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Large-eddy simulation of flow over an open cavity corresponding to the experimental setup of Liu and Katz (2008, 'Cavitation Phenomena Occurring Due to Interaction of Shear Layer Vortices With the Trailing Corner of a Two-Dimensional Open Cavity,' Phys. Fluids, 20(4), p. 041702)is performed. The filtered, incompressible Navier--Stokes equations are solved using a co-located grid finite-volume solver with the dynamic Smagorinsky model for a subgrid-scale closure. The computational grid consists of around 7 x [10.sup.6] grid points with 3 x [10.sup.6] points clustered around the shear layer, and the boundary layer over the leading edge is resolved. The only input from the experimental data is the mean. velocity profile at the inlet condition. The mean flow is superimposed with turbulent velocity fluctuations generated by solving a forced periodic duct flow at a freestream Reynolds number. The flow statistics, including mean and rms velocity fields and pressure coefficients, are compared with the experimental data to show reasonable agreement. The dynamic interactions between traveling vortices in the shear layer and the trailing edge affect the value and location of the pressure minima. Cavitation inception is investigated using two approaches: (i) a discrete bubble model wherein the bubble dynamics is computed by solving the Rayleigh--Plesset and the bubble motion equations using an adaptive time-stepping procedure and (ii) a scalar transport model for the liquid volume fraction with source and sink terms for phase change. Large-eddy simulation, together with the cavitation models, predicts that inception occurs near the trailing edge similar to that observed in the experiments. The bubble transport model captures the subgrid dynamics of the vapor better, whereas the scalar model captures the large-scale features more accurately. A hybrid approach combining the bubble model with the scalar transport is needed to capture the broad range of scales observed in cavitation. [DOI: 10.1115/1.4002744]

A numerical method including a macroscopic cavitation model based on the homogeneous flow theory and a microscopic cavitation model based on the bubble dynamics is proposed for the prediction of the impact force caused by cavitation bubble collapse in cavitating flows. A large eddy simulation solver, which is incorporated with a macroscopic cavitation model, is applied to simulate the unsteady cavitating flows. Based on the simulated flow field, the evolution of the cavitation bubbles is determined by a microscopic cavitation model from the resolution of a Rayleigh--Plesset equation including the effects of the surface tension, the viscosity and compressibility of fluid, the thermal conduction and radiation, the phase transition of water vapor at the interface, and the chemical reactions. The cavitation flow around a hydrofoil is simulated to validate the macroscopic cavitation model. A good quantitative agreement is obtained between the prediction and the experiment. The proposed numerical method is applied to predict the impact force at cavitation bubble collapse on a KT section in cavitating flows. It is found that the shock pressure caused by cavitation bubble collapse is very high. The impact force is predicted qualitatively compared with the experimental data. [DOI: 10.1115/1.4002506] Keywords: cavitating flows, bubble collapse, impact force, large eddy simulation

This paper discusses and analyzes the control volume of a piston bore constrained by the valve plate in axial piston pumps. The vacuum within the piston bore caused by the rise volume needs to be compensated by the flow; otherwise, the low pressure may cause the cavitations and aerations. In the research, the valve plate geometry can be optimized by some analytical limitations to prevent the piston pressure below the vapor pressure. The limitations provide the design guide of the timings and overlap areas between valve plate ports and barrel kidneys to consider the cavitations and aerations. [DOI: 10.1115/1.4002058] Keywords: cavitation, optimization, valve plate, pressure undershoots

The noncavitating and cavitating flows over a cross-flow water turbine are simulated by using an unsteady Navier-Stokes formulation. For the cavitating flow case, a homogeneous mixture with a varying density is considered and one additional transport equation is explicitly solved in time for the liquid volume fraction. The instantaneous rate of vapor production and absorption appearing as a source term is governed by a hydrodynamic model based on a simplified bubble dynamic equation. The spatial discretization is achieved by a 2D multiblock technique consisting of fixed and rotating blocks, which were especially adapted for Darrieus geometry. Several test cases corresponding to experiments performed on fixed and rotating blades are selected to compare the numerical results with experimental data. Finally, a calculation of a monobladed cavitating cross-flow turbine is presented. The effect of cavitation on the dynamic stall phenomenon and on the turbine performance is analyzed. In particular, it is shown that cavitation earlier reveals the stall phenomenon on the blades and magnifies the size of the shedding vortex structures in the turbine. [DOI: 10.1115/1.4001966] Keywords: Navier-Stokes, cross-flow water turbine, numerical modeling, unsteady cavitation

The paper presents full 3D numerical simulations and experimental investigations of the cavitating flow through three axial inducers. These inducers are identified by the tip blade angle at the leading edge [[beta].sub.1T]=8, 10, and 13 deg. The numerical and experimental investigations were carried out at the LEMFI laboratory (Laboratoire d'Energetique et de Mecanique de Fluides Interne) of the ENSAM-Paris center (Ecole Nationale Superieure d'Arts et Metiers). A review of the cavitating regime modeling and the cavitation homogeneous model used for this paper's calculations is first presented. The numerical model is based on a combination of the multiphase flow equations with a truncated version of the Rayleigh-Plesset model predicting the complicated growth and collapse processes of bubbles. The mass transfers due to cavitation are source/sink terms in continuity equations of the liquid and vapor phases. The cavitation model also features a solution methodology which implicitly couples the continuity and momentum equations together. The main results are presented for the inducers at a range of flow rates and cavitation numbers: (1) Experimental results concerning: (i) the overall performances: Pressure head coefficient and efficiency versus flow rates; (ii) critical cavitation number (5% and 15% of drop) versus the flow rate; (2) Numerical results concerning: (i) the overall performances; (ii) the numerically investigated water vapor volume fraction distributions and other CFD results, which enable us to explain the cavitating behavior for these inducers; (iii) the location and sizes of the blade cavity and backflow vortex. Finally, the comparisons between experimental and simulated results on the overall performances, cavity sizes and cavity location are discussed. A qualitative agreement between experimental and predicted results was found for two inducers for a range of flow rates. The head breakdown in the simulations started at a different cavitation coefficient than that in the experiment. [DOI: 10.1115/1.2353265] Keywords: cavitation, inducer, CFD, experiment, head-drop

The use of cavitation impact is a practical method for improving the fatigue strength of metals in the same way as shot peening. In the case of peening using cavitation impact, cavitation is produced by a high-speed submerged water jet with cavitation, i.e., a cavitating jet. A cavitating jet in air was successfully generated by injecting a high-speed water jet into a low-speed water jet injected into air using a concentric nozzle. In order to investigate the various appearances of cavitating jets in air, an observation was carried out using high-speed photography and high-speed video recording. In this study, periodical shading of the cavitation cloud was observed and the frequency of the shading was found to be a function of the injection pressure of the low-speed water jet. Unsteadiness of the low-speed water jet, which is related to the periodical shading of the cloud, was also observed. [DOI: 10.1115/1.2060737]

A Reynolds-averaged Navier-Stokes computational model of homogeneous multiphase flow is presented. Cavitation driven thrust and torque breakdown over a wide range of advance ratios is modeled for an open propeller. Computational results are presented as a form of validation against water tunnel measured thrust and torque breakdown for the propeller. Successful validation of the computational model is achieved. Additional observations are made with regards to cavity size and shape as well as cavitation breakdown behavior. [DOI: 10.1115/1.1988343]

The cavitating flow around a marine propeller is studied using an unstructured grid based Reynolds-averaged Navier-Stokes computational fluid dynamics method. A cavitation model based on a single-fluid multi-phase flow method is implemented in the Navier-Stokes solver. The proposed computational approach for cavitation is validated against a benchmark database for a cavitating hydrofoil as well as measured data for a cavitating marine propeller. The leading edge and mid-chord cavitation on the hydrofoil is reproduced well and shows good comparison with the well-known experimental data. The predicted noncavitating open water performance of the marine propeller geometry agrees well with the measured one. Finally, the cavitating propeller performance as well as cavitation inception and cavity shape are in good agreement with experimental measurements and observation. The overall results suggest that the present approach is practicable for actual cavitating propeller design procedures without lengthy preprocessing and significant preliminary knowledge of the flow field. [DOI: 10.1115/1.1989370]

One of the important research areas in the water-entry problem is the cavity dynamics. A theoretical analysis is presented to predict the dynamics of water-entry cavity up to the first cavity closure, which is generated by a solid body entering a semi-infinite free surface of water at a wide range of entry speed. Two types of cavity closure, which are surface closure and the deep closure, depending on the magnitude of ambient atmosphere pressure and entry speed are described by the proposed theory. The time of surface closure at the relatively low-speed entry regime is estimated and compared with published experimental data. Currently no experimental data are available for the high-speed entry case.

The fundamental characteristics of the two-dimensional cavitating flow of liquid helium through a horizontal converging-diverging nozzle near the lambda point are numerically investigated to realize the further development and high performance of new multiphase superfluid cooling systems. First, the governing equations of the cavitating flow of liquid helium based on the unsteady thermal nonequilibrium multifluid model with generalized curvilinear coordinates system are presented, and several flow characteristics are numerically calculated, taking into account the effect of superfluidity. Based on the numerical results, the two-dimensional structure of the cavitating flow of liquid helium though a horizontal converging-diverging nozzle is shown in detail, and it is also found that the generation of superfluid counterflow against normal fluid flow based on the thermomechanical effect is conspicuous in the large gas phase volume fraction region where the liquid to gas phase change actively occurs. Furthermore, it is clarified that the mechanism of the He I to He II phase transition caused by the temperature decrease is due to the deprivation of latent heat for vaporization from the liquid phase. [DOI: 10.1115/1.1601253]

The current study considers the prediction of tip vortex cavitation inception at a fundamental physics based level. Starting form the observation that cavitation inception detection is based on the 'monitoring' of the interaction between bubble nuclei and the flow field, the bubble dynamics is investigated in detail. A spherical model coupled with a bubble motion equation is used to study numerically the dynamics of a nucleus in an imposed flow field. The code provides bubble size and position versus time as well as the resulting pressure at any selected monitoring position. This model is used to conduct a parametric study. Bubble size and emitted sound versus time are presented for various nuclei sizes and flow field scales in the case of an ideal Rankine vortex to which a longitudinal viscous core size diffusion model is imposed. Based on the results, one can deduce cavitation inception with the help of either an 'optical inception criterion' (maximum bubble size larger than a given value) or an 'acoustical inception criterion' (maximum detected noise higher than a given background value). We use here such criteria and conclude that scaling effects can be inherent to the way in which these criteria are exercised if the bubble dynamics knowledge is not taken into account. [DOI: 10.1115/1.1521956]

An Eulerian/Lagrangian computational procedure was developed for the prediction of cavitation inception by event rate. The carrier-phase flow field was computed using an Eulerian Reynolds-averaged Navier-Stokes (RANS) solver. The Lagrangian analysis was one-way coupled to the RANS solution, since at inception, the contributions of mass, momentum, and energy of the microbubbles to the carrier flow are negligible. The trajectories were computed using Newton's second law with models for various forces acting on the bubble. The growth was modeled using the Rayleigh-Plesset equation. The important effect of turbulence was included by adding a random velocity component to the mean flow velocity and by reducing the local static pressure. Simulation results for the Schiebe body indicate agreement with experimentally observed trends and a significant event rate at cavitation indices above visual inception. [DOI: 10.1115/1.1522411]

Unsteady cavitation in a Venturi-type section was simulated by two-dimensional computations of viscous, compressible, and turbulent cavitating flows. The numerical model used an implicit finite volume scheme (based on the SIMPLE algorithm) to solve Reynolds-averaged Navier-Stokes equations, associated with a barotropic vapor/liquid state law that strongly links the density variations to the pressure evolution. To simulate turbulence effects on cavitating flows, four different models were implemented (standard k-[epsilon] RNG; modified k-[epsilon] RNG; k-[omega] with and without compressibility effects), and numerical results obtained were compared to experimental ones. The standard models k-[epsilon] RNG and k-[omega] without compressibility effects lead to a poor description of the self-oscillation behavior of the cavitating flow. To improve numerical simulations by taking into account the influence of the compressibility of the two-phase medium on turbulence, two other models were implemented in the numerical code: a modified k-[epsilon] model and the k-[omega] model including compressibility effects. Results obtained concerning void ratio, velocity fields, and cavitation unsteady behavior were found in good agreement with experimental ones. The role of the compressibility effects on turbulent two-phase flow modeling was analyzed, and it seemed to be of primary importance in numerical simulations. [DOI: 10.1115/1.1524584]

This paper focuses on the onset of tip-leakage cavitation on a fixed hydrofoil. The objectives are to investigate the effect of gap size on the flow structure, conditions of cavitation inception, the associated bubble dynamics and cavitation noise. The same hydrofoil with three tip gap sizes of 12%, 28%, and 52% of the maximum tip thickness are studied. Controlled cavitation tests are performed after de-aerating the water in the tunnel and using electrolysis to generate cavitation nuclei. The experiments consist of simultaneously detecting cavitation inception using a 2000 fps digital camera (visual) and two accelerometers ('acoustic') mounted on the test section windows. Good agreement between these methods is achieved when the visual observations are performed carefully. To obtain the time-dependent noise spectra, portions of the signal containing cavitation noise are analyzed using Hilbert-Huang transforms. Rates of cavitation events as a function of the cavitation index (sigma) for the three gap sizes are also measured. The cavitation inception index decreases with increasing gap sizes. The experiments demonstrate that high-amplitude noise spikes are generated when the bubbles are distorted and 'shredded'--broken to several bubbles following their growth in the vortex core. Mere changes to bubble size and shape caused significantly lower noise. High-resolution particle image velocimetry (PIV) with a vector spacing of 180 [micro]m is used to measure the flow, especially to capture the slender tip vortices where cavitation inception is observed. The instantaneous realizations are analyzed to obtain probability density functions of the circulation of the leakage vortex. The circulation decreases with increasing gap sizes and minimum pressure coefficients in the cores of these vortices are estimated using a Rankine model. The diameter of the vortex core varied between 540-720 [micro]m. These coefficients show a very good agreement with the measured cavitation inception indices. [DOI: 10. 1115/1.1514496]

A novel technique for vibro-acoustical diagnostics of turbine cavitation is introduced and its use demonstrated on a Francis turbine. The technique enables identification of different cavitation mechanisms functioning in a turbine and delivers detailed turbine cavitation characteristics, for each of the mechanisms or for the total cavitation. The characteristics specify the contribution of every critical turbine part to the cavitation intensity. Typical diagnostic results: (1) enable optimization of turbine operation with respect to cavitation erosion; (2) show how a turbine's cavitation behavior can be improved; and (3) form the basis for setting up a high-sensitivity, reliable cavitation monitoring system. [DOI: 10.1115/1.1511162]

Wylie's discrete gas cavity model offers a simple way to simulate transients in liquids with a small amount of free gas, and to model vaporous and gaseous cavitations. It uses a constant and gas-free wave speed to avoid interpolations and a weighting factor to control numerical oscillations. The model has an intriguing ability to capture features associated with pressure-dependent wave speeds. This paper describes a yon Neumann analysis on this model shows why the need for the weighting factor and how to select it, and explains why the model exhibits variable wave speed features.

The cavitation inception process in trailing vortices has been studied for several years. One of the important findings from these studies is the strong sensitivity to nuclei size and number as well as significant viscous effects. In order to understand the nucleation and bubble growth process in more detail a photographic study was conducted with the aim of developing high quality visualizations of the dynamical growth of bubbles.

This paper illustrates the effects of the dynamics of bubbles with arbitrary vapor-gas contents on the inviscid and viscous stability of two-dimensional parallel bubbly flows of low void fraction. The linear perturbation equations derived for the stability analysis include the effects of bubble compressibility, inertia, and energy dissipation due to the viscosity of the liquid and the transfer of heat and mass as a consequence of compression/ expansion of the noncondensable gas and evaporation/condensation of the vapor contained in the bubbles. Numerical solution of the spatial stability problem for two-dimensional inviscid shear layers and Blasius boundary layers confirms that the presence of the dispersed phase is generally in favor of stability. Significant deviations from the classical results for compressible and incompressible single phase fluids are observed, especially when the occurrence of large compliant and/or resonant oscillations of the bubbles greatly enhances their dynamic coupling with the perturbation field. More importantly, the present analysis points out some major differences in the stability of parallel flows with noncondensable gas bubbles with respect to cavitating flows containing bubbles with a dominant content of vapor. Unconditional stability is predicted in the travelling bubble cavitation limit for low pressures and high vapor mass fraction of the bubble contents. Results are shown to illustrate these effects for some representative flow configurations and conditions.

Cavitation observations were made using a highly instrumented 2D NACA 0015 hydrofoil mounted in a specially designed water tunnel. It was found that the dynamic characteristics of the cavitation vary considerably with various combinations of angle of attack and cavitation number, (sigma). At higher angles of attack, two types of flow unsteadiness are observed. At low (sigma), a low frequency shedding of cloud cavitation results in a strong oscillation in lift and (Delta)p at a Strouhal number, based on chord length, fc/U, of about 0.15. This frequency is relatively insensitive to changes in (sigma). As (sigma) is raised, the harmonic content of the oscillations changes significantly. A spectral peak at much higher frequency is noted that increases in frequency almost linearly with cavitation number. Similar behavior is noted in the lift fluctuations.

Exposure to ultrasonic acoustic waves can greatly enhance various chemical reactions. Ultrasonic acoustic irradiation of organic compounds in aqueous solution results in oxidation of these compounds. The mechanism producing this behavior is the inducement of the growth and collapse of cavitation bubbles driven by the high frequency acoustic pressure fluctuations. Cavitation bubble collapse produces extremely high local pressures and temperatures. Such conditions are believed to produce hydroxyl radicals which are strong oxidizing agents. We have applied hydrodynamic cavitation to contaminated water by the use of submerged cavitating liquid jets to trigger widespread cavitation and induce oxidation in the bulk solution. Experiments were conducted in recirculating flow loops using a variety of cavitating jet configurations and operating conditions with dilute aqueous solutions of p-nitrophenol (PNP) of known concentration. Temperature, pH, ambient and jet pressures, and flow rates were controlled and systematically varied. Samples of the liquid were taken and the concentration of PNP measured with a spectrophotometer. Experiments were conducted in parallel with an ultrasonic horn for comparison. Submerged cavitating liquid jets were found to generate a two order of magnitude increase in energy efficiency compared to the ultrasonic means.

An analysis of alternate blade cavitation on flat plate cascade is made using a singularity method based on a closed cavity model. In the steady flow analysis, it was found that two kinds of steady cavitation patterns exist. One is equal length cavitation in which the cavity lengths of all blades are the same. The other is alternate blade cavitation in which the cavity length changes alternately from blade to blade. Although the present model fails to predict the range of cavitation number where alternate blade cavitation occurs, it predicts alternate blade cavitation fairly well in terms of cavity length. A parameter study shows that the development of alternate blade cavitation is quite different depending on the solidity of cascade. The stability of equal length and alternate blade cavitation is then examined allowing the cavity length freely to change. It was found that alternate blade cavitation is stable for the cascades with larger solidity and unstable for the cascades with smaller solidity. The equal length cavitation is stable in both cases only in the region of cavitation number larger than that where the alternate blade cavitation solution separates from the equal length cavitation.

Surface electrical impedance probes are used to examine the bubbly flow beneath and in the closure region of partial attached cavities. A series of electrodes were mounted flush to the surface of a cavitating hydrofoil to detect the presence of liquid or vapor through changes in the impedance of the local fluid medium. Signals from the electrical probes were used to determine the near-surface gas-phase velocity and the shedding frequency of the gas phase. The impedance technique is shown to have the potential to measure advection velocities within a partial cavity, and the frequency content of the signal is used to determine the dynamics of the vapor shedding process.

The nonlinear dynamics of a spherical cloud of cavitation bubbles have been simulated numerically in order to learn more about the physical phenomena occurring in cloud cavitation. A finite cloud of nuclei is subject to a decrease in the ambient pressure which causes the cloud to cavitate. A subsequent pressure recovery then causes the cloud to collapse. This is typical of the transient behavior exhibited by a bubble cloud as it passes a body or the blade of a ship propeller. The simulations employ the fully nonlinear continuum bubbly mixture equations coupled with the Rayleigh-Plesset equation for the dynamics of bubbles. A Lagrangian integral method is developed to solve this set of equations. It was found that, with strong bubble interaction effects, the collapse of the cloud is accompanied by the formation of an inward propagating bubbly shock wave. A large pressure pulse is produced when this shock passes the bubbles and causes them to collapse. The focusing of the shock at the center of the cloud produces a very large pressure pulse which radiates a substantial impulse to the far field and provides an explanation for the severe noise and damage potential in cloud cavitation.

In the 1st report, the dynamic behavior of a cavitating centrifugal pump was related to the transient phenomena at the sudden opening/closure of the discharge valve. In this paper, the experimental study was extended to the transient behavior of the cavitating centrifugal pump at rapid starting/stopping of the pump. Unsteady pressures and flowrate were related to time-dependent cavitation behavior in a similar manner as for the rapid operation of the discharge valve. As a result of the present study, pressure fluctuations were found to occur due to water column separation at the sudden stop of the pump similarly to pressure oscillations associated with the sudden closure of the discharge valve. Moreover, the experimental results on the transient behavior at pump startup indicated that the transient fluctuations of delivery pressure and discharge flowrate are caused by oscillating cavitation similarly to the ones occurring at the opening of the discharge valve.

Analytical studies were developed on the transient behavior of a cavitating centrifugal pump during the transient operations, including the sudden opening/closure of the discharge valve and the pump startup/shutdown. In order to investigate the mechanism of the low cycle oscillations of both the pressure and the flowrate at a rapid change of the pump system conditions, an unsteady flow analysis was made for the cavitating pump-system by assuming the transient pump performance to be quasisteady. The calculated unsteady pressure and flowrate during the transient period agree with the corresponding measured time histories. It is shown that the fluctuations of delivery pressure and discharge flowrate at pump rapid startup or sudden valve opening are caused by peculiar oscillating cavitation dynamics inside the pump at rapid increase in flowrate, while the fluctuations at pump rapid shutdown or sudden valve closure are related to the collapse of cavitation bubbles or water column separation in the suction pipe at rapid decrease in flowrate. Moreover, the occurrence of transient fluctuations in pressure and flowrate was predicted by examining the critical condition which creates the occurrence of two different flow mechanisms i.e., (A) oscillating cavitation and (B) water column separation including also the collapse of the cavitation bubbles. These flow mechanisms were represented with two flow models i.e., (A) unsteady cavitating flow incorporating effects of cavitation compliance and mass flow gain factor and expressed by a set of ordinary differential equations solved with the Cardano Method and (B) water-hammer type model including Discrete Free Gas Model and solved with method of characteristics. The calculated critical conditions for. the occurrence of the oscillating cavitation and water column separation agree qualitatively with measured ones.

A three-dimensional linear analysis of rotating cavitation is carried out using an annular cascade model. The purpose is to investigate three-dimensional effects of cavitation, including the radial change of peripheral velocity and the hub/tip ratio of the impeller, on rotating cavitation in inducers. A semi-actuator disk method is employed. It is assumed that the mean stream surface does not radially shift across the impeller. It is shown that there are many modes of instabilities corresponding to rotating cavitation with various radial modes travelling forward and backward. The 0th radial modes are found to correspond to the forward and backward travelling modes predicted by a previous two-dimensional analysis (Tsujimoto et al., 1993). The three-dimensionality of the geometry has the effects of diminishing the amplifying region of these fundamental modes. It is also shown that the amplifying regions of higher radial modes may be larger than those of 0th radial modes. However, it is shown that the three-dimensionality of cavitation does not significantly affect rotating cavitation.

A series of studies on the dynamic characteristics of noncavitating centrifugal pumps were extended to the cavitating case. An experimental study was carried out on the transient behavior of a cavitating centrifugal pump at the sudden opening/closure of the discharge valve. Cavitation behavior in the centrifugal pump was visualized during the transient period by using high speed video camera, and instantaneous pressure and flowrate were measured at the pump suction and discharge section with rotational speed during the transient period. Unsteady pressure, as well as flowrate, was related to the time-dependent cavitation behavior. As a result of the present study, pressure and flowrate fluctuations were found to occur due to oscillating cavitation or water column separation at rapid transient operations.

A new method is proposed for the stability analysis of cavitating flow. In combination with the singularity method, a closed cavity model is employed allowing the cavity length freely to oscillate. An eigen-value problem is constituted from the boundary and supplementary conditions. This method is applied for the analysis of rotating cavitation in a cascade with a finite pitch and a finite chordlength. Unlike previous semi-actuator disk analyses (Tsujimoto et at., 1993 and Watanabe et al., 1997a), it is not required to input any information about the unsteady cavitation characteristics such as mass flow gain factor and cavitation compliance. Various kinds of instability are predicted. One of them corresponds to the forward rotating cavitation, which is often observed in experiments. The propagation velocity ratio of this mode agrees with that of experiments, while the onset range in terms of cavitation number is larger than that of experiments. The second solution corresponds to the backward mode, which is also found in semi-actuator disk analyses and identified in an experiment. Other solutions are found to be associated with higher order cavity shape fluctuations, which have not yet been identified in experiments.

