The growth of a vapor bubble in a superheated liquid is controlled by three factors: the inertia of the liquid, the surface tension, and the vapor pressure. As the bubble grows, evaporation takes place at the bubble boundary, and the temperature and vapor pressure in the bubble are thereby decreased. The heat inflow requirement of evaporation, however, depends on the rate of bubble growth, so that the dynamic problem is linked with a heat diffusion problem. Since the heat diffusion problem has been solved, a quantitative formulation of the dynamic problem can be given. A solution for the radius of the vapor bubble as a function of time is obtained which is valid for sufficiently large radius. This asymptotic solution covers the range of physical interest since the radius at which it becomes valid is near the lower limit of experimental observation. It shows the strong effect of heat diffusion on the rate of bubble growth. Comparison of the predicted radius‐time behavior is made with experimental observations in superheated water, and very good agreement is found.

The growth of vapor bubbles in superheated liquids. report no. 26-6

This paper mainly summarizes the recent progresses for the cavitation study in the hydraulic machinery including turbo-pumps, hydro turbines, etc.. Especially, the newly developed numerical methods for simulating cavitating turbulent flows and the achievements with regard to the complicated flow features revealed by using advanced optical techniques as well as cavitation simulation are introduced so as to make a better understanding of the cavitating flow mechanism for hydraulic machinery. Since cavitation instabilities are also vital issue and rather harmful for the operation safety of hydro machines, we present the 1-D analysis method, which is identified to be very useful for engineering applications regarding the cavitating flows in inducers, turbine draft tubes, etc. Though both cavitation and hydraulic machinery are extensively discussed in literatures, one should be aware that a few problems still remains and are open for solution, such as the comprehensive understanding of cavitating turbulent flows especially inside hydro turbines, the unneglectable discrepancies between the numerical and experimental data, etc.. To further promote the study of cavitation in hydraulic machinery, some advanced topics such as a Density-Based solver suitable for highly compressible cavitating turbulent flows, a virtual cavitation tunnel, etc. are addressed for the future works.

A review of cavitation in hydraulic machinery

Computational modelling of flash boiling flows: A literature survey

The cavitating flow around the asymmetric leading edge (ALE) 15 hydrofoil is investigated through large eddy simulation with the modified Schnerr–Sauer cavitation model, which considers the effect of noncondensable gas. The statistical average velocity profiles obtained by simulation and experimentation show good agreement. The time evolution of cavity shape shows that cavity growth and separation start from the short side and spread toward the long side due to a side-entrant jet. The variation frequency of the cavity length of ALE15 hydrofoil at the long side is 163.93 Hz, and the cavitation shedding frequency at the short side is 306.67 Hz, which is about twice the value of the former. The filtered vorticity transport equation is employed to investigate the cavitation–vortex–turbulence interaction. Results indicate that vortex stretching is the major promoter of cavitation development, and vortex dilatation links vapor cavity and vortices. Baroclinic torque is noticeable at the liquid–vapor interface, and turbulent stress is related to cavitation inception. Moreover, a one-dimensional model for predicting pressure fluctuation is proposed, and results show that the model can effectively predict cavitation-induced pressure fluctuation on a hydrofoil, even on a three-dimensional ALE15 hydrofoil.

Cavitation–Vortex–Turbulence Interaction and One-Dimensional Model Prediction of Pressure for Hydrofoil ALE15 by Large Eddy Simulation

This research treats the effect of impeller inlet geometry on performance improvement for a boiler feed pump, who is a centrifugal pump having specific speed of 183 m·m3min−1·min−1 and close type impeller with exit diameter of 450 mm. The hydraulic performance and cavitation performance of the pump have been tested experimentally. In order to improve the pump, five impellers have been considered by extending the blade leading edge or applying much larger blade angle at impeller inlet compared with the original impeller. The 3-D turbulent flow inside those pumps has been analyzed basing on RNG k-ɛ turbulence model and VOF cavitation model. It is noted that the numerical results are fairly good compared with the experiments. Based on the experimental test and numerical simulation, the following conclusions can be drawn: (1) Impeller inlet geometry has important influence on performance improvement in the case of centrifugal pump. Favorite effects on performance improvement have been achieved by both extending the blade leading edge and applying much larger blade angle at impeller inlet; (2) It is suspected that the extended leading edge have favorite effect for improving hydraulic performance, and the much larger blade angle at impeller inlet have favorite effect for improving cavitation performance for the test pump; (3) Uniform flow upstream of impeller inlet is helpful for improving cavitation performance of the pump.

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Impeller inlet geometry effect on performance improvement for centrifugal pumps

The unsteady turbulent cloud cavitation around a NACA66 hydrofoil was simulated using the filter-based density corrected model (FBDCM). The cloud cavitation was treated as a homogeneous liquid-vapor mixture and the effects of turbulent eddy viscosity were reduced in cavitation regions near the hydrofoil and in the wake. The numerical results (in terms of the vapor shedding structure and transient pressure pulsation due to cavitation evolution) agree well with the available experimental data, showing the validity of the FBDCM method. Furthermore, the interaction of vortex and cavitation was analyzed based on the vorticity transport equation, revealing that the cavitation evolution has a strong connection with vortex dynamics. A detailed analysis shows that the cavitation could promote the vortex production and flow unsteadiness by the dilatation and baroclinic torque terms in the vorticity transport equation.

Cavitation shedding dynamics around a hydrofoil simulated using a filter-based density corrected model

A thermodynamic cavitation model is developed to simulate the cavitating water flow in a wide temperature range. The thermal effect on bubble growth during cavitation is introduced in the developed model by considering both pressure difference and heat transfer between the vapor and liquid phase. The cavitating turbulent flow over a NACA0015 hydrofoil has been simulated at various temperatures from room temperature to 150°C by using the present cavitation model, which has been validated by the experimental data. It is seen that the thermodynamic effects of cavitation, vapor depression and temperature depression are much more predominant in high temperature water compared with those in room temperature water. These results indicate that the proposed thermodynamic cavitation model is reasonably applicable to the cavitating water flow in a wide temperature range.

https://iopscience.iop.org/article/10.1088/0256-307X/27/1/016401/pdf

A Thermodynamic Cavitation Model for Cavitating Flow Simulation in a Wide Range of Water Temperatures

Cavitation in miniature pumps was investigated experimentally for two semi-open centrifugal impellers. Although both impellers had the same blade cross-section, one impeller had a two-dimensional blade, while the other had a leaned blade. The flows were also analyzed using a numerical model of the three-dimensional turbulent flow in the pumps near the peak efficiency point using the k-ɛ turbulence model and the VOF cavitation model. The average cavitation performance of each impeller was satisfactorily predicted by the numerical simulations. The results show that the miniature pumps have similar cavitation performances as an ordinary-size pump, with the cavitation performance of the semi-open impeller reduced by increased axial tip clearances. Also, both the hydraulic and cavitation performance of the semi-open impeller were improved by the leaned blade. The results also show that uniform flow upstream of the impeller inlet will improve the cavitation performance of a miniature pump.

Cavitation in semi-open centrifugal impellersfor a miniature pump

A three-component model based on mass transfer equation is proposed to simulate both the natural and ventilated cavitations. In the present cavitation model, the content of nuclei in the local flow field is updated synchronously, and is coupled with the Rayleigh–Plesset equation so as to capture the cavity development. The proposed model is applied for simulating the cavitating flow around a super-cavitating vehicle in different cavitation conditions. In the case of the natural cavitation simulation, the predicted cavitation characteristics including the cavity length and cavity diameter agrees fairly well with the analytical results. In the case of the mixed cavitation simulation, the gas ventilation obviously influences the development of cavity. With the increase of the gas ventilated rate, the natural cavitation is suppressed remarkably, and a super cavitation is formed even at a relatively larger natural cavitation number.

https://iopscience.iop.org/article/10.1088/0256-307X/27/9/096401/pdf

A Three-Component Model Suitable for Natural and Ventilated Cavitation

The application of wave guide vanes with bio-inspired leading-edge protuberances to the hump characteristic of a pump-turbine is examined in this study. Numerical simulation with a shear-stress tra...

Luo Xianwu

Papers

Cavitation shedding dynamics around a hydrofoil simulated using a filter-based density corrected model

A Thermodynamic Cavitation Model for Cavitating Flow Simulation in a Wide Range of Water Temperatures

Cavitation in semi-open centrifugal impellersfor a miniature pump

A Three-Component Model Suitable for Natural and Ventilated Cavitation

Suppression of hump characteristic for a pump-turbine using leading-edge protuberance: