic sensor developed at City University London for acoustic monitoring purposes is also examined. Acoustic signals from both sensors are analysed, by means of a fast Fourier transform, showing a very good agreement in terms of captured frequencies.

Cavitation plays a critical role in the internal flow of nozzles such as those used in direct fuel injection systems. However, quantifying the vapor fraction in the nozzle is difficult. The gas-liquid interfaces refract and multiply scatter visible light, making quantitative extinction measurements difficult. X-rays offer a solution to this problem, as they refract and scatter only weakly. In this paper, we report on current progress in the development of several x-ray diagnostics for cavitating nozzle flows. X-ray radiography experiments undertaken at the Advanced Photon Source at Argonne National Laboratory have provided measurements of total projected void fraction in a 500 μm submerged nozzle, which have been directly compared with numerical simulations. From this work, it has been shown that dissolved gases in the liquid also result in the formation of vapor regions, and it is difficult to separate these multiple phenomena. To address this problem, the liquid was doped with an x-ray fluorescent bromine tracer, and the dissolved air substituted with krypton. The fluorescent emission of Br and Kr at x-ray wavelengths provide a novel measurement of both the total void fraction and the dissolved gas component, allowing both cavitation and dissolved gas contributions to be measured independently. [199/200 words]

Small particles, especially bubbles in the micro-meter range, influence the cavitation of the propellers. The prediction of cavitation inception and water quality measurements are important in cavitation research. The Hydrodynamic Nuclei Concentration (HDNC) technique can be used for reliable bubble concentration measurements in fluid flows. The HDNC technique bases on the analysis of scattered light from the cavitation nuclei in the water. The HDNC technique can distinguish between bubbles and solid particles. The particle type classification is important, because the number concentration of solid particles is often much higher than the nuclei concentration in cavitation tunnels and in seawater. Verification experiments show, that the HDNC technique reaches similar capabilities in number concentration estimation as Phase Doppler (PD) technique in much shorter acquisition time.

We introduce a Cavitation Intensifying Bag as a versatile tool for acoustic cavitation control. The cavitation activity is spatially controlled by the modification of the inner surface of the bag with patterned pits of microscopic dimensions. We report on different measurements such as the transmission of ultrasound, temperature increase inside the bag during sonication. Several applications of interest to other scientific activities are also demonstrated.

This study presents measurements on air release of V-oil 1404 in the back flow of a micro orifice at choked flow conditions using a shadowgraph imaging method. The released air was determined at three positions downstream of the orifice for different pressure conditions. It was found that more than 23% of the initially dissolved air is released and appears downstream of the orifice in the form of bubbles.

In this paper, we investigate the use of laser diagnostic tools for in-plane imaging of bubble induced spray using a laser sheet and Mie scattering technique. A perspex plate of thickness 10 mm with a hole of diameter 1 mm in the center is placed in the middle of a glass tank filled with water such that the top surface of the plate coincides with the water surface. A bubble is created just below the hole using a low-voltage spark circuit such that it expands against the hole. This leads to the formation of two jets which impact leading to a spray and break-up into droplets. The spray evolution is observed using a laser sheet directed in a plane through the center of the hole. The illuminated plane is imaged using a high-speed camera based on the Mie scattering from glass beads suspended in the liquid. Results show that Mie scattering technique has potential in studying bubble-induced sprays with applications such as in fuel sprays, drug-delivery etc, and also for validation of numerical codes. We present results from our ongoing experiments in this paper.

This paper presents visualization and image processing of spray structure affected by cavitation bubbles and cavitating flow patterns. Experiments were conducted for a better understanding of cavitation and resulting flow regimes. Cavitation is generated with sudden pressure drop across a 4.5 mm long short micro-channel with an inner diameter of 152 μm connected to the setup using proper fittings. Generated cavitation bubbles and fluid flow patterns were observed by using a high speed camera. The spray structure was observed in four different segments and mainly the droplet evaluation in the lower segments for low upstream pressures was analyzed using several image processing techniques including contrast adjustments and morphological operators. Moreover, fluid flow regimes for different upstream pressures were investigated, and the flow patterns were analyzed in the separated regions of the spray.

Flow visualization is necessary to characterize the fluid flow properties during a hydrodynamic ram event. The multiphase flow during a hydrodynamic ram event can make traditional image processing techniques such as contrast feature detection and PIV difficult. By stacking the imagery to form a multidimensional tensor array, feature detection to determine flow field velocities are visualized.

Ultrasound techniques such as washing, fine-particle manipulation and mixing have been investigated. MHz-band ultrasound was usually used in the previous work, and studies of kHz-order ultrasound are very rare. In the usual manipulation technique, μm- order particles are targeted due to wavelength limitations. We discovered an interesting phenomenon that holds promise for a novel particle separation technique using kHz-order ultrasound. Here, particles with sub-mm- or mm-order diameters were flocculated into a swarm in water irradiated by 20-kHz ultrasound. To develop a practical separation process, we investigated the stationary position and dia. of the particle swarms and the sound- pressure profiles in a vessel, as well as the flocculation mechanism, by varying the irradiation frequency, water level, particle diameter and particle amount. The primary stationary position corresponded to the wavelength calculated from the resonant frequency regardless of the particle diameter. Subtle changes in the frequency and water level resulted in a significant change in the stationary position. Based on these results, we propose a new separation process based on the particle diameter for sub-mm- or mm-order particles.

In several studies the beneficial influence of pre-treatment of waste activated sludge with cavitation on the biogas production was demonstrated. It is however, still not fully certain whether this effect should be mainly contributed to an increase in conversion rate of organics into biogas by anaerobic bacteria, and how much cavitation increases the total biogas yield. An increase in yield is only the case if cavitation can further disrupt otherwise inaccessible cell membrane structures and long chain organic molecules. In this study the influence of hydrodynamic cavitation on sludge that was already digested for 30 days was investigated. The total biogas yield could indeed be increased. The effect of the backpressure behind the venturi tube on the yield could not yet be established.

The paper describes the use of a white light interformeter to measure the cavitation bubble and oil film thickness in a tribological contact and compares the results to theory. It is found that oil film thickness is best predicted by the theory proposed by Coyne and Elrod.

The application of ultrasound to industrial casting processes has attracted research interest during the last 50 years. However, the transfer and scale-up of this advanced and promising technology to the industry have been hindered by difficulties in treating large volumes of liquid metal due to the lack of understanding of certain fundamentals. In the current study, experimental results on ultrasonic processing in deionised water and in liquid aluminium (Al) are reported. Cavitation activity was determined in both liquid environments using an advanced high-temperature cavitometer sensor. In water, the highest cavitation activity is obtained for the lowest sonotrode tip amplitudes. Below the sonotrode, the cavitation intensity in liquid aluminium is found to be four times higher than in water.

A numerical method was developed to predict the supercavity around axi-symmetric bodies. Employing potential flow, the proposed method computes the cavity shape and drag force, which are the important features of practical concern for supercavitating objects. A method to calculate the frictional drag acting on the wetted body surface was implemented, which is called the viscous-potential method. The results revealed details of the drag curve appearing in the course of an increase in speed and cavity growth. In addition, the supercavity and drag features of the actual shape of the supercavitating torpedo were investigated according to the different depth conditions.

In this contribution, we examine transient dynamics and cavitation patterns of periodically shedding partial cavities by numerical simulations. The investigation reproduces reference experiments of the cavitating flow over a sharp wedge. Utilizing a homogeneous mixture model, full compressibility of the two-phase flow of water and water vapor is taken into account by the numerical method. We focus on inertia-dominated mechanisms, thus modeling the flow as inviscid. Based on the assumptions of thermodynamic equilibrium and barotropic flow, the thermodynamic properties are computed from closed-form analytical relations. Emphasis is put on a validation of the employed numerical approach. We demonstrate that computed shedding dynamics are in agreement with the references. Complex flow features observed in the experiments, including cavitating hairpin and horse-shoe vortices, are also predicted by the simulations. Furthermore, a condensation discontinuity occurring during the collapse phase at the trailing portion of the partial cavity is equally obtained.

In this article we numerically investigate the non-linear response of a bubble cloud against a periodic pressure excitation. By exciting a planar bubble curtain with an external acoustic pulse of given amplitude and frequency, we characterize the global dynamic response of the system using phase diagrams representing the void fraction against the excitation pressure. Even in the absence of mass transfer, the void fraction around which the system oscillates increases when increasing the excitation amplitude. We show how the maximum pressures reached during the collapse of bubbles are higher in polydisperse bubble clouds than in monodisperse clouds for strong pressure pulses.

Superhydrophobicity is realized by entrapping gas bubbles inside surface roughness. While this strategy affords remarkable surface properties, it enhances the risk of cavitation from these gas nuclei at negative pressures. Here we use free energy molecular dynamics simulations and an extension of the classical nucleation theory to show that the relevant nucleation rates and barriers can be controlled by engineering the surface structure. Mimicking the re-entrant and chemically heterogeneous structure found in the leaves of the Salvinia molesta allows one both to stabilize the gas pockets against liquid intrusion and to reduce the risk of cavitation.

An Euler-Lagrange model is developed to simulate bubbly flow around an obstacle with the aim to resolve large and meso-scales of cavitation phenomena. The volume averaged Navier-Stokes equations are discretized using finite elements on an unstructured grid with a variational multiscale method. The trajectory of each bubble is tracked using Newton's second law. Furthermore, bubble interaction is modeled with a soft sphere contact model to obtain a four-way coupled approach. The new features presented in this work, besides using a variational multiscale method in an Euler-Lagrange framework, is an improved computation of the void fraction. A second order polynomial is used as filtering function and the volume integral is transformed by applying the divergence theorem twice, leading to line integrals which can be integrated analytically. Therefore, accuracy of void fraction computation is increased and discontinuities are avoided as is the case when the kernel touches a Gauss point across time steps. This integration technique is not limited to the chosen spatial discretization. The numerical test case considers flow in a channel with a cylindrical obstacle. Bubbles are released close to the inflow boundary and void fractions up to 30% occur at the stagnation point of the obstacle.

The closely coupled approach combined the Finite Volume Method (FVM) solver and the Finite Element Method (FEM) solver is applied to simulation the cavitation-structure interaction of a 3D cantilevered flexible hydrofoil in water tunnel. In the cavitating flow, the elastic hydrofoil would deform or vibrate in bending and twisting mode. And the motion of the foil would affect the characteristics of the cavity and the hydrodynamic load on the foil in turn. With smaller cavitation numbers (σ_v=2.15), the frequency spectrum of the lift on the foil would contain two frequencies which are associated to the cavity shedding and the first bend frequency of the hydrofoil. With larger cavitation number (σ_v=2.55), the frequency of the lift is completely dominated by the natural frequency of the foil.

Results of cavitating turbulent flow simulation around a twisted hydrofoil were presented in the paper using the Partially-Averaged Navier-Stokes (PANS) method (Ji et al. 2013a), Large-Eddy Simulation (LES) (Ji et al. 2013b) and Reynolds-Averaged Navier-Stokes (RANS). The results are compared with available experimental data (Foeth 2008). The PANS and LES reasonably reproduce the cavitation shedding patterns around the twisted hydrofoil with primary and secondary shedding, while the RANS model fails to simulate the unsteady cavitation shedding phenomenon and yields an almost steady flow with a constant cavity shape and vapor volume. Besides, it is noted that the predicted shedding vapor cavity by PANS is more turbulent and the shedding vortex is stronger than that by LES, which is more consistent with experimental photos.

This paper compares two physical mechanisms for the collapse of a bubble near a rigid wall: a traveling shock-induced collapse and a Rayleigh-like collapse due to a uniform rise of the pressure around the bubble. A multi-material compressible flow solver capable of handling material interfaces under high pressures is used to investigate these two scenarios for different levels of the driving pressure ranging from 1 MPa to 400 MPa. The two mechanisms are differentiated on the basis of the resulting bubble dynamics, the reentrant jet velocity, and the pressures imparted to the wall.

It has been known that cavity volume is underestimated and there is a discrepancy between predicted and measured breakdown characteristics for the numerical simulation of unsteady cavitation around a hydrofoil at high angle of attack. Therefore, in this study, in order to predict the cavity volume with high accuracy, the phenomena that gas phase increases even at a pressure higher than saturated vapour pressure which is known as aeration is modelled, and applied to phase change term. It was assumed that the precipitation of dissolved air is promoted by mechanical stimulation such as Reynolds stress in unsteady flow. The effectivity of the proposed model is discussed through the comparison among some kinds of components of the pressure variation.

For an elliptic Arndt's hydrofoil numerical simulations of vortex cavitation are presented. An equilibrium cavitation model is employed. This single-fluid model assumes local thermodynamic and mechanical equilibrium in the mixture region of the flow, is employed. Furthermore, for characterizing the thermodynamic state of the system, precomputed multiphase thermodynamic tables containing data for the appropriate equations of state for each of the phases are used and a fast, accurate, and efficient look-up approach is employed for interpolating the data. The numerical simulations are carried out using the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations for compressible flow. The URANS equations of motion are discretized using an finite volume method for unstructured grids. The numerical simulations clearly show the formation of the tip vortex cavitation in the flow about the elliptic hydrofoil.

The present study deals with a numerical method for cryogenic cavitating flows. Recently, we have developed an accurate and efficient baseline numerical scheme for all-speed water-gas two-phase flows. By extending such progress, we modify the numerical dissipations to be properly scaled so that it does not show any deficiencies in low Mach number regions. For dealing with cryogenic two-phase flows, previous EOS-dependent shock discontinuity sensing term is replaced with a newly designed EOS-free one. To validate the proposed numerical method, cryogenic cavitating flows around hydrofoil are computed and the pressure and temperature depression effect in cryogenic cavitation are demonstrated. Compared with Hord's experimental data, computed results are turned out to be satisfactory. Afterwards, numerical simulations of flow around KARI turbopump inducer in liquid rocket are carried out under various flow conditions with water and cryogenic fluids, and the difference in inducer flow physics depending on the working fluids are examined.

This paper deals with a numerical simulation of cavitation flow around a hybrid contra-rotating shaft propeller operating in wake field. The simulation for the cavitating flow is performed for straight operating and turning condition of podded propeller located behind the main propeller using unsteady Reynolds-Averaged Navier-Stokes. The behavior of the main propeller is almost similar regardless of the turning angle. In contrast, the cavitation behavior of the podded propeller depending on the turning angle appears to be entirely different due to the change of the load distribution on the podded propeller. At the large angle of the turning condition, the unstable cavity flow due to the large amount of cavitation and the hub vortex separated from the forward propeller as well as face cavitation is observed. Thus, a great caution on the cavitation phenomena is needed when designing and operating the HCRSP.

In this work, the interaction between a ventilated supercavity and a jet are examined using computational fluid dynamics (CFD). The CFD model is validated using experimental data, and shows to capture the correct trend in the bulk cavity behavior (qualitatively and quantitatively). Using these models, a number of novel insights into the physical characteristics of the interaction are developed. These interactions are described by: (1) the jet gas and ventilation gas poorly mix within the cavity, (2) the jet appears to cause additional gas leakage by transitioning the cavity from a recirculating flow to an axial flow, (3) the jet has the ability to lengthen the cavity, and (4) the jet invokes wake instabilities that drive cavity pulsation. These phenomena are documented and discussed in the following paper.

Numerical modelling is a useful tool for the fundamental study of acoustic cavitation treatment in liquid metals. This treatment, also known as ultrasonic melt processing, significantly improves the properties and quality of metallic materials. However, the mechanisms leading to these observed improvements are still unclear and a fundamental study of cavitation treatment is required to understand this process. In this endeavour, this paper compares the use of high-order discretization schemes for solving acoustic pressures in cavitating liquids with its low-order counterpart. A fourth order scheme is shown to be more stable and accurate than a second order scheme when taking into account the acceleration of bubbles before their collapse, and is recommended for the full cavitation modelling of acoustic treatment of liquid metals.

Large Eddy Simulation is employed to study two turbulent cavitating flows: over a cylinder and a wedge. A homogeneous mixture model is used to treat the mixture of water and water vapor as a compressible fluid. The governing equations are solved using a novel predictor- corrector method. The subgrid terms are modeled using the Dynamic Smagorinsky model. Cavitating flow over a cylinder at Reynolds number (Re) = 3900 and cavitation number (σ) = 1.0 is simulated and the wake characteristics are compared to the single phase results at the same Reynolds number. It is observed that cavitation suppresses turbulence in the near wake and delays three dimensional breakdown of the vortices. Next, cavitating flow over a wedge at Re = 200, 000 and σ = 2.0 is presented. The mean void fraction profiles obtained are compared to experiment and good agreement is obtained. Cavity auto-oscillation is observed, where the sheet cavity breaks up into a cloud cavity periodically. The results suggest LES as an attractive approach for predicting turbulent cavitating flows.

The objective of this study is to evaluate the performance of finite rate homogeneous mixture models in three key aspects: (a) the ability of the model to predict the dynamics of resolved small scale vapor regions, (b) the importance of finite rate mass transfer and (c) the impact of assuming 2D flow as is done in RANS simulations with a statistically homogeneous direction. We consider a bubble collapse problem to evaluate all these effects.

The paper presents the development of a cavitation erosion prediction method. The approach is tailored to marine applications and embedded into a VoF-based procedure for the simulation of turbulent flows. Supplementary to the frequently employed Euler-Euler models, Euler-Lagrange approaches are employed to simulate cavitation. The study aims to convey the merits of an Euler-Lagrange approach for erosion simulations. Accordingly, the erosion model is able to separate different damage mechanisms, e.g. micro-jets, single and collective bubble collapse, and also quantifies their contribution to the total damage. Emphasis is devoted to the prediction of the cavitation extend, the influence of compressible effects and the performance of the material damage model in practical applications. Examples included refer to 2D validation test cases and reveal a fair predictive accuracy.

The work focuses on the numerical optimization of converging diverging cavitating nozzles through nozzle dimensions and wall shape. The objective is to develop design rules for the geometry of cavitating nozzles for desired end-use. Two main aspects of nozzle design which affects the cavitation have been studied i.e. end dimensions of the geometry (i.e. angle and/or curvature of the inlet, outlet and the throat and the lengths of the converging and diverging sections) and wall curvatures(concave or convex).

Angle of convergence at the inlet was found to control the cavity growth whereas angle of divergence of the exit controls the collapse of cavity. CFD simulations were carried out for the straight line converging and diverging sections by varying converging and diverging angles to study its effect on the collapse pressure generated by the cavity. Optimized geometry configurations were obtained on the basis of maximum Cavitational Efficacy Ratio (CER)i.e. cavity collapse pressure generated for a given permanent pressure drop across the system. With increasing capabilities in machining and fabrication, it is possible to exploit the effect of wall curvature to create nozzles with further increase in the CER. Effect of wall curvature has been studied for the straight, concave and convex shapes. Curvature has been varied and effect of concave and convex wall curvatures vis-à-vis straight walls studied for fixed converging and diverging angles.It is concluded that concave converging-diverging nozzles with converging angle of 20° and diverging angle of 5° with the radius of curvature 0.03 m and 0.1530 m respectively gives maximum CER.

Preliminary experiments using optimized geometry are indicating similar trends and are currently being carried out. Refinements of the CFD technique using two phase flow simulations are planned.

The blade tip loading is often reduced as an effort to restrain sheet and tip vortex cavitation in the design of marine propellers. This CFD analysis demonstrates that an excessive reduction of the tip loading can cause cloud cavitation responsible for much of noise and surface erosion. Detached eddy simulations (DES) are made for cavitating flows on three tip- modified propellers, of which one is a reference propeller having an experimental result from a cavitation tunnel test with a hull model, and the other two are modified from the reference propeller by altering the blade tip loading. DES results have been validated against the experiment in terms of sheet and cloud cavitation. In DES, non-uniform hull wake is modelled by using the inlet flow and momentum sources instead of including a hull model. A 4-bladed Kappel propeller with a smooth tip bending towards the suction side is used as the reference propeller. For the reference propeller, sheet cavitation extends over a whole chord length in the hull wake peak. As the blade gets out of the wake peak, the rear part of sheet cavity is detached in a form of cloud cavitation. For the reference propeller, the tip pitch reduction from the maximum is about 35%. When decreasing the tip pitch reduction to 10%, tip vortex cavitation is formed and cloud cavitation is significantly weakened. When increasing the tip pitch reduction to 60%, sheet cavitation slightly moves to inner radii and cloud cavitation grows larger.

A panel method is applied to predict the performance of tip loaded propeller with and without cavitation modeling. For fully wetted cases, the geometry of the wake is shown to be critical to the computational accuracy. To align the wake surface, two methods are proposed and the full wake alignment scheme behaves better then PSF2 alignment. The boundary layer correction can also improve the pressure distribution especially near the trailing edge region. Finally, for cavitating cases, the results based on full wake alignment tend to create larger cavitation region and higher cavitation thickness compared to results based on PSF2 alignment.

A numerical simulation method of compressible gas-liquid two-phase flow is developed for analyses of a cavitation bubble. Thermodynamic state of both phases is described with stiffened gas equation of state. Interface of two phases is captured by Level-Set method. As internal energy jump between two phases is critical for the stability of computation, total energy equation is modified so that inviscid flux of energy is smoothly connected across the interface. Detail of governing equations as well as their discretization is described followed by the result of one-dimensional simple example computation.

3D LES numerical simulations were performed to investigate cavitation performance inside a jet pump. The results were found to match the test data most closely. The cavitation characteristics of the jet pump were then analyzed using changes in the inlet and outlet pressure to isolate its effect on cavitation. Both results shows that the increase of the inlet pressure generally increases the Renolds number but decrease the cavitation number, thus aggravate cavitation. The closing of the outlet valve increase the outlet pressure but decrease the flowrate ratio, resulting in the increase of velocity difference and vorticity in the mixing layer. So the cavitation first declines and then grows. The cavities appear slender and extended longer in the throat with high flowrate ratio. Conversely, the cavities look short and located in the front part of the throat with low flowrate ratio. Flow analysis indicated that the turbulence behavior in the shear layer and the overall mean pressure has great influence on the local pressure in jet pump, which reveal the reason of different cavitation shape observed in experiment.

A new algorithm for fast DNS cavitating flows simulations is developed. The algorithm is based on Kim and Moin projection method form. Homogeneous mixture approach with transport equation for vapour volume fraction is used to model cavitation and various cavitation models can be used. Influence matrix and matrix diagonalisation technique enable fast parallel computations.

Supercavitating vehicles are capable of achieving unprecedented speeds due to the presence of a large gas cavity surrounding their bodies. The control design and validation of these vehicles is challenging because planing forces, oscillations, and instability arise when the vehicle pierces the supercavity. In this paper, we propose a methodology to test control algorithms for a supercavitating vehicle subject to planing. With a free-to-rotate scale vehicle in a high-speed water tunnel, we reproduce planing and are capable of assessing active control technologies experimentally. Sponsored by the Office of Naval Research.

The present work reports some interesting experimental results for ventilated supercavitation in steady and unsteady flows. First, a variety of closure modes obtained as a result of systematic variation in Froude number and air entrainment, are reported. The closure mechanisms were found to differ from the standard criterion reported in the literature. Further, the occurrence of a variety of stable and unstable closure mechanisms were discovered that have not been reported in the literature. Next, a hypothesis is presented to explain the cause behind these different closure mechanisms. The proposed hypothesis is then validated by synchronized high-speed imaging and pressure measurements inside and outside of the supercavity. These measurements show that the supercavity closure is a function of instantaneous cavitation number under unsteady flow conditions. (Research sponsored by Office of Naval Research, USA)

A compressible density-based time-explicit low Mach number consistent viscous flow solver is utilised in combination with a barotropic cavitation model for the analysis of cloud cavitation on a circular leading edge (CLE) hydrofoil. For 5° angle of attack, cloud structure and shedding frequency for different cavitation numbers are compared to experimental data. A strong grid sensitivity is found in particular for high cavitation numbers. On a fine grid, a very good agreement with validation data is achieved even without explicit turbulence model. The neglect of viscous effects as well as a two-dimensional set-up lead to a less realistic prediction of cloud structures and frequencies. Comparative simulations with the Sauer-Schnerr cavitation model and modified pre-factors of the mass transfer terms underestimate the measured shedding frequency.

We present a CFD characterization of a new type of super-cavitating hydrofoil section designed to have optimal performance both in super-cavitating conditions and in sub-cavitating conditions (including transitional regime). The basic concepts of the new profile family are first introduced. Lift, drag and cavity shapes at different cavitation numbers are calculated for a new foil and compared with those of conventional sub-cavitating and super-cavitating profiles. Numerical calculations confirm the superior characteristics of the new hydrofoil family, which is able to attain high lift and efficiency both in sub-cavitating and super-cavitating conditions. Numerical calculations are based on a multi-phase fully turbulent URANSE solver with a bubble dynamic cavitation model to follow the generation and evaporation of the vapor phase. The new profile family, initially devised for ultra-high speed hydrofoil crafts, may result useful for diverse applications such as super-cavitating or surface-piercing propellers or high-speed sailing boats.

A compressible, two-phase, one-fluid solver has been developed to investigate the behaviour of cavitation models. The model is based on a transport equation for the volume fraction of gas. Numerical simulations are performed on a cavitating Venturi flow where a selfsustained cavitation pocket develops. The sheet dynamics involving traveling pressure waves is investigated.

In this work, the dynamic behavior of the non-equilibrium cavitation occurring around the underwater projectiles navigating with variable speed was numerically and theoretically investigated. The cavity collapse induced by the decelerating motion of the projectiles can be classified into two types: periodic oscillation and damped oscillation. In each type the evolution of the total mass of vapor in cavity are found to have strict correlation with the pressure oscillation in far field. By defining the equivalent radius of cavity, we introduce the specific kinetic energy of collapse and demonstrate that its change-rate is in good agreement with the pressure disturbance. We numerically investigated the influence of angle of attack on the collapse effect. The result shows that when the projectile decelerates, an asymmetric-focusing effect of the pressure induced by collapse occurs on its pressure side. We analytically explained such asymmetric-focusing effect.

Submerged structures that operate under extreme flows are prone to suffer large scale cavitation attached to their surfaces. Under such conditions the added mass effects differ from the expected ones in pure liquids. Moreover, the existence of small gaps between the structure and surrounding bodies filled with fluid also influence the dynamic response. A series of experiments and numerical simulations have been carried out with a truncated NACA0009 hydrofoil mounted as a cantilever beam at the LMH-EPFL cavitation tunnel. The three first modes of vibration have been determined and analysed under various hydrodynamic conditions ranging from air and still water to partial cavitation and supercavitation. A remote nonintrusive excitation system with piezoelectric patches has been used for the experiments. The effects of the cavity properties and the lateral gap size on the natural frequencies and mode shapes have been determined. As a result, the significance of several parameters in the design of such structures is discussed.

Bubbly shocks act as the dominant mechanism of shedding of partial cavities under certain conditions. The compressible nature of low void fraction regions in a partial cavity can provide conditions necessary for the existence of such bubbly shocks. Using X-ray densitometry as a flow visualisation mechanism, the dynamics of bubbly shock fronts with and without the presence of an obstacle are presented. Different flow features associated with the shock dynamics are identified and the associated flow physics explained.

We present the experimental results of water-entry cavity on a slender projectile, which moves in the opposite direction of gravity. The regime of the cavity including sheet cavity, supercavity and trailing cavity is exhibited and its relevance to Euler and Weber numbers are illuminated. Meanwhile, various pinch-off performances of the supercavity are analysed and the resulting re-entrance jet or cavity ripples are presented.

Simulations involving a large number of interacting bubbles in a bubble cloud are conducted to assess the effect of frequency and amplitude of a sinusoidal driving pressure on the bubble cloud behavior. As the pressure amplitude increases strong nonlinear bubble dynamics become more pronounced and higher pressures are generated at the wall. A resonance frequency, corresponding to the highest collective bubble behavior, results in a pressure peak orders of magnitudes higher than the excitation pressure. This frequency is significantly different from the natural frequency of a spherical cloud executing small amplitude oscillations.

The objectives of this paper are to investigate the unsteady structures and hydrodynamics of cavitating flows. Experimental results are presented for a Clark-Y hydrofoil, which is fixed at α=0°, 5° and 8°. The high-speed video camera and Particle Image Velocimetry (PIV) are applied to investigate the transient flow structures. The dynamic measurement system is used to record the dynamic characteristics. The cloud cavitation exhibits noticeable unsteady characteristics. For the case of α=0°, there exit strong interactions between the attached cavity and the re-entrant flow. While for the case of α=8°, the re-entrant flow is relatively thin and the interaction between the cavity and re-entrant flow is limited. The results also present that the periodic collapse and shedding of the large-scale cloud cavitation, which leads to substantial increase of turbulent velocity fluctuations in the cavity region. Experimental evidence indicates that the hydrodynamics are clearly affected by the cavitating flow structures, the amplitude of load fluctuation are much higher for the cloud cavitating cases.

Cavitation characteristics of hydrofoils with sinusoidal leading edge were examined experimentally at a Reynolds number of 7.2 × 10⁵. The hydrofoils had an underlying NACA 63₄-021 profile and an aspect ratio of 4.3. The sinusoidal leading edge geometries included three amplitudes of 2.5%, 5%, and 12% and two wavelengths of 25% and 50% of the mean chord length. Results revealed that cavitation on the leading edge-modified hydrofoils existed in pockets behind the troughs whereas the baseline hydrofoil produced cavitation along its entire span. Moreover, cavitation on the modified hydrofoils appeared at consistently lower angles of attack than on the baseline hydrofoil.

Various closure conditions of a ventilated cavity enveloping all or part of a high-speed underwater body are introduced, including those involving a propulsion jet. The flow regimes for the latter are described based on Efros-Paryshev theory, which is extended to estimate the efficiency and fundamental limitations of a rocket-type propulsor.

In this paper, the unsteady cavitation phenomena on a NACA0015 hydrofoil is numerically simulated by unsteady Reynolds-Averaged Navier-Stokes (URANS) method and Large Eddy Simulation (LES) in single-fluid approaches to multiphase modelling, respectively. It is observed that the large-scale structures and characteristic periodic shedding predicted by the URANS with the modified SST k-ω turbulence model show a good qualitative match with the experimental observations but with quantitative discrepancies, such as a different cavity length and volume, and a different location of shedding. Compared to the URANS results, the LES results reproduce more details of unsteady dynamics with an improved quantitative agreement.

Finite volume based modeling of ventilated supercavity pulsation and its mitigation via a priori modulation of ventilation flow was investigated. Simulated pulsation was numerically achieved, as was mitigation of pulsation via sinusoidal modulation of the ventilation flow. In addition to confirmation that the numerical approach is sufficient to capture mitigation, it was found that modulated ventilation, without altering the mean ventilation mass flow rate, results in altered cavity size, pressure, and closure condition.

The added mass effects on a NACA0009 hydrofoil under cavitation conditions determined in a cavitation tunnel have been numerically simulated using finite element method (FEM). Based on the validated model, the effects of averaged properties of the cavity considered as a two-phase mixture have been evaluated. The results indicate that the void ratio of the cavity plays an increasing role on the frequency reduction ratio and on the mode shape as the mode number increases. Moreover, the sound speed shows a more important role than the average cavity density.

An Eulerian/Lagrangian multi-scale two-phase flow model is developed to simulate the various types of cavitation including bubble, sheet, and tip vortex cavitation. Sheet cavitation inception, unsteady breakup, and cloud shedding on a hydrofoil are used as an example here. No assumptions are needed on mass transfer between phases; instead, the method tracks bubble nuclei, which are in the bulk of the liquid and those generated by nucleation from solid boundaries and this is- sufficient to accurately capture the sheet dynamics. The multi-scale model includes a micro-scale model for tracking the bubbles, a macro-scale model for describing large cavity dynamics and a transition scheme to bridge the micro and macro scales. Nuclei are treated as flow singularities until they grow into large bubbles, which eventually merge to form a large scale discretised sheet cavity. The sheet performs large scale oscillations with a periodic reentrant jet forming under the sheet cavity, traveling upstream, and breaking the cavity. This results in bubble cloud formation and in high pressure peaks as the broken pockets shrink and collapse while travelling downstream. The results for a NACA0015 foil are in good agreement with the experimental data.

Partial cavities can undergo auto-oscillation causing large pressure pulsations, unsteady loading of machinery and generate significant noise. In the current experiments fully shedding cavities forming in the separated flow region downstream of a wedge were investigated. The Reynolds number based on hydraulic diameter was of the order of one million. The cavity dynamics were studied with and without injection of non-condensable gas into the cavity. Gas was injected directly into the cavitation region downstream of the wedge's apex, or into the recirculating region at mid cavity so that for the same amount of injected gas less ended up in the shear layer. It was found that relatively miniscule amounts of gas introduced into the shear layer at the cavity interface can reduce vapour production and dampen the auto oscillations, and the same amount of gas injected into the mid cavity would not have the same effect. The authors also examined whether the injected gas can switch the shedding mechanism from one dominated by condensation shock to one dominantly by reentrant jet.

An experimental study was performed to evaluate some of the claims of Paryshev (2006) regarding changes to ventilated cavity behavior caused by the interaction of a jet with the cavity closure region. The experiments, conducted in the 1.22m dia. Garfield Thomas Water Tunnel, were performed for EDD to tunnel diameter of 0.022, Fr = 14.5 and 26.2. The model consisted of a converging-section nozzle mounted to the base of a 27.9mm 37° cone cavitator placed on the tunnel centerline at the end of a 138.4mm long streamlined strut. A ventilated cavity was formed over the model, then an air jet, issuing from a converging nozzle, was initiated. Changes to cavity behavior were quantified in terms of cavitation number, thrust-to- drag ratio, and stagnation pressure ratio at the jet nozzle. The results show that, while the overall trends predicted by Paryshev were observed, the data did not fully collapse, suggesting that many of the effects neglected by Paryshev's model have measureable effect.

To study the cavity dynamics behind a two-dimensional wedge, a pressure-based numerical solver for incompressible cavitating flow and a density-based numerical solver for compressible cavitating flow solvers were developed, respectively, using a cell-cantered finite volume method. Cavity interface was captured based on an approximation of homogeneous mixture flow. Cavity dynamics analysed by the two developed solvers were compared and validated against experimental data. Cavity shape and length, re-entrant jet, and vortical cavity shedding were compared and discussed.

Ventilated cavities detaching from a backward facing step (BFS) are investigated for a range of upstream boundary layer thicknesses in a cavitation tunnel. The upstream turbulent boundary layer thickness is varied by artificial thickening of the test section natural boundary layer using an array of transversely injected jets. Momentum thickness Reynolds numbers from 6.6 to 44 x 10³ were tested giving boundary layer thickness to step height ratios from 1.25 to 3.8. A range of cavity lengths were obtained by variation of the ventilation flow rate for several freestream Reynolds numbers. Cavity length to step height ratios from 20 to 80 were achieved. Cavity length was found to be linearly dependent on ventilation rate and to decrease with increasing boundary layer thickness and/or Reynolds number. This result may have implications in the practical optimization of these flows which occur in applications such as drag reduction on marine hull forms.

The control of cloud cavitation, especially large scale cloud cavitation(LSCC), is always a hot issue in the field of cavitation research. However, there has been little knowledge on the evolution of cloud cavitation since it is associated with turbulence and vortex flow. In this article, the structure of cloud cavitation shed by sheet cavitation around different hydrofoils and a wedge were observed in detail with high speed camera (HSC). It was found that the U-shaped vortex structures always existed in the development process of LSCC. The results indicated that LSCC evolution was related to this kind of vortex structures, and it may be a universal character for LSCC. Then vortex strength of U-shaped vortex structures in a cycle was analyzed with numerical results.

Cavitation on two symmetric foils, a NACA0015 hydrofoil and a scaled-down model of a Francis turbine guide vane (GV), was investigated by high-speed visualization and PIV. At small attack angles the differences between the profiles of the mean and fluctuating velocities for both hydrofoils were shown to be insignificant. However, at the higher angle of incidence, flow separation from the GV surface was discovered for quasi-steady regimes including cavitation-free and cavitation inception cases. The flow separation leads to the appearance of a second maximum in velocity fluctuations distributions downstream far from the GV surface. When the transition to unsteady regimes occurred, the velocity distributions became quite similar for both foils. Additionally, for the GV an unsteady regime characterized by asymmetric spanwise variations of the sheet cavity length along with alternating periodic detachments of clouds between the sidewalls of the test channel was for the first time visualized. This asymmetric behaviour is very likely to be governed by the cross instability that was recently described by Decaix and Goncalvès [8]. Moreover, it was concluded that the existence of the cross instability is independent on the test body shape and its aspect ratio.

The planar and axially symmetric problems of cavitational flow around the body are considered by the Riaboushinsky scheme. The running-on flow is considered to be established for vortex-free ideal and incompressible fluid. In order to find the flow around the body the boundary elements numerical method is used which incorporates the quadrature formulas without saturation. To find the free boundary the gradient descent method based on the Riabushischinsky method is proposed. The resistance force acting on the cavitator is expressed in terms of the Riabushischinsky function, enabling us to calculate the force with rather high precision for small cavitation numbers. The dependence of the resistance coefficient for cavitators of different shape is studied: for wedge and cone, the circular arc and the spherical segment.

Spatio-temporal description of the cavitating flow around hydrofoil with 8 degrees incidence using proper orthogonal decomposition (POD) is presented. POD is a suitable tool, which provides information not only about the flow dynamics, but also about relevance of different flow structures. POD also enables to track energy transport within the domain and energy transfer among the eigenmodes of the flow field. Analysis documents change of the flow structure for decreasing cavitation number, which can be most likely attributed to sheet/cloud cavitation transition.

The article presents a number of dependences for reliable calculation of parameters required when performing supercavitation experiments. They include the equations and dependences for calculation of the shape and basic dimensions of cavities formed behind axisymmetric cavitators, influence of the free surface, cavity buoyancy, and cavitator lift, as well as compensation for certain scale effects.

A method for mitigating ventilated supercavity pulsation is presented. The method, which has its roots in parametric oscillators, shifts the supercavity resonance frequency by modulating its gas ventilation rate. When appropriately modulated, the supercavity is driven off resonance by the waves on the gas/water interface (that remain unchanged) and pulsation is, therefore, suppressed. Initial experimental results indicate that the gas ventilation rate modulation frequency must be sufficiently different from the supercavity resonance frequency to mitigate pulsation. If the modulation frequency is not sufficiently different from the supercavity resonance frequency, pulsation is simply shifted in frequency with a corresponding small reduction in the supercavity interior pressure spectrum level and radiated noise.

The fact of injecting bubbles into a cavitating flow influences typical cavitating behavior. Cavitation and aerated cavitation experiments has been carried out on a symmetrical venturi nozzle with convergent/divergent angles of 18° and 8°, respectively. A snapshot Proper Orthogonal Decomposition (POD) technique is used to identify different modes in terms of discharge flow velocity, pressure and injected quantity of air. The energy spectrum per given mode is also presented. The first four modes are outlined in the present paper for an aerated and non-aerated cavitating flows.

The nucleation process on an isolated roughness element, located at the point of minimum pressure of a NACA 0015 hydrofoil was studied experimentally and computationally. The objective of this study was to investigate the working mechanism of bubble-induced sheet cavitation inception. High-speed micro-scale observations show the generation of a streak of cavitation—attached to the roughness element—in the wake of the bubble. Below its critical diameter, the bubble can detach from the streak cavity and travel on while the streak cavity remains. The solutions of a Rayleigh-Plesset equation along a streamline extracted from a RANS calculation show strong similarities with the experimental observations, but a factor 5 to 10 higher frame rate is needed to validate the calculations.

The paper presents the formulation of the problems and calculation method of the cavity geometry in real conditions. The calculating procedure used here is based on the method of small perturbations of the thin body. The calculation results and their comparison with the experimental data for the following cases are presented: cavity axis deformation under the effect of gravity forces, cavity behind elliptical cavitator, cavity behind cavitator at nonzero attack angle, the pressure pulsations in the cavity, the motion near boundaries and others.

The influence of the free surface on the cavitating flow is an important issue involved in the design of high speed surface vehicles. In the present paper, unsteady cavitating turbulent flow around an axisymmetric body near the free surface was investigated by both launching experiment and LES simulation. The vortex motion induced by cavity shedding under the effect of the free surface is emphatically analyzed by comparing with the submerged condition. The vortex shedding process around the projectile is not synchronized, while the asymmetric characteristic in collapse process is more remarkable, with the generation of multiple vortex ring structures.

An experimental study of the axisymmetric slender body underwater movement was conducted using high-speed photography technology. From the results of the experiment, the characteristics of cavitation and ballistic of the axisymmetric, including the formation, development, evolution and collapse of the cavity, are presented in the paper. The experimental results show that the axisymmetric slender body moves in a supercavity, and the slender body rotate in the supercavity on its head at the same time due to the perturbation of launching. The supercavity wall is transparent and smooth except the tail itself. The impact between the tail of slender body and supercavity wall resulted from the slender body's rotation is termed as tail- slap which is one way to keep the stabilization of the movement. Series of different flow mechanisms and the relationship between ballistic characteristics and cavity characteristics with defferent initial velocities are discussed. The slender bodies have different accelerations and ballistics with different initial velocity which means they have different drag forces.

Study on dynamics of a projectile running with a cavity in the process of water entry closely relates to the development of new generation of air-to-water vehicle. It becomes a key concern to develop a flexible model of the high-speed water-entry projectile. The projectile is modelled using the unsteady cavity model from Serebryakov in the frame of the rigid-body dynamics theory. Based on the model, without loss of generality, oblique water-entry projectile running with an open cavity is simulated, and numerical results are in good agreement with measured data available. The model proves effective and has a great potential to investigate ballistics of an air-dropped vehicle at the early stage of water entry.

This paper discusses a collective quantum effect which might play an important role in sonoluminescence experiments. We suggest that it occurs during the final stages of the collapse phase and enhances the heating of the particles inside the bubble.

This paper presents the real-time and in-situ synchrotron X-ray high speed imaging studies of ultrasound bubbles and bubble cloud in a liquid Sn-30%Cu alloy. The collective behaviour of the ultrasound bubbles generated by ultrasound powders of 60 W and 100W were successfully captured. The number density of the individual bubbles and the density of the continuous bubble cloud were calculated from the information extracted from the images sequences and presented for the first time for the liquid Sn-30%Cu alloy.

The thermodynamic effects in cavitating flow are observed on a simple Venturi profile. A thorough experimental investigation of the temperature field on cavitating flow has been performed in water of 100°C at different operating conditions. Temperature measurements were performed with Infra-Red (IR) high-speed camera, while visualisation was made with conventional high-speed camera. Both, average temperature fields and temperature dynamics are presented at different operating conditions and compared with collected data in visual spectrum. In the vicinity of the throat a temperature depression up to 0.5 K was recorded.

Developing a robust computational strategy to address the rich physics characteristic involved in the thermodynamic effects on the cryogenic cavitation remains a challenging problem. The objective of this present study is to model the numerical methodology to simulate the cryogenic cavitation by implanting the thermodynamic effects to the Schnerr-Sauer cavitation model, and coupling the energy equation considered the latent heat. For this purpose, cavitating flows are investigated over a three dimensional hydrofoil in liquid hydrogen and nitrogen. Experimental measurements of pressure and temperature are utilized to validate the extensional Schnerr-Sauer cavitation model. Specifically, the further analysis of the cavitation solution with respect to the thermodynamic term is conducted. The results show that the extensional Schnerr-Sauer cavitation model predicts better accuracy to the quasi-steady cavitation over hydrofoil in the two cryogenic fluids.

The aims of this paper are to study the thermo-fluid cavitating flows and to evaluate the effects of physical properties on cavitation behaviours. The Favre-averaged Navier-Stokes equations with the energy equation are applied to numerically investigate the liquid nitrogen cavitating flows around a NASA hydrofoil. Meanwhile, the thermodynamic parameter Σ is used to assess the thermodynamic effects on cavitating flows. The results indicate that the thermodynamic effects on the thermo-fluid cavitating flows significantly affect the cavitation behaviours, including pressure and temperature distribution, the variation of physical properties, and cavity structures. The thermodynamic effects can be evaluated by physical properties under the same free-stream conditions. The global sensitivity analysis of liquid nitrogen suggests that ρ_v, C_l and L significantly influence temperature drop and cavity structure in the existing numerical framework, while p_v plays the dominant role when these properties vary with temperature. The liquid viscosity μ_l slightly affects the flow structure via changing the Reynolds number R_e equivalently, however, it hardly affects the temperature distribution.

An important input parameter for a recently developed semi-empirical prediction method for the noise generated by cavitating vortices is the diameter of the cavitating vortex. This diameter may be obtained from models of non-cavitating vortices that describe the radial distribution of the azimuthal velocity, for given vortex strength and size of the viscous core. The present paper discusses several vortex models that suit this purpose and compares the distribution of the azimuthal velocity as well as that of the pressure with detailed experimental data for the tip vortex of a rectangular wing obtained from literature.

The present study is related to the development of the tip vortex cavitation in Kaplan turbines. The investigation is carried out on a simplified test case consisting of a NACA0009 blade with a gap between the blade tip and the side wall. Computations with and without cavitation are performed using a R ANS modelling and a transport equation for the liquid volume fraction. Compared with experimental data, the R ANS computations turn out to be able to capture accurately the development of the tip vortex. The simulations have also highlighted the influence of cavitation on the tip vortex trajectory.

This paper presents the calculation method of tip cavitation with wake alignment. Tip cavitation consists of tip vortex cavitation and tip super cavitation which means the undeveloped and local super cavitation around blade tip. The feature of this study is that the method applies the wake alignment model in order to express the realistic phenomena of tip cavitation and predict the pressure fluctuation more accurately. In the present method, the wake sheet is deformed according to the induced velocity vector on the vortex lines. The singularity of the potential vortex can be removed by using the Rankine Vortex model. This paper shows the calculated results regarding cavitation pattern, pressure fluctuation etc. comparing with published experimental data and calculated results without wake alignment.

The phenomenon of vortex singing in tip vortex cavitation is studied experimentally in this paper. It is revealed that the vortex singing can be observed during the vortex cavity transfer from one phase to another in the same incoming flow condition. The state of vortex singing can only exist in a short duration from several seconds to several minutes. The sound of the vortex singing for different water qualities, including air content and nuclei populations of water are measured by a hydrophone. It is found that the tones of vortex singings are very different under different flow conditions and water qualities.

The design of an efficient propeller is limited by the harmful effects of cavitation. The insufficient understanding of the role of vortex cavitation in noise and vibration reduces the maximum efficiency by a necessary safety margin. The aim in the present study is to directly relate propeller cavitation sound to tip vortex cavity dynamics. This is achieved by a dedicated experiment in a cavitation tunnel on a specially designed two-bladed propeller using a high-speed video camera and a hydrophone. The sound signature of a tip vortex cavity is not evidently present in the sound spectrum above the tunnel background. The addition of a simulated wake inflow results in a high amplitude broadband sound. With a decrease in the free-stream pressure the centre frequency of this sound decreases as a result of a larger vortex cavity diameter. In the near future each blade passage in the high-speed video will be analyzed in detail. The frequency content of the cavity dynamics can then be directly related to the measured sound. An analytic model for vortex cavity dynamics resulting in a cavity eigenfrequency using a vortex velocity model can finally be evaluated as a design instrument for estimation of broadband sound from propeller cavitation.

Effects of turbulence models on the simulations of tip vortex wetted flows and cavitating flows are studied. Two types RANS turbulence models, with and beyond the Boussinesq turbulent-viscosity hypothesis, are investigated by examining experimental results regarding strain rate and Reynolds shear stress distributions in the vortex region. The numerical results imply that the spatial phase shift between the mean strain rate and Reynolds stresses can be accurately modeled by the nonlinear k-ε turbulence model; the tip vortex cavitation region can only be predicted using the nonlinear turbulence model. The mechanism of the over-dissipation due to the turbulence model is analyzed in terms of the turbulence production, which is one of the dominant source terms in the transport equations of energy. The numerical results imply that the nonlinear k-ε model is a promising candidate for predicting tip vortex cavitation flows in practical applications at a reasonable computational cost.