In order to evaluate the quantitative cavitation-erosion resistance of materials, a pressure-detector-installed specimen was developed, which can measure both the impact load produced by cavitation bubble collapse and the volume loss simultaneously. Test specimens (pressure-detection rod) used were nine kinds of metals and were exposed to vibratory cavitation. A linear relation was obtained for all materials between the accumulated impact energy [Sigma][Fi.sup.2] calculated from the distribution of impact loads and the volume loss, independent of test conditions. Impact energy accumulated during the incubation period and the energy for a unit material removal in steady-state period were obtained from the relation. These values are very important concerning quantitative erosion resistance evaluation. That is, when the distribution of impact loads is acquired for different cavitation conditions, the volume loss can be estimated. This idea was applied to the venturi cavitation erosion. The experimental results for venturi test corresponds well with the prediction using these impact energy values. It was concluded that the quantitative impact energy values of materials can be determined independent of the apparatus and the test condition by using the newly developed pressure-detector-installed specimen.

A Navier-Stokes solver based on artificial compressibility and pseudo-time stepping, coupled with the energy equation, is used to model the thermodynamic effects of cavitation in cryogenic fluids. The analysis is restricted to partial sheet cavitation in two-dimensional cascades. Thermodynamic effects of cavitation assume significance in cryogenic fluids because these fluids are generally operated close to the critical point and also because of the strong dependence of the vapor pressure on the temperature. The numerical approach used is direct and fully nonlinear, that is, the cavity profile evolves as part of the solution for a specified cavitation pressure. This precludes the necessity of specifying the cavity length or the location of the inception point. Numerical solutions are presented for two-dimensional flow problems and validated with experimental measurements. Predicted temperature depressions are also compared with measurements for liquid hydrogen and nitrogen. The cavitation procedure presented is easy to implement in engineering codes to provide satisfactory. predictions of cavitation. The flexibility of the formulation also allows extension to more complex flows and/or geometries.

This paper summarizes recent research on the relation between boundary layer flow, tip vortex structure for a finite span wing, and cavitation. Three hydrofoils of elliptic planform of aspect ratio 3 were constructed with different NACA cross sections. Using a sprayed oil droplet technique to visualize the boundary layer flow, each foil was found to have dramatically different flow separation characteristics on both the suction and pressure sides. Careful examination of the tip region suggests that while the initial stages of vortex roll-up from the pressure side are similar for each hydrofoil section, the vortex boundary layer interaction on the suction side differs for each section. The degree of interaction was observed to increase as the lifting efficiency decreased. Over the Reynolds number range tested, tip vortex cavitation inception has been observed to follow an almost universal scaling. Differences in this scaling law are correlated with the degree of vortex/boundary layer interaction.

A relatively high amplitude, discrete tone is radiated from fully, developed tip vortex cavitation under certain conditions. The phenomenon of the 'singing vortex' was first reported by Higuchi et al. (1989). This study more closely examines the singing phenomenon by varying the hydrofoil cross-section, scale, angle of attack, water quality, and cavitation number in two different facilities. Noise data were collected for each condition with visual documentation using both still photography and high speed video in an effort to explain the mechanism of vortex singing. The theory of Kelvin (1880) provides a framework for correlating all the data obtained.

A novel hydrofoil design, consisting of a small diameter flow-through duct affixed to the tip, has been studied. The tip vortex cavitation inception index, [[Sigma].sub.i], of this hydrofoil geometry is about a factor of 2 lower than that of a conventional rounded hydrofoil tip. This inception improvement comes with little associated performance penalty. For angles of attack greater than 8 deg the noncavitating lift-drag ratio is actually superior to that of an unducted hydrofoil of equal span, although with lower wing loadings the hydrofoil performance is diminished by application of the ducted tip. The ducted tip is effective at reducing the tip vortex inception index because, in contrast with the rounded tip, for which vorticity in the Trefftz plane is confined to a line, the ducted tip shed vorticity at the trailing edge is distributed over a line and circle. Distributing the vorticity in this fashion causes the trailing vortex to roll up less tightly, and hence have a higher core pressure and lower [[Sigma].sub.i], than a conventional hydrofoil tip. It is also suspected that the interaction at the microscale level between the flow through the duct, and the flow around it, makes the vortex core size larger, and therefore [[Sigma].sub.i] smaller. The ducted tip design has many potential marine applications, including to ship and submarine propellers, submarine control fins, and ship rudders.

Tip clearance flow in turbomachinery can lead to losses in efficiency and stall margin. In liquid handling turbomachinery, the vortical flow field, formed from the interaction of the leakage flow with the through-flow, is subject to cavitation. Furthermore, this flow field is complex and not well understood. A correlation of variables which predict the vortex minimum pressure has been formulated. Measurements of the important variables for this correlation have been made on a high Reynolds number (3 X [10.sup.6]) axial-flow test rig. The correlation has been applied to the measured data and other data sets from the literature with good agreement. An optimum tip clearance has been theoretically identified as experiments have shown. Observations of cavitation indicate a second vortex originating along the suction side trailing edge.

A boundary element method (BEM) is used for the numerical analysis of sheet cavitation on a propeller subjected to the non-axisymmetric wakes of marine vehicles. This method is extended in order to treat mixed partial and supercavity patterns on both the face and back of the blades with searched cavity detachment. The convergence of the method is studied. The predicted cavity shapes and forces by the present method agree well with experiments and with those predicted by another numerical method. [DOI: 10.1115/1.1363611]

The linear stability analysis of cavitation in flat plate cascades corresponding to 2, 3, 4, and 5-bladed impeller was carried out to clarify the effect of the blade count on cavitation instabilities. Each blade is treated independently so that all possible modes in those impellers can be found. In steady flow analysis the alternate blade cavitation was found only for impellers with even number of blades. For 2 or 4-bladed impeller, it was confirmed that there exists no additional destabilizing mode to those found in the previous analysis in which the inter-blade phase difference of disturbance was assumed. It was shown that the modes with total cavity volume fluctuation depend on the inlet duct length while the modes without total cavity volume fluctuation are independent on the system. [S0098-2202(00)01304-3]

When a high-speed projectile penetrates into water, a cavity is formed behind the projectile. The gas enclosed in the cavity experiences a nonequilibrium process, i.e., the gas pressure decreases as the projectile moves more deeply into water. As a result, the cavity is sealed near the free surface (surface closure) and subsequently the cavity breaks up in water (deep closure). Accompanying the break-up of the cavity, secondary shock waves appear. This is the so-called supercavitation in water entry. This paper describes an experimental investigation into the water entry phenomenon. Projectiles of 342 m/s were generated from a small-bore rifle that was fixed vertically in the experimental facility. The projectiles were fired into a windowed water tank. A shadowgraph optical observation was performed to observe the entry process of the projectile and the formation and collapse of the cavity behind the projectile. A number of interesting observations relating to the motion of the free surface, the splash, the underwater bubbly flow and so on were found. [S0098-2202(00)00204-2]

A continuum bubbly mixture model coupled to the Rayleigh-Plesset equation for the bubble dynamics is employed to study one-dimensional steady bubbly cavitating flows through a converging-diverging nozzle. A distribution of nuclei sizes is specified upstream of the nozzle, and the upstream cavitation number and nozzle contraction are chosen so that cavitation occurs in the flow. The computational results show very strong interactions between cavitating bubbles and the flow. The bubble size distribution may have significant effects on the flow; it is shown that it reduces the level of fluctuations and therefore reduces the 'cavitation loss' compared to a monodisperse distribution. Another interesting interaction effect is that flashing instability occurs as the flow reaches a critical state downstream of the nozzle. A stability analysis is proposed to predict the critical flow variables. Excellent agreement is obtained between the analytical and numerical results for flows of both equal bubble size and multiple bubble sizes. [S0098-2202(00)00702-1]

In Part I, it was found that the alternate blade cutback of the leading edge causes a peculiar behavior in the development of steady cavitation. A stability analysis showed that the alternate blade cutback can reduce the onset region of rotating cavitation by enhancing the stability of alternate blade cavitation. In this report, we examine the effects of the amount of cutback. It was found that the development of steady cavity is significantly different depending on the amount of cutback. Those steady cavity developments are explained by the interaction of local flow near the cavity closure with the leading edge of the opposing blade just in the same way as for the development of alternate blade cavitation. It is also shown that the range of cavitation number with stable cavitation can be increased by increasing the amount of cutback. [S0098-2202(00)00502-2]