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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.

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.

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.

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.

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.

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.

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.

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.

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.

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

Rotating cavitation in inducers is known as one type of cavitation instability, in which an uneven cavity pattern propagates in the same direction as the rotor with a propagating speed ratio of 1.0-1.2. On the other hand, cavitation in cryogenic fluids has a thermodynamic effect because of the thermal imbalance around the cavity. To investigate the influence of the thermodynamic effect on rotating cavitation, we conducted experiments in which liquid nitrogen was set at different temperatures (74 K, 78 K and 83 K) with a focus on the cavity length. At higher cavitation numbers, super-synchronous rotating cavitation occurred at the critical cavity length of Lc/h approximately equal to 0.5 with a weak thermodynamic effect in terms of the fluctuation of cavity length. In contrast, synchronous rotating cavitation occurred at the critical cavity length of Lc/h approximately equal to 0.9-1.0 with a strong thermodynamic effect in terms of the unevenness of cavity length. Furthermore, we confirmed that the amplitude of the shaft vibration depended on the degree of the unevenness of the cavity length through the thermodynamic effect., 資料番号: AA0064094000, レポート番号: JAXA-RM-08-004

Bubble behavior in cavitating flow is analyzed for the development of practical erosion prediction method. CFD analysis with cavitation model is carried out for the flow field around a hydrofoil. Afterwards computation of bubble dynamics is carried out coupled with flow field CFD results by one way approach. For the bubble dynamic calculation, Rayleigh-Plesset equation is adopted. Bubble behaviors in the collapse of cloud cavitaion and in the break off of sheet cavity are analyzed. Bubble behavior at the trailing edge of sheet cavity is also calculated. It is observed that steep pressure change in the flow causes oscillation of the bubbles. Based on this qualitative information of bubble behaviors, numerical cavitation aggressiveness is simply defined. This numerical cavitation aggressiveness is a function of local void fraction and pressure over the solid surface and can be calculated directly from the cavitating flow field CFD results without concerning bubble dynamics.Copyright © 2008 by ASME

A Numerical method for solving the cavity flow is proposed and applied to simulate unsteady cavitating flows through a two-dimensional decelerating cascade. A finite-difference Runge-Kutta method combined with MUSCL TVD scheme is used, and a mesoscopic model which is based on a model of compressible gas-liquid twophase media is applied to solve above cavitating flows. The present method permits us to treat simply the whole gas-liquid two-phase flow field including wave propagation and large interface deformation in spite of the use of a fixed mesh system. Numerical results such as detailed observations of the unsteady cavity flows and the comparisons of predicted results with available experimental data are provided.

To clarify cavitation behaviours of submerged high-speed water-jets, systematic experimental studies were carried out by using a flow visualization technique. The cavitation behaviours were studied for both the free jet and the impinging jet at various stand-off distances x from the outlet edge of the nozzle. Effects of the injection pressure P 1 and the nozzle structure on the behaviours were also examined. The behaviours of the jets are largely dominated by explosive cavity clouds and by remarkably developed vortex cavitation. Therefore the structure of the submerged jet differs from that of jet in still air. The distribution of impulsive pressure P sh , which is measured by pressure sensitive films, clearly shows the existence of two pressure peaks along the jet. At the stand-off distance where P sh shows the “1st peak,” the impinging jet results in the severe erosion on the ambient solid surfaces. Because of this, the performance of cutting- or drilling- fabrications is considered to be remarkably improved when jet impinging is conducted at x 1 of the “1st peak.” On the other hand, at x 2 of the “2nd peak” downstream from the “1st peak,” numerous pressure pulses are produced on the solid surfaces, but mass loss due to cavitation erosion is barely detected. Clearly, x 2 of the “2nd peak” is believed to be suitable for precise peening fabrications.

The cavitation flow in a low specific centrifugal pump is analyzed by using two types of cavitation CFD codes. A locally homogeneous model of compressible air-vapor-liquid two-phase medium is applied to calculate the objective flow. Constant Enthalpy Vaporization model is also applied. Numerical results are compared to measured results. At the cavitation breakdown of the BEP flow rate, the throat is choked by cavities on both suction surface and pressure surface and head drops steeply. The steep head drop is well captured by both CFD codes. The NPSH value at the breakdown point can be predicted reasonably. At the high flow rate further modification is necessary for both codes to achieve stable and accurate results.

In order to clarify the role of cavitation nuclei upon inception, the behavior of inception was carefully investigated in an extremely limited water flow through very small orifices less than 1.0 mm in diameter under a prescribed nuclei condition. The following facts of technical interest were determined: a) The desinent cavitation number (σd) decreased rapidly and exponentially with the orifice diameter d, up to one hundredth in magnitude; and b) the cavitation appearance in such limited flows was quite different from that in fully turbulent flows through larger orifices.

An “accurate” analysis based on momentum theorem is proposed for finite cavity cascade foils of arbitrary shape. Some numerical results are given which show that (i) In the existing cascade flow models, the momentum theorem is not always satisfied. Therefore, the cavity drag contains an error. (ii) Low drag cascade foils are considerably cambered in the rear half and should be used within a certain required incidence limit.