Improved Cavitation Model Research Articles

Numerical simulations of cavitating water jet by an improved cavitation model of compressible mixture flow with an emphasis on phase change effects

Focusing on cavitation phenomena caused by high-speed submerged water jets, this paper presents an improved cavitation model for a compressible fluid mixture based on a concise estimation of fluid compressibility that considers phase change effects. The homogeneous two-phase flow assumption is adopted, and the gas phase is assumed to consist of vapor and non-condensable components. Equations of state for a pure liquid and an ideal gas are employed to evaluate the compressibility of the liquid and non-condensable components, and the compressibility of the vapor is treated semi-empirically as a constant. The model is embedded in an unsteady Reynolds-averaged Navier–Stokes solver, with the realizable k-ε model employed to evaluate the eddy viscosity. The turbulent cavitating flow caused by an impulsively started submerged water jet is treated. The pattern of periodic cavitation cloud shedding is acceptably captured, and the mass flow rate coefficient and its fluctuation frequency evaluated by simulations agree with the experimental results well. The validity of the proposed method is confirmed. The results reveal that cavitation occurs when pin/Pin reaches 0.65 and fluid flow begins to pulsate. In the well-developed stage, the leading cavitation cloud and a subsequent cloud are successively shed downstream, and this process is repeated. The subsequent cloud catches the leading cloud, and they coalesce in the range x/d≈ 2–3. The pressure fluctuations concentrate in the range of x/d≈2–5 corresponding to the periodic shedding of cavitation clouds. The mass flow rate coefficient pulsates from 0.59–0.66 under the effect of cavitation.

Assessment of influences of needle lift and hole height on string cavitation in liquid injection

This work uses an improved cavitation model to comprehensively study the impacts of needle lift and hole height on the dynamics of in-nozzle string cavitation. The numerical models can provide a satisfying prediction on internal string cavitation and multiphase vortex flow features in liquid nozzles. Results indicate that the driving mechanism behind the string cavitation inception was the vortex evolution, and the stronger the vortex flow, the stronger the string cavitation. Moreover, the string cavitation patterns were remarkably different under various hole heights due to the evolution characteristics of in-hole longitudinal vortices; specifically, there was an in-nozzle large scale well-organized longitudinal vortices at higher hole heights, while the interaction between the two weaker counter-rotating vortices at lower hole heights resulted in there was no continuous longitudinal vortex inside the nozzles. Furthermore, the quantitative comparison of the inner string cavitation at all of the examined cases under different needle lifts and hole heights shows that appropriately reducing the maximum needle lift of the injector and simultaneously increasing the hole height of nozzles were conducive to inducing the string cavitation on the premise of the large enough flow velocity.

An improved cavitation model with thermodynamic effect and multiple cavitation regimes

Mechanical feed pumps in organic Rankine cycle (ORC) power plants can suffer from cavitation to lose their normal feeding performance or even damage. Cavitation models for organic fluids in ORC systems are lacking presently. Hence, a new cavitation model with thermodynamic effect was proposed. Surface tension-controlled, inertia-controlled, intermediate and heat transfer-controlled cavitation regimes, and two key elements: vapour bubble growth rate and vapour bubble number density are included in the model. A known air or non-condensable gas concentration in the liquid was employed to determine cavitation nuclei number density. The model was coded in ANSYS CFX as user defined model and validated with cavitating flows of organic fluid R114 in a venturi, liquid nitrogen and liquid hydrogen on a tapered hydrofoil and warm water around a hydrofoil NACA 0015 in cavitation tunnels based on visualised cavity length. Two model constants, temperature depression, and minimal cavitation number were correlated to bulk liquid temperature, Reynolds number, and Jakob number. The temperature and pressure profiles of liquid nitrogen and hydrogen on hydrofoil surface were examined against the experimental data. The model was applied to simulate unsteady cavitating flows of organic fluid R245fa in a diaphragm pump. It was shown that the temperature depression and minimal cavitation number cannot be correlated to bulk liquid temperature, Reynolds number and Jakob number. Two model constants can be correlated fairly to Reynolds number. The model underestimates the thermodynamic effect by 43% for R114, 18.6% for liquid nitrogen and 32.6% for liquid hydrogen based on temperature depression. The predicted temperature and pressure profiles on hydrofoil surface agree with the experimental data for liquid nitrogen. The model can produce an expected curve of mean pump flow rate against net positive suction head available.

