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Cavitation often involves an abrupt phase change phenomenon. This phenomenon causes cavitation erosion on the material surface. In particular, violent bubble collapse near the material surface causes severe erosion. Numerical simulation is a powerful approach by which to clarify the high-speed, complex bubble collapse behavior near the wall boundary. In the present study, numerical analysis of nonspherical bubble collapse behavior and induced impulsive pressure at several initial standoff distance from the wall boundary is performed using a locally homogeneous model of a gas-liquid two-phase medium. The second collapse is confirmed to be more violent than the first collapse, and a circular erosion pattern is predicted owing to a toroidal bubble collapse attached to the wall boundary at a certain standoff distance. The influence of the symmetry breaking of the initial spherical bubble shape on the collapse behavior is investigated, and the asymmetry is found to influence the second bubble collapse, especially the generation of the high impulsive pressure in the central area.

To take up the three-dimensional axisymmetric gate slot concerining with the gate slot possessed in hydraulic equipment, such as, a gate valve, the state of cavitation of the gate slot was investigated by Acoustic Emisson (AE) measurement. The relationship between AE energy level and cavitation condition was analyzed by the root-mean-square (RMS) of acoustic wave. Moreover, a new AE parameter "relative accumulated intensity (RAI)" was defined in order to estimate the erosion tendency of cavitation. Combining with the result of impulsive pressure measurement, the relationship between the erosive damage and the high amplitude generation of AE wave is confirmed by using RAI. In consideration of deflector effect, the AE measurement showed that the conical shape installed on the upstream side of gate slot makes the cavitation erosion increased, and the offset shape on the downstream side of gate slot makes the cavitation erosion decreased significantly.

A numerical prediction method of cavitation erosion is proposed. In this method, the analysis of bubbles in cavitating flows is performed and the intensity of cavitation erosion is evaluated by the impact pressure induced by spherical bubble collapse. In the present study, two-dimensional cavitating flow around the Clark Y 11.7 % hydrofoil is used to examine the proposed numerical prediction method. The proposed numerical method predicts that the intensities of cavitation erosion in noncavitating, attached cavitating and pseudo-supercavitating flows are far weaker than the intensity of cavitation erosion in a transient cavitating flow, and the intensity in the vicinity of the sheet cavity termination is high. These results correspond well to experimental results, and it is confirmed that systematic erosion characteristics are generally captured by this method. Furthermore, the velocity dependence of cavitation erosion is examined, and it is found that the exponent n in the relation between the intensity I and main flow velocity Uin (I ∝ Uinn) becomes large when the bubble radius is large and ranges between 4.3 and 7.0 in the present study. According to the bubble dynamics, the ambient pressure and the rate of increases in pressure increase as the main flow velocity, and the maximum internal pressure increase. Therefore, it is thought that smaller bubbles cause cavitation erosion when the main flow velocity is large.

To evaluate the effect of substrate morphology on the adhesion of diamond film, two types of substrate morphology of molybdenum (Mo) were compared. The two morphology types were formed by polishing a Mo substrate with SiC abrasive paper along one direction (anisotropic morphology) and by polishing the Mo substrate with diamond powder in a random direction (isotropic morphology). Ultrasonic cavitation tests were conducted to evaluate the adhesion of the diamond films on these Mo substrates. In the case of low surface roughness, there was very little difference between the effects of SiC abrasive paper polishing and diamond powder polishing. In the case of high surface roughness, the adhesion of the diamond film on the SiC paper polished Mo substrate was larger than that of the diamond film on the diamond powder polished Mo substrate. Detachment of the diamond film from the SiC paper polished Mo substrate progressed along the polishing direction; while detachment of the diamond film from the diamond powder polished Mo substrate progressed in a random direction. It was thought that the detachment of the diamond film from a Mo substrate having an anisotropic polishing trace was suppressed because the anisotropic grooves restricted the formation of connections between the points of detachment at right angles to the groove direction. Therefore, the anisotropic surface morphology of the Mo substrate is effective for improving the adhesion of diamond film.

Hybridization comprised of an algebraic turbulence model based on the Reynolds average Navier–Stokes (RANS) equations with a monotonically integrated large eddy simulation (MILES) is proposed to simulate transient fluid motion during separation and vortex shedding at high Reynolds numbers. The proposed hybridization utilizes the Baldwin–Lomax model with the Degani–Schiff modification as the RANS model in the near-wall region and a MILES far from the wall. Although the hybridization is assumed to be a MILES with wall modeling, the transition line between the RANS and the MILES modes is determined by the turbulent intensity that is dominated by the large eddies in the grid-scale. This hybrid model is applied to the flows past three different types of airfoils (NACA633-018, NACA631-012 and NACA64A-006) near stall, at a chord Reynolds number of Re = 5.8 × 106. These airfoils are classified as trailing-edge-stall, leading-edge-stall and thin-airfoil-stall airfoils, respectively. The computed results are compared with wind tunnel experiments. The hybrid model successfully demonstrates accurate stall angle and surface pressure distribution predictions near the stall for each type of airfoil. The airfoil simulation results confirmed that the hybrid model provides a better prediction than the RANS model for unsteady turbulent flows with separation and vortex shedding simulations.

In this study, unsteady cavitation and cavitation instabilities are numerically analyzed around flat-plate cascade with three blades cyclic condition in water / air working fluid. The numerical method employing an original model “locally homogeneous model of compressible gas-liquid two-phase medium” is applied to numerical simulation. The method can simply treat the entire flow field inside and outside the cavity by one system equations. As a result of numerical analysis, occurrence and oscillation characteristics of three types of cavitation instabilities are reproduced, which are “cavitation surge”, “super-synchronous rotating cavitation” and “rotating-stall cavitation”. Additionally, flow fields around flat-plate cascade with slits on blades are analyzed in the conditions where the cavitation instabilities arise in the cascade without slit. Consequently, the suppression effect of the slit on the cavitation instabilities is confirmed.

Asymmetric cavitation is known as one type of the sources of cavitation induced vibration in turbomachinery. Cavity lengths are unequal on each blade under condition of synchronous rotating cavitation, which causes synchronous shaft vibration. To investigate the relationship of the cavity length, fluid force, and shaft vibration in a cavitating inducer with three blades, we observed the unevenness of cavity length at the inception of synchronous rotating cavitation. The fluid force generated by the unevenness of the cavity length was found to grow exponentially, and the amplitude of shaft vibration was observed to increase exponentially. These experimental results indicate that the synchronous shaft vibration due to synchronous rotating cavitation is like selfexcited vibrations arising from the coupling between cavitation instability and rotordynamics.

Synchronous rotating cavitation is known as one type of cavitation instability, which causes synchronous shaft vibration or head loss. On the other hand, cavitation in cryogenic fluids has a thermodynamic effect on cavitating inducers because of thermal imbalance around the cavity. It improves cavitation performances due to delay of cavity growth. However, relationships between the thermodynamic effect and cavitation instabilities are still unknown. To investigate the influence of the thermodynamic effect on synchronous rotating cavitation, we conducted experiments in which liquid nitrogen was set at different temperatures (74K, 78K, and 83K). We clarified the thermodynamic effect on synchronous rotating cavitation in terms of cavity length, fluid force, and liquid temperature. Synchronous rotating cavitation occurs at the critical cavity length of Lc∕h≅0.8, and the onset cavitation number shifts to a lower level due to the lag of cavity growth by the thermodynamic effect, which appears significantly with rising liquid temperature. Furthermore, we confirmed that the fluid force acting on the inducer notably increases under conditions of synchronous rotating cavitation.

It is known that when surface roughness is changed, that the adhesiveness of CVD diamond thin film also changes. However, it has not been clarified whether the cause of this is based on an increase of mechanical bonding strength or based on an increase in chemical bonding strength accompanying the change in nucleation density due to the change in surface roughness. To clarify whether the underlying factor is mechanical bonding strength or chemical bonding strength, nucleation density and adhesiveness were evaluated.In order to evaluate the influence of surface roughness only, polishing was performed with single-phase Mo abrasive paper to prepare substrates with different surface roughness, and film formation of diamond thin films was done using the microwave plasma CVD method. Measurement of nucleation density of the diamond thin film was done using an SEM (Scanning Electron Microscope) and adhesiveness was evaluated using the ultrasonic cavitation method.No significant difference in nucleation density was observed as a result of changing the surface roughness. However, ultrasonic cavitation tests revealed that the damaged area tended to increase as the surface roughness became smaller. In particular, it deteriorated sharply when the elevation difference of polishing marks was approximately equal to or less than the film thickness (Ra=200nm) of the diamond thin film. These results indicate that, rather than the influence of nucleation density, changing the surface roughness itself has a direct effect on the mechanical bond : when the elevation difference of polishing marks is relatively small compared to the film thickness, the mechanical bond (anchor effect) becomes weaker, allowing the surface to become damaged more easily.

Three-dimensional unsteady cavitating flow around a NACA0015 hydrofoil fixed between the sidewalls was simulated and the mechanism of U-shaped cloud cavity formation was clarified. A local homogeneous model was used for the modeling of the vapor–liquid two-phase medium. The compressible two-phase Navier–Stokes equations as the governing equations were solved. To describe the phase change between water and vapor, the mass transfer model based on the theory of evaporation/condensation on a plane interface was introduced. The cell-centered finite volume method was employed to discretize the governing equations. Assuming turbulent flow, the turbulent eddy viscosity coefficient was computed by using the Baldwin–Lomax model with the Degani–Schiff modification. As a result, even in the case of cavitating flow without sidewalls, the shed cloud cavities has slightly 3D structure, which was not so much large as extending across the whole spanwise direction. On the other hand, in the case of cavitating flow with sidewalls, the end of sheet cavities bows in the spanwise direction because of the development of boundary layer near both sidewalls. After that, due to the occurring of the reentrant jet towards the mid-span region, the sheet cavities breaks off from mid-span region near the leading edge of the hydrofoil, and became the vortical cloud cavities, which have the large-scale U-shaped structure.

Three types of cavitation instabilities through flat plate cascades, which are similar to “forward rotating cavitation,” “rotating-stall cavitation” and “cavitation surge” occurring in high-speed rotating fluid machinery, are represented numerically under the three-blade cyclic condition. A numerical method employing a locally homogeneous model of compressible gas-liquid two-phase medium is applied to solve the above flow fields, because this permits the entire flow field inside and outside the cavity to be treated through only one system of governing equations. In addition, the numerical method suites to analyze unsteady cavitating flow with a long time evolution. From the calculated results of the present numerical simulation with wide range of cavitation number and flow rate, we obtain a cavitation performance curve of the present three-blade cyclic cascade, analyze the aspects of unsteady cavitation, and discuss the characteristics and mechanisms of cavitation.

Cavitation in a 3D axisymmetric rectangular groove occurred in various types of cavitation, such as vortex cavitation, cloud cavitation, traveling cavitation and sheet cavitation. In this experimental study, some aspects of cavitating flow were clarified. Prediction and experimental calculations were also made for incipient cavitation of both the cavitating vortex ring in the groove and the sheet cavitation at the downstream of the groove. The calculations indicate that the observed cavitation is not vaporous cavitation, but gaseous cavitation. The results of this study are useful for understanding the cavitation in this type of groove structure in order to control cavitation damage.

2-D unsteady cavity flows through hydrofoils in cascade which is the most fundamental element of turbomachinery are numerically calculated. In particular, attention was paid to instability phenomena of the sheet cavity in transient cavitation condition and the mechanism of break-off phenomenon was examined. A TVD MacCormack's scheme employing a locally homogeneous model of compressible gas-liquid two-phase media was applied to analyze above cavity flows. The present method permits us to treat the whole cavitating/noncavitating unsteady flow field. By analyzing numerical results in detail, it became clear that there are at least two mechanisms in the break-off phenomena of sheet cavity; one is that re-entrant jets play a dominant role in such a break-off phenomenon, and the other is that pressure waves propagating inside the cavity bring about an another type of break-off phenomenon accompanied with cavity surface waves.

Numerical simulations of two-dimensional cavity flows around a flat plate normal to flow and flows through a 90∘ bent duct are performed to clarify unsteady behavior under various cavitation conditions. A numerical method applying a TVD-MacCormack scheme with a cavitation model based on a homogenous equilibrium model of compressible gas-liquid two-phase media proposed by the present authors, is applied to solve the cavitating flow. This method permits the simple treatment of the whole gas-liquid two-phase flow field including wave propagation and large interface deformation. Numerical results including detailed observations of unsteady cavity flows and comparisons of predicted results with experimental data are provided.

This paper is concerned with the dynamic behavior of a magnetic fluid-permanent magnet system subjected to the vertical vibration. The surface response of magnetic fluid adsorbed to a disc permanent magnet is investigated experimentally. Experiment is performed on a vibration-testing system. The electrodynamic shaker is operated at a given frequency, displacement, and acceleration. The dynamic behavior of magnetic fluid surface is analyzed by a three-dimensional motion analysis system. The displacement of the permanent magnet is also measured with an optical displacement detector system. It is shown that the response amplitude depends on the excitation frequency at the constant excitation amplitude. The 1=2-sub harmonic response on the surface of magnetic fluid is observed at higher frequencies. This response is observed as polygonal modes with large amplitude azimuthal waves. The response of the system such as jumping motion is also shown at the resonance frequency of the system.

This paper is concerned with the functional design and hydrodynamic characteristics of fish scales. The rough surfaces of fish scales were measured with a three-dimensional, optical shape measuring system. The measurement was carried out on embiotocid fish Ditrema temminck, rockfish Sebastes inermis, and dogfish Mustelus manago Bleeker. Some scales of a dogfish Mustelus manago Bleeker were also observed microscopically making use of the scanning electron microscope as a faster fish. From the viewpoint of hydrodynamics, the microscopic structure and morphological characteristics of fish scales were discussed.

Large eddy simulation (LES) of compression ramp flow with a shock wave was successfully performed at a free-stream Mach number of 2.9 and a Reynolds number of 10 6 based on the boundary layer thickness. A compressible Smagorinsky-type eddy viscosity model was employed. It was shown that the present LES predicts not only the time-averaged quantities but also fluctuations such as pressure deviation and shock motion near the compression corner. Also, the present simulation predicts the three-dimensional structure of shock/turbulent boundary interaction, which is difficult to simulate by using Reynolds averaged Navier-Stokes equations (RANS)

Stationary and non-stationary characteristics of attached, turbulent cavitating flows around solid objects are reviewed. Different cavitation regimes, including incipient cavitation with traveling bubbles, sheet cavitation, cloud cavitation, and supercavitation, are addressed along with both visualization and quantitative information. Clustered hairpin type of counter-rotating vapor vortices at incipient cavitation, and finger-like structure in the leading edge and an oscillatory, wavy structure in the trailing edge with sheet cavitation are assessed. Phenomena such as large-scale vortex structure and rear re-entrant jet associated with cloud cavitation, and subsequent development in supercavitation are described. Experimental evidence indicates that the lift and drag coefficients are clearly affected by the cavitating flow structure, reaching minimum and maximum, respectively, at cloud cavitation. Computationally, progress has been made in Navier–Stokes (N–S) based solution techniques. Issues including suitable algorithm development for treating large density jump across phase boundaries, turbulence and cavitation models, and interface tracking are discussed. While satisfactory predictions in wall pressure distribution can be made in various cases, aspects such as density and stress distributions exhibit higher sensitivity to modeling details. A perspective of future research needs in computational modeling is offered.

When hydraulic machinery start to operate, the flow around the blades has to be transient, so that hydraulic losses have to come out within very specified regions transiently. To clarify such behavior of the losses, we take up a typical vortical flow around a highspeed hydrofoil and numerically simulate such transient behavior of the losses arisen around the foil, especially near the stagnation point, the backward separation region and the trailing edge. Even within the transient : range, the boundary layer develops on the entire foil surface and the starting vortex sheds off from the trailing edge, in the manner of pseudo-potential response. The losses limitedly appear around the above-mentioned regions, but the wake accompanying with Karman vortices scarcely appears.

This paper describes an experimental study of the dynamic behavior of magnetic fluid jets which are injected from a vibrating nozzle into the atmosphere. It was found that an intact liquid jet can be made to bifurcate continuously into a pronged jet by vibrating the nozzle with certain combinations of frequency and acceleration. The effects of the magnetic fields on the drops produced by the jet breakup are also revealed.

When hydraulic machinery start to operate, the flow around the blade elements has to be typically transient. To clarify such flow behavior, we attempt numerical simulations of the viscous transient flow around a typical hydrofoil, by using the QUICK method of high resolution accuracy. For such a viscous flow, our simulations show not only the step response of expectable through potential concept, but also the rather slow viscous response, which is almost linear to the elapse time t.

In this study, cavitation-induced sonoluminescence under conditions of cathodic protection was measured and examined in three percent sodium sulfate solution using an electrostrictive vibratory apparatus. It was found that the relative intensity of sonoluminescence increases as the cathodic current becomes larger. This is because the hydrogen gas bubbles which evolve can also give off sonoluminescence in the same way as cavitation bubble. This fact suggests that cavitation accompanied by an electrolytic reaction can result in more intense sonoluminescence.

This study is concerned with the wing structure and aerodynamic characteristics of a dragonfly in flight. The structural properties of dragonfly wings were studied through measurements of certain morphological parameters. The scanning electron microscopic observation showed the morphological characteristics of the dragonfly wing. Dragonflies were examined in a small low-turbulence wind tunnel. In the experiment on the measurements of wing flapping, an optical displacement detector was used to measure the displacement of the dragonfly wing. In the experiment on the measurements of the velocity fluctuation, a hot-wire anemometer was used to measure the velocity field. The spectrum of dragonfly flight was revealed by the measurements of velocity fluctuation.

Hollow-jet valve has been utilized to control the water supply extensively under high static pressure. For the valve used underwater, cavitation erosion will probably be caused. However, such a trouble has not been studied yet in detail. Therefore a similar model of hollow-jet valve was made in which plunger stroke is changeable as the prototype valve. The aim of this paper is to clarify the characteristics of cavitation-induced vibration related to the erosion around the upstream casing and six splitters in the valve, to estimate the ventilation effect to decrease the erosion as well as the vibration, and also to make clear the difference of flow pattern in the valve between underwater and in air.

In this paper, to make clear the mechanism of cavitation damage around a hollow-jet valve, cavitation damage test was conducted in a hollow-jet model valve. The eroded surfaces of specimens were observed by Scanning Electron Microscope (SEM) at different times of the test. Cavitation aspects were also observed photographically by a high-speed camera. It was found that the damage occurs in cavitating flows around a hollow-jet valve with two patterns. One is characterized by a big plastic crater, which seems to be generated by one blow event of cavitating vortex collapse near a specimen surface. Another is due to a small brittle irregular pit formed by the cumulative effects of many weaker blows. The former is the main cause to lead serious damage. The high-speed photographic observations of the cavitation aspects showed that more cavitating vortices in middle cavitation number state occur than these in other states. The damage tests also illustrated that the middle state is the most dangerous for cavitation damage around a hollw-jet valve.

To obtain information on the cavity flow behavior, an experimental study of the external and internal flows of a cavity occurring on a 2-D hydrofoil was performed in a closed-type cavitation tunnel. The liquid phase velocities and their fluctuations in the flow field inside and outside the cavity were measured by using a Laser Doppler Velocimeter (LDV) in different cavitation states. In addition, the corresponding cavitation aspects were observed photographically by means of a xenon flach lamp with an exposure time of 1 μs and a high-speed video. The results show that the averaged velocity profiles inside the cavity are similar to those in the single phase boundary layer. However, strong fluctuation and intermittent reverse flow occur within the cavity, especially in the region near the bottom.

In order to study the effect of cathodic protection on cavitation erosion, a series of experiments using 3 percent aqueous sodium sulfate solution is carried out by means of a vibratory erosion apparatus, and the erosion patterns on an eroded specimen surface are observed using a scanning electron microscope (SEM). The results show that the mass loss decreases markedly with increasing cathodic current. Although the process of cavitation erosion development shows a similar tendency whether cathodic current is applied or not, the erosion rate is markedly suppressed by hydrogen gas evolving from the cathodic specimen surface, resulting in a monotonic decrease in mass loss.

Some peculiar phenomena occur around ultrahigh-speed submerged water jets accompanied by very severe cavitation erosion. Using the flow visualization technique with a xenon flash, the water jets were carefully observed, and the spatial distributions of highly erosive impulsive pressures around the jets were measured by means of a pressure-sensitive film technique. The effects of the injection pressure and the nozzle configuration are systematically clarified. Thus, the characteristics and structures of ultrahigh-speed submerged water jets are clearly shown.

In order to clarify the effects of cathodic protection on cavitation erosion, cavitation erosion tests are carried out using a vibratory erosion apparatus, and the cavitation aspects are photographed with a xenon flash lamp of 1μs exposure time. With increasing cathodic current, cavitation noises and mass losses (ML) of cavitation erosion markedly decrease when the number of tiny hydrogen bubbles on the specimen surface as well as in the test water increases, and the mass loss rate (MLR) is related to the square of sound pressure level (SPL2) of cavitation ultrasonic noise. The decreases in SPL and ML are due to marked absorption of cavitation energy by hydrogen bubbles produced on the specimen surface.

In order to establish a useful monitoring method for predicting the erosion induced by high-speed submerged water jets, we attempt to clarify the relation between the jet-structure and the cavitation noise arising around the free jets, by using two hydrophones, and also analyze the AE characteristics of the impulsive pressures induced by cavitation on the specimen of the impinging jets. It is found that the energies of high-frequency components in the jets change markedly with the injection pressure and the standoff distance. It is found that the AE characteristics are closely related to the impinging erosion.

In order to investigate the complex behavior of collapsing bubbles in cloud cavitation, numerical simulations have been performed by solving the 2-D governing equations for gas-liquid two-phase media. Here, the equation of state for such media is derived from the locally homogeneous assumption, so that the apparent compressibility can be taken into account. The interface of a bubble or a cloud of bubbles is treated as a contact discontinuity surface, where the values of density and void fraction are allowed to jump. When the void fraction in a bubble cloud is almost 100%, the collapsing behavior agrees well with that of a single bubble. Numerical results of the interaction between some bubbles and an incident shock wave show qualitative agreement with experimental results. Therefore, complex interaction phenomena between multibubbles can be simulated when some small bubbles are arranged in a bubble cloud by distributing the corresponding void fractions nonuniformly.

To date the Rankine vortex or the viscous vortex has been used for the vortex method. Since these vortices do not have actual turbulent characteristics, a new vortex model is required for turbulent flow analysis. In this study, we proposed a turbulent vortex model including logarithmic circulaticm region and applied it to predict the growth of a large-scale turbulent vortex. The present turbulent vortex model is proven to predict the turbulent vortex structure, while neither the Lamb vortex model nor the Squire vortex model are necessarily appropriate.

In order to extend the working range of high-speed submerged water jets and to improve its accuracy confidence, the jet working characteristics are studied under the condition of widely varying ambient pressures P2. The erosion tests were systematically carried out by using aluminum-alloy specimens, and the aspects of the cavitation clouds around the jets were simultaneously observed. Clearly, the pressure P2 drastically affects the aspects of cavitation and its occurrence region. With increasing P2, the length of the cavitating jet decreases, so that the standoff distance, where the most severe erosion appears, shifs upstream. In short, the intensity and the distribution of the impulsive pressures induced by the cavitating jets also drastically change with P2. The impinging erosion characteristics are also sensitive to the standoff distance and the injection time.

Cavitation erosion is a material damage phenomenon caused by the repeated application of impulsive pressure on a material surface induced by bubble collapse, and the establishment of a method by which to numerically predict cavitation erosion is desired. In the present study, a numerical quantitative prediction method of cavitation erosion in a cavitating flow is proposed. In the present method, a one-way coupled analysis of a cavitating flow field based on a gas-liquid two-phase Navier–Stokes equation (Eulerian) and bubbles in the cavitating flow by bubble dynamics (Lagrangian) is used to treat temporally and spatially different scale phenomena, such as the macroscopic phenomenon of a cavitating flow and the microscopic phenomenon of bubble collapse. Impulsive pressures acting on a material surface are evaluated based on the bubble collapse position, time, and intensity, and the erosion rate is quantitatively predicted using an existing material-dependent relationship between the impulsive energy (square of the impulsive force) and the maximum erosion rate. The erosion rate on a NACA0015 hydrofoil surface in an unsteady transient cavitating flow is predicted by the proposed method. The distribution of the predicted erosion rate corresponds qualitatively to the distribution of an experimental surface roughness increment of the same hydrofoil. Furthermore, the predicted erosion rate considering the bubble nuclei distribution is found to be of the same order of magnitude as the actual erosion rate, which indicates that considering bubble nuclei distribution is important for the prediction of cavitation erosion and that the present prediction method is valid to some degree.

In order to clarify structures of high-speed submerged water jets and to predict the jet working capacity, we systematically measured the cavitation noise around the jets using a hydrophone, for several nozzles. The power spectra and the rms values of the cavitation noise are carefully analyzed. Clearly, cavitation noise created by the jets is related to the behavior of cavitation bubble clouds, and the cavitation noise characteristics are markedly changed with the injection pressure and nozzle geometry.

A high-resolution finite difference method to simulate the gas-liquid two-phase flow is proposed taking account of the apparent compressibility which characterizes high -speed two -phase flow phenomena. The speed of sound and the total energy for the gas-liquid two-phase fluid flows are re-estimated based on the assumption of homogeneous and the thermodynamic relations. Here, the homogeneous two-phase flow model assuming a local equilibrium is adopted. The basic equations for the two-phase mixture flow similar to those of the ordinary single-phase compressible gas flow are solved using the upwind finite difference scheme based on the theory of characteristics. To elucidate the applicability of the present scheme, some numerical calculations of wet-steam nozzle flows with condensation were implemented. The calculated results are in good agreement with the existing experimental data.

High-Speed submerged water jets have two characteristic peaks with respect to the stand-off distance, in the same manner as high-speed water jets in air. In order to clarify the behavior of the impulsive pressures at these two peaks, we systematically carried out erosion tests using an aluminum-alloy specimen in a wide range of the injection pressure P1 from 10 to 70 MPa, and microscopically observed the eroded surfaces by SEM. We find that the mass loss rate Δm^^· at the 1st peak is decidedly due to the water-column impact, so that it is very sensitive to the injection pressure P1, while Δm^^· at the 2nd peak is due to the shock pressures of cavitation bubble collapse, so that it is not necessarily sensitive to P1. We also indicate that the form and the speed of erosion change markedly with the differences in the jet structure with the stand-off distance x/D.

In the present work, the two-dimensional turbulent liquid-particle flow around a blade-to blade surface of a centrifugal impeller has been simulated by using a two-phase turbulence model, that is, the k-e liquid turbulence model and the algebraic particulate phase flow turbulence model. The interaction between the liquid phase and the solid phase has been considered in the conservative momentum equations of the two-phase flow. Calculated results show that the turbulence model can predict essential features of the complex liquid-particle flow through the impeller.

An experimental investigation is conducted in order to determine the discharge coefficients for a water jet discharged into the surrounding air from a standard orifice located on the side wall of a square duct. Six different orifice diameters are tested. Experiments are made for a wide range of Reynolds and Weber numbers, and an empirical equation is obtained for the discharge coefficients, which reproduces the experimental results accurately. The efflux angle is deduced from the momentum theorem which takes into account the loss coefficients in the duct due to dividing flow, and it agrees well with the measurements.

The unsteady two dimensional CFD for the cavitation in a orifice passage were carried out by using a commercial software ANSYS-CFX. The mass flow rate and the static pressure were controlled at the inlet and the outlet boundaries respectively. The CFD result showed periodic fluctuation of the cavitation flow. The time derivative of the cavitation volume showed relatively good agreement with the difference of the inlet and the outlet volume flow rate. The periodic fluctuation was ceased by the extension of the passage length downstream of the cavitation. The periodic fluctuation of cavitation flow was also induced by the fluctuation of the inlet volume flow rate or the fluctuation of the outlet static pressure. The dynamic flow behavior of the closed loop system including the orifice were analyzed by using the orifice cavitation CFD with the inlet and the outlet boundary conditions derived from the lumped parameter system dynamics for the tank, the pump and the pipes in the loop.

A finite-difference method based on the SMAC (Simplified Marker and Cell) scheme for analyzing two-dimensional unsteady incompressible viscous flows is developed. The fundamental equations are the incompressible Navier-Stokes equations of contravariant velocities and the elliptic pressure equation in general curvilinear coordinates. With application of the Crank-Nicholson scheme, unsteady flow is calculated iteratively by the Newton method at each time step, and the elliptic pressure equation is solved by the Tschebyscheff SLOR method with alternating the computational directions. Therefore, the elliptic character of incompressible flow is well described. The present implicit scheme is stable under the proper boundary conditions, since spurious error and numerical instabilities can be suppressed by employing the staggered grid and upstream differences such as the modified QUICK scheme. Numerical results for two-dimensional flows through a decelerating cascade at high Reynolds numbers are shown. Some computed results of the surface pressure coefficient are in satisfactory agreement with the experimental data.

This paper aims to clarify peculiar phenomena arising around a ultra high-speed submerged water jet accompanied by very severe cavitation. By means of a flow visualization technique with a xenon flash light, three kinds of water jets are carefully observed, and the spatial distributions of cavitation-pressure pulses around the jets are also measured with pressure-sensitive film. The effects of the working pressure and the shape of nozzles are clarified systematically. Thus, the characteristics and the structures of ultra high-speed cavitating submerged water jets are clearly shown.

An implicit time-marching finite-difference method, which has been developed previously to solve the incompressible Navier-Stokes equations of contravariant velocities in curvilinear coordinates, is extended to a turbulent flow scheme employing a suitable low Reynolds number κ-e model. The present method has second-order accuracy in time with application of the Crank-Nicholson scheme, and utilizes the QUICK (Quadratic Upstream Interpolation for Convective Kinematics) upwind-difference scheme in space. The elliptic equation of pressure is solved by means of the Tschebyscheff SLOR (Successive Line Over Relaxation) method with alteration of the computational directions. The present implicit turbulent flow scheme is stable under the proper boundary conditions, since spurious error and numerical instabilities can be suppressed by employing a staggered grid. Numerical calculations are performed for turbulent flows through a two-dimensional cascade. Computed results of the cascade turbulent boundary layers and the wake profiles are shown. The calculated surface pressure distribution is in good agreement with the experimental data.

Cavitation of a hydrofoil is observed in detail by using a high speed video camera. A paint removal test is also carried out in order to evaluate cavitation aggressiveness for erosion. 2D hydrofoil profile is Clark Y 11.7% and its angle of attack is seven degrees. Cavitation number is σ = 1.08. The experimental results are compared with cavitation CFD. Numerous features of unsteady cavitation are observed such as cyclic fluctuation of the sheet cavity, existence of the glassy cones on a sheet cavity, generation of the cloud cavitation from the sheet cavity and the isolated bubbles traveling over the suction surface of the blade. The isolated traveling bubbles and their collapses are thought to be one of the main causes of the severe paint removals. The isolated traveling bubbles are derived from the flowing cavitation nucleus or from abrupt onset at the leading edge of the blade. For computing these complicated phenomena, combination of grid scale bubbles (GSB) and sub grid scale bubble model (SGSB) are proposed. GSB shall be computed by using the computational scheme for the free surface with phase change model. SGSB can be computed with conventional cavitation model. The breakup of GSB generates SGSB, and the coalescence of SGSB makes GSB. Upper limit of void fraction of SGSB is estimated in the range of five or ten percent from the simple speculation of the structure of packed spheres. The two types of cavitation bubble inception model are also discussed based on the generation of the isolated bubbles observed in the experiments. To verify the proposed concepts of cavitation model, a traveling air bubble over a hydrofoil is computed by using the free surface flow scheme of Volume of Fluid (VOF) approach. Cavitation on the hydrofoil is also computed by VOF approach with boiling model concerning the heat transfer. Both the computed results show qualitatively similar characteristics of the bubble dynamics to those in experimental results.Copyright © 2010 by ASME

An implicit finite-difference scheme based on the SMAC method for solving steady three-dimensional incompressible viscous flows is proposed. The three-dimensional incompressible Navier-Stokes equations in general curvilinear coordinates, in which the contravariant velocities and the pressure are used as the unknown variables, have been derived by the authors. The momentum equations for the contravariant velocity components and the elliptic equation for the pressure are solved directly in the transformed space by applying the delta-form approximate-factorization scheme and the Tschebyscheff SLOR method, respectively. The present implicit scheme is stable under correctly imposed boundary conditions, since the spurious error and the numerical instabilities can be suppressed by satisfying the continuity condition identically, and by employing the staggered grid and the TVD upwind scheme. Some numerical results for three-dimensional flow over a backward-facing step are shown to demonstrate the reliability of the present scheme and to clarify the three-dimensional effects of such complex flows.