At present, pumped-storage power technology is the only available and effective way for the load balancing and energy storage in the grid network scale. During the frequent switch back and forth conditions, there are severe pressure pulsation and cavitation in pump-turbines. However, their generation mechanism has not been determined yet. This work contributes to the numerical simulation of the transient behaviors in a prototype pump-turbine during the load rejection process with special emphasis on cavitation effect. In this study, the two-dimensional dynamic remesh and variable speed slide mesh methodologies were employed to perform the simulation of the transient single-phase flow and cavitation flow in a pump-turbine. The simulation results of single-phase flow and cavitation flow were both consistent with the experimental data except in local regions based on the experimental validation of prototype tests. However, the numerical results considering cavitation effects have a better behavior than those of single-phase flow in the predictions of pressure pulsation and rotational speed. Then, the cavitation flow simulation results were analyzed deeply, especially in pressure pulsation and cavitation flow field. Analysis revealed that three typical complex frequency components of pressure were captured in the cavitation flow, which significantly affect the axial hydraulic thrust on the runner. And it is validated that they are primarily induced by the cavity collapse near the trailing edges of the runner blades in reverse pump mode and the interaction between cavitation and vortex rope in draft-tube in turbine mode.

In the maritime industry, cavitation erosion prediction becomes more and more critical, as the requirements for more efficient propellers increase. Model testing is yet the most typical way a propeller designer can, nowadays, get an estimation of the erosion risk on the propeller blades. However, cavitation erosion prediction using computational fluid dynamics (CFD) can possibly provide more information than a model test. In the present work, we review erosion risk models that can be used in conjunction with a multiphase unsteady Reynolds‐averaged Navier–Stokes (URANS) solver. Three different approaches have been evaluated, and we conclude that the energy balance approach, where it is assumed that the potential energy contained in a vapor structure is proportional to the volume of the structure, and the pressure difference between the surrounding pressure and the pressure within the structure, provides the best framework for erosion risk assessment. Based on this framework, the model used in this study is tested on the Delft Twist 11 hydrofoil, using a URANS method, and is validated against experimental observations. The predicted impact distribution agrees well with the damage pattern obtained from paint test. The model shows great potential for future use. Nevertheless, it should further be validated against full scale data, followed by an extended investigation on the effect of the driving pressure that leads to the collapse.

In the present study, cavitation erosion is investigated by implementing an Eulerian–Lagrangian approach. Three-dimensional two-phase flow is simulated in a microscale nozzle using Reynolds-averaged Navier–Stokes (RANS) solver along with realizable k − ε turbulence model and Schnerr–Sauer cavitation model. The numerical results are in agreement with experimental observations. A modified form of Rayleigh–Plesset–Keller–Herring equation along with bubble motion equation is utilized to simulate bubble dynamics. Average values of mixture properties over bubble surface are used instead of bubble-center values in order to account for nonuniformities around the bubble. A one-way coupling method is used between Lagrangian analysis and RANS solution. The impact pressure resulted from bubble collapse is calculated for evaluation of erosion in diesel and soy methyl ester (SME) biodiesel in different situations. The results show that the initial size of the bubbles is an important factor for determining the intensity of erosion. So, the bubbles erosive power increases when their initial radius increases. It is also found that the intensity of erosion in diesel is much higher than that of biodiesel and this is because of the differences in fuels properties, especially in viscosity and vapor pressure. The effect of bubbles initial position on erosion intensity is also investigated in this study, and it is found that bubbles with the highest distance from sheet cavity termination have the highest contribution in erosion rate.

A computational tool is introduced and applied to the emergence of supersonic liquid jets in quiescent compressible gas. A diffuse interface wave propagation method along with an interface sharpening technique is employed to solve the governing equations of compressible multiphase flows. Adaptive mesh refinement (AMR) strategy is utilized to improve the ability of the solver in better resolving the flow features. The accuracy of our method is benchmarked with four experimental and numerical test problems. Then, the evolution of supersonic liquid jets in compressible gaseous media is simulated; demonstrating a good agreement with experimental observations. Moreover, the impact of physical parameters, such as increment in ambient pressure and inlet velocity on the flow characteristics, is examined. The results indicate that the penetration length of the liquid jet decreases with an increase in the ambient pressure. The values of this parameter compare reasonably well with the experiment-based correlations. Further, with lower ambient pressure the Mach cone generated ahead of the liquid jet has a narrower half angle, situated closer to the jet tip. A similar behavior is demonstrated by the induced shock-front when the inlet Mach number of the liquid jet is increased. The simulations indicate the applicability of our numerical methodology to supersonic liquid jet flows for the analysis of shock waves dynamics and shock–interface interaction.

We are comparing results of numerical simulations against high-speed simultaneous observations of cavitation and cavitation erosion. We performed fully compressible, cavitating flow simulations to resolve the formation of the shock waves at cloud collapse—these are believed to be directly related to the formation of the damage. Good agreements were noticed between calculations and tests. Two high pressure peaks were found during one cavitation cycle. One relates to the cavitation collapse and the other one corresponds to the cavitation shed off, both contributing to a distinctive stepwise erosion damage growth pattern. Additional, more precise, simulations with much shorter time step were performed to investigate the processes of cavitation collapse and shedding off in more detail. There the importance of small cavitation structures which collapse independently of the main cloud was found. The present work shows a great potential for future development of techniques for accurate predictions of cavitation erosion by numerical means only.

A mathematical method was conducted to investigate the mechanism of formation of cavitation cloud, while the inlet stream contains a fluctuating flow. Based on the Rayleigh–Plesset equation and the static pressure distribution in a cone flow channel, parameters related to cavitation cloud are estimated, and the collapse pressure of the cavitation cloud is obtained by solving the equation of Mørch’s model. Moreover, the effect of the amplitude and frequency of inlet fluctuation on cavitation is studied. Results revealed that the smaller the amplitude, the smaller the cloud and the lower the collapse pressure. And frequency of fluctuating stream was found to have a relative great effect on frequency of peak pressure but not so significant on peak collapse pressure and size of cloud. It is concluded that limiting the inlet fluctuation reduces the erosion and noise generated by cavitation collapse.

An assessment of the cavitation erosion risk by using a contemporary unsteady Reynolds-averaged Navier–Stokes (URANS) method in conjunction with a newly developed postprocessing procedure is made for an NACA0015 hydrofoil and an NACA0018-45 hydrofoil, without the necessity to compute the details of the actual collapses. This procedure is developed from detailed investigations on the flow over a hydrofoil. It is observed that the large-scale structures and typical unsteady dynamics predicted by the URANS method with the modified shear stress transport (SST) k-ω turbulence model are in fair agreement with the experimental observations. An erosion intensity function for the assessment of the risk of cavitation erosion on the surface of hydrofoils by using unsteady RANS simulations as input is proposed, based on the mean value of the time derivative of the local pressure that exceeds a certain threshold. A good correlation is found between the locations with a computed high erosion risk and the damage area observed from paint tests.

An original approach based on energy balance between vapor bubble collapse, emitted pressure wave, and neighboring solid wall response was proposed, developed, and tested to estimate the aggressiveness of cavitating flows. In the first part of the work, to improve a prediction method for cavitation erosion (Fortes-Patella and Reboud, 1998, “A New Approach to Evaluate the Cavitation Erosion Power,” ASME J. Fluids Eng., 120(2), pp. 335–344; Fortes-Patella and Reboud, 1998, “Energetical Approach and Impact Efficiency in Cavitation Erosion,” Proceedings of Third International Symposium on Cavitation, Grenoble, France), we were interested in studying the pressure waves emitted during bubble collapse. The radial dynamics of a spherical vapor/gas bubble in a compressible and viscous liquid was studied by means of Keller's and Fujikawa and Akamatsu's physical models (Prosperetti, 1994, “Bubbles Dynamics: Some Things we did not Know 10 Years Ago,” Bubble Dynamics and Interface Phenomena, Blake, Boulton-Stone, Thomas, eds., Kluwer Academic Publishers, Dordrecht, the Netherlands, pp. 3–15; Fujikawa and Akamatsu, 1980, “Effects of Non-Equilibrium Condensation of Vapor on the Pressure Wave Produced by Collapse of a Bubble in Liquid,” J. Fluid Mech., 97(3), pp. 481–512). The pressure amplitude, the profile, and the energy of the pressure waves emitted during cavity collapses were evaluated by numerical simulations. The model was validated by comparisons with experiments carried out at Laboratoire Laser, Plasma et Procédés Photoniques (LP3-IRPHE) (Marseille, France) with laser-induced bubble (Isselin et al., 1998, “Investigations of Material Damages Induced by an Isolated Vapor Bubble Created by Pulsed Laser,” Proceedings of Third International Symposium on Cavitation, Grenoble, France; Isselin et al., 1998, “On Laser Induced Single Bubble Near a Solid Boundary: Contribution to the Understanding of Erosion Phenomena,” J. Appl. Phys., 84(10), pp. 5766–5771). The efficiency of the first collapse ηwave/bubble (defined as the ratio between pressure wave energy and initial bubble potential energy) was evaluated for different bubble collapses. For the cases considered of collapse in a constant-pressure field, the study pointed out the strong influence of the air contents on the bubble dynamics, on the emitted pressure wave characteristics, and on the collapse efficiency. In the second part of the study, the dynamic response and the surface deformation (i.e., pit profile and pit volume) of various materials exposed to pressure wave impacts was simulated making use of a 2D axisymmetric numerical code simulating the interaction between pressure wave and an elastoplastic solid. Making use of numerical results, a new parameter β (defined as the ratio between the pressure wave energy and the generated pit volume) was introduced and evaluated for three materials (aluminum, copper, and stainless steel). By associating numerical simulations and experimental results concerning pitted samples exposed to cavitating flows (volume damage rate), the pressure wave power density and the flow aggressiveness potential power were introduced. These physical properties of the flow characterize the cavitation intensity and can be related to the flow hydrodynamic conditions. Associated to β and ηwave/bubble parameters, these power densities appeared to be useful tools to predict the cavitation erosion power.

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.

Large eddy simulation of turbulent cavitating flow in a venturi nozzle is conducted. The fully compressible Favre-filtered Navier–Stokes equations are coupled with a homogeneous equilibrium cavitation model. The dynamic Smagorinsky subgrid-scale turbulence model is employed to close the filtered nonlinear convection terms. The equations are numerically integrated in the context of a generalized curvilinear coordinate system to facilitate geometric complexities. A sixth-order compact finite difference scheme is employed for the Navier–Stokes equations with the AUSM + -up scheme to handle convective terms in the presence of large density gradients. The stiffness of the system due to the incompressibility of the liquid phase is addressed through an artificial increase in the Mach number. The simulation predicts the formation of a vapor cavity at the venturi throat with an irregular shedding of the small scale vapor structures near the turbulent cavity closure region. The vapor formation at the throat is observed to suppress the velocity fluctuations due to turbulence. The collapse of the vapor structures in the downstream region is a major source of vorticity production, resulting into formation of hair-pin vortices. A detailed analysis of the vorticity transport equation shows a decrease in the vortex-stretching term due to cavitation. A substantial increase in the baroclinic torque is observed in the regions where the vapor structures collapse. A spectra of the pressure fluctuations in the far-field downstream region show an increase in the acoustic noise at high frequencies due to cavitation.

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.

In this technical brief we report the results of a systematic numerical investigation of developing laminar flow in axisymmetric concentric annuli over a wide range of radius ratio ( 0.01 < R i / R o < 0.8 ) and Reynolds number ( 0.001 < Re < 1000 ) . When the annular gap is used as the characteristic length scale we find that for radius ratios greater than 0.5 the development length collapses to the channel-flow correlation. For lower values of radius ratio the wall curvature plays an increasingly important role and the development length remains a function of both radius ratio and Reynolds number. Finally we show that the use of an empirical modified length scale to normalize both the development length and the characteristic length scale in the Reynolds number collapses all of the data onto the channel-flow correlation regardless of the radius ratio.

The collapse of transient bubble clouds near a solid surface was investigated to test a scheme for mitigation of cavitation-induced damage. The target was a porous ceramic disk through which air could be forced. Transient cavitation bubbles were created using a shock-wave lithotripter focused on the surface of the disk. The dynamics of bubble clouds near the ceramic disks were studied for two boundary conditions: no back pressure resulting in surface free of bubbles and 10 psi (0.7 atm) of back pressure, resulting in a surface with a sparse (30% of area) bubble layer. Images of the cavitation near the surface were obtained from a high-speed camera. Additionally, a passive cavitation detector (3.5 MHz focused acoustic transducer) was aligned with the surface. Both the images and the acoustic measurements indicated that bubble clouds near a ceramic face without a bubble layer collapsed onto the boundary, subsequently leading to surface erosion. When a sparse bubble layer was introduced, bubble clouds collapsed away from the surface, thus mitigating cavitation damage. The erosion damage to the ceramic disks after 300 shock waves was quantified using micro-CT imaging. Pitting up to 1 mm deep was measured for the bubble-free surface, and the damage to the bubble surface was too small to be detected.

Investigation on cavitation in multicomponent (solid-liquid and liquid-liquid) mixtures has many applications in the industries and engineering. In this paper, for simulation of multicomponent mixtures, a set of equations with first-order bubble-wall Mach number is derived for a single spherical bubble in quasihomogeneous mixtures. Cavitation bubble behaviors in several kinds of liquid-liquid and solid-liquid mixtures are numerically calculated based on the current model, including the temporal variations in the bubble radius, pressure, and temperature inside the bubble. Specifically, the analysis is focused on the impact of pressure and temperature, while the bubble collapses in the mixtures. The computed results are compared with the previously reported experimental ones to demonstrate the validity of the current model and the numerical procedures.

A phenomenological analysis of the cavitation erosion process of ductile materials is proposed. On the material side, the main parameters are the thickness of the hardened layer together with the conventional yield strength and ultimate strength. On the fluid side, the erosive potential of the cavitating flow is described in a simplified way using three integral parameters: rate, mean amplitude, and mean size of hydrodynamic impact loads. Explicit equations are derived for the computation of the incubation time and the steady-state erosion rate. They point out two characteristic scales. The time scale, which is relevant to the erosion phenomenon, is the covering time—the time necessary for the impacts to cover the material surface—whereas the pertinent length scale for ductile materials is the thickness of the hardened layer. The incubation time is proportional to the covering time with a multiplicative factor, which strongly depends on flow aggressiveness in terms of the mean amplitude of impact loads. As for the erosion rate under steady-state conditions, it is scaled by the ratio of the thickness of hardened layers to the covering time with an additional dependence on flow aggressiveness, too. The approach is supported by erosion tests conducted in a cavitation tunnel at a velocity of 65 m/s on stainless steel 316 L. Flow aggressiveness is inferred from pitting tests. The same model of material response that was used for mass loss prediction is applied to derive the original hydrodynamic impact loads due to bubble collapses from the geometric features of the pits. Long duration tests are performed in order to determine experimentally the incubation time and the mean depth of penetration rate and to validate the theoretical approach.

In order to investigate the erosion extent and mode of cavitation in different states by the commercial code FLUENT and evaluate the reliability of the software, the collapse processes of a vapor bubble, which was near or on the wall under the conditions in the stationary water or the high speed water, were simulated by the numerical calculation by using a 2D model. The results are in accordance with results presented by other researchers, so the simulation may testify to the validation of the code. We suppose that a bevel jet, which is generated contrary to the flow direction when the bubble collapses in high speed flow, may cause the ripple and fish-scale pit damage found on the transition parts of many hydraulic systems.

A three-dimensional twisted hydrofoil with an attached cavitaty closely related to propellers was observed with a high-speed camera at the University of Delft Cavitation Tunnel. Reentrant flow coming from the sides of the cavity aimed at the center plane—termed side-entrant flow—collided in the closure region of the cavity, pinching off a part of the sheet resulting in a periodic shedding. The collapse of the remainder of the sheet appears to be a mixing layer at the location of the colliding reentrant flows. Collision of side-entrant jets in the closure region of a cavity is identified as a second shedding mechanism, in addition to reentrant flow impinging the sheet interface at the leading edge.

In the current study, we report the results of a detailed and systematic numerical investigation of developing pipe flow of inelastic non-Newtonian fluids obeying the power-law model. We are able to demonstrate that a judicious choice of the Reynolds number allows the development length at high Reynolds number to collapse onto a single curve (i.e., independent of the power-law index n ). Moreover, at low Reynolds numbers, we show that the development length is, in contrast to existing results in the literature, a function of power-law index. Using a simple modification to the recently proposed correlation for Newtonian fluid flows ( Durst, F. et al., 2005, “The Development Lengths of Laminar Pipe and Channel Flows,” J. Fluids Eng., 127, pp. 1154–1160 ) to account for this low Re behavior, we propose a unified correlation for X D ∕ D , which is valid in the range 0.4 < n < 1.5 and 0 < Re < 1000 .

The direct numerical simulation (DNS) method has been used to the study of the linear and shock wave propagation in bubbly fluids and the estimation of the efficiency of the cavitation mitigation in the container of the Spallation Neutron Source liquid mercury target. The DNS method for bubbly flows is based on the front tracking technique developed for free surface flows. Our front tracking hydrodynamic simulation code FronTier is capable of tracking and resolving topological changes of a large number of interfaces in two- and three-dimensional spaces. Both the bubbles and the fluid are compressible. In the application to the cavitation mitigation by bubble injection in the SNS, the collapse pressure of cavitation bubbles was calculated by solving the Keller equation with the liquid pressure obtained from the DNS of the bubbly flows. Simulations of the propagation of linear and shock waves in bubbly fluids have been performed, and a good agreement with theoretical predictions and experiments has been achieved. The validated DNS method for bubbly flows has been applied to the cavitation mitigation estimation in the SNS. The pressure wave propagation in the pure and the bubbly mercury has been simulated, and the collapse pressure of cavitation bubbles has been calculated. The efficiency of the cavitation mitigation by bubble injection has been estimated. The DNS method for bubbly flows has been validated through comparison of simulations with theory and experiments. The use of layers of nondissolvable gas bubbles as a pressure mitigation technique to reduce the cavitation erosion has been confirmed.

We developed a method of hybrid particle/cubic interpolated propagation (CIP) to predict the motion of micro- and macrofree surfaces within gas-liquid flows. Microfree surfaces (smaller than the grid sizes) were simulated with the particle method, and macrofree surfaces (larger than the grid sizes) were simulated with the grid method (CIP is a kind of grid method). With the hybrid, velocities given by the advection part of the particle method were combined with those given by the advection part of CIP. Furthermore, the particles used with the particle method were assigned near the macrofree surfaces by using the volume fraction of liquid that was calculated with CIP. The method we developed was used to predict the collapse of a liquid column. Namely, it was simultaneously able to predict both large deformation in the liquid column and its fragmentation, and the predicted configurations for the liquid column agreed well with the experimentally measured ones. It was also used to predict the behavior of liquid films at the outlet of a fuel injector used for automobile engines. The particle method in the simulation was mainly used for liquid films in the air region and the grid method was used for the other regions to shorten the computational time. The predicted profile of the liquid film was very sharp in the air region where the liquid film became thinner than the grid sizes; there was no loss of liquid film with numerical diffusion.