Numerical study of cavitation in centrifugal pump conveying different liquid materials

Abstract A numerical study on cavitation in the centrifugal pump during the transportation of pure water and diesel is carried out. An improved cavitation model based on the Zwart–Gerber–Belamri Model is employed in the simulation. A Cash–Karp fourth–fifth order Runge–Kutta method was used to solve the original Rayleigh-Plesset equation to get the numerical solution. The effects from viscosity and surface tension on bubbles’ expansion and compression are taken into account in the improved model instead of the traditional simplification in which the bubble radius is just a function of pressure and density. The coefficients got by fitting the numerical solution are added to the constant pre-multiplier of the Zwart-Gerber-Belrami cavitation model and finally enhance the model. The vapor volume fraction was predicted to be larger in diesel compared to water. The distribution of pressure in diesel is more homogenous than that in pure water.

Numerical analysis on cavitation effects in submerged water jet added with turbulent drag-reducing additives of CTAC

In this paper the cavitation phenomenon and bubble collapse in submerged water jet added with CTAC were studied. The cavitation simulation was based on an improved cavitation model established by introducing coefficients into traditional cavitation model. The coefficients were obtained by fitting the numerical solutions of Rayleigh-Plesset equation in which the viscosity term and surface tension term were not neglected. Cross model was also employed to express the shear-thinning character of the surfactant solution. Simulation results show that the whole cavitation intensity decreased but the scale of cavitation region increased in drag-reducer solution. The submerged water jet added with drag-reducer was less dispersed and the stagnation pressure near the wall was significantly improved. Simulation results of the bubble collapse process show that the bubble collapsed more slowly in drag-reducer solution in comparison with that in pure water. The two pressure peaks near the wall during the collapse process appeared later in drag-reducer solution and the maximum value of the pressure generated in drag-reducer solution was less than that in pure water.

Numerical Study on Cavitation Generation in a Water Jet Added with Turbulent Drag-Reducing Additives Based on Improved Cavitation Model and Cross Model

An improved cavitation model was proposed to simulate the cavitation phenomenon in water jet added with turbulent drag-reducing additives. The Cross model which expressed the shear-thinning properties of drag-reducer solution was also employed. The neglected viscous term and surface tension term in traditional cavitation models were reconsidered as viscosity and surface tension force were important factors affecting bubbles’ motion in drag-reducer solution. The numerical solutions of bubble radius in drag-reducer solutions of different concentrations were fitted and the change rates were added to the original mass transfer mechanism equations. The results showed the modified cavitation model described the cavitation characteristics in drag-reducer solutions more accurately and effectively reflected that the cavitation region’s wake became longer with the increase concentration of the drag reducing agent. With the concentration increasing, the distribution of cavitation cloud became more homogeneous and th...

The effect of the clearance geometries on the cavitating vortices near the foil tip

The blade tip clearance is inevitable for an axial flow rotor. The clearance flow contains various vortices and the resulting vortex cavitation is a concern in hydraulic machineries. In the narrow gap, the vortex features are sensitive to the change of the clearance size, and then the geometry factors may influence the vortex cavitation characteristics. As a simplification of a blade, an isolated hydrofoil is convenient for adjusting the clearance geometries in different cases. The effects of the clearance shape, gap height and gap width on the cavitating vortices are discussed in present paper. As the limited space and the cavitation phenomenon make it difficult to measure the vortex flow features, the numerical simulation is widely used to investigate the cavitating vortices. An improved cavitation model, which is suitable for the vortex cavitation, is used in present work. Under the different geometrical conditions, the vortex structures, the pressure features and the cavitation characteristics are revealed from the simulation.

Symmetrical and unsymmetrical tip clearances on cavitation performance and radial force of a mixed flow pump as turbine at pump mode

Abstract Transient cavitating flows of a mixedflow PAT (pump as turbine) at pump mode are investigated experimentally and numerically. Radial force on principal axis is recorded and compared between pump with symmetrical and unsymmetrical tip clearance. Numerical simulation with improved cavitation model by modifying the vapor pressure is conducted, and the simulation results agree well with the experiments. Tip clearance has great influence on pump cavitation performance. The pump energy performance will deteriorate with tip clearance increasing. In addition, in comparison with the symmetrical tip clearance, the unsymmetrical tip clearance makes the pump cavitation performance worse. As the cavitation develops, the unsymmetrical tip clearance simultaneously influences the magnitude and direction of radial force, while the symmetrical tip clearance only influences the magnitude of radial force. The dominant frequencies of radial force of symmetrical and unsymmetrical tip clearances are related to the blade number and guide vane number, respectively. The maximum amplitude of force fluctuation for unsymmetrical tip clearance is 7 times that for symmetrical tip clearance.

Application of the semi-analytical cavitation model to flows in a centrifugal pump

Visualization experiments are carried out to investigate the cavitating flows in a centrifugal pump at different flow rates. The cavity lengths under different pump inlet pressure are obtained. The semi-analytical cavitation model is improved since it is not suitable for predicting large cavities full of vapor. The improved cavitation model is used to numerically study the steady and rotating cavitation in the centrifugal pump. Compared with the Zwart cavitation model, the numerical results predicted by the semi-analytical model agree much better with the experiments, especially for large cavities. The cavity lengths at the suction side are overestimated during the simulations, especially by using the Zwart model. At low flow rates, the prediction of the rotating cavitation effect is weaker and the cloud shedding frequency is smaller than those in the experiments.

Application of the improved cavitation model to turbulent cavitating flow in fuel injector nozzle

Cavitation phenomenon occurring inside diesel injector nozzles plays a key role in atomization of fuel spray. The most common approach to numerically model the cavitating flow is Volume-Of-Fluid (VOF) method, which employs the governing equations for a perfect gas–liquid mixture often in combination with a transport equation for liquid or gas volume fraction. A mass transfer model is required to evaluate the phase change between liquid and vapor. Most of the mass transfer models use the simplest bubble dynamics model, Rayleigh (R) equation which is sometimes called simplified Rayleigh–Plesset (RP) equation, to simulate the growth and collapse of bubbles based on the vapor saturation pressure Pv. We have found that R equation over-predicts cavitation when local pressure is slightly below Pv. We have proposed the Modified Rayleigh (MR) equation taking into account the critical pressure Pc, and showed its validity in some simple test cases with uniform pressure. In this study, the applicability of the MR equation to turbulent cavitating flows in a fuel injector nozzle is examined. OpenFOAM is used for the numerical simulation of turbulent cavitating flows in an one-side rectangular nozzle whose images have been captured by a high-speed camera and the turbulent velocity has been measured by a Laser Doppler Velocimetry (LDV). Turbulent effect is taken into account using RNG k-ɛ model. The numerical results are compared with the experimental data and the turbulent recirculation flow, re-entrant jet and cloud cavitation shedding are well simulated by the MR model.

Influence of noncondensible gas on flowing characteristics of multiple nozzle oil jet pump for lubrication system in steam turbine

The full cavitation model introduced by Singhal et al. was partly improved based on experimental results. The improved cavitation model is used to simulate cavitating flow in multiple nozzle oil jet pump for lubrication system in steam turbine. The influence of noncondensible gas on flowing characteristics of multiple nozzle oil jet pump was studied with noncondensible gas content in the range of 0.01–500 ppm. Results show that noncondensible gas has little influence on nonchoking flow while imminent choking flow and deep choking flow are greatly affected. With the increase of noncondensible gas, multiple nozzle oil jet pump enters choking flow earlier. The maximum suction flow rate per unit throat area of multiple nozzle oil jet pump remains constant with varying pressure ratios and area ratios under choking flow, which is only determined by the noncondensible gas content. It is suggested that the maximum suction flow rate per unit throat area is used for the prediction of choking flow in multiple nozzle oil jet pump. This study also provides qualitative criteria for the upper limit of water content in lubrication oil, which avoids multiple nozzle oil jet pump working under choking flow.

Numerical investigation of the hump characteristic of a pump–turbine based on an improved cavitation model

For the safe and stable operation of a pump–turbine at pump mode, the hump characteristics must be studied and the hump region should be avoided. 3-D (three dimensional), compressible, cavitating flows in a pump–turbine at pump mode were numerically studied using SST k–ω turbulence model and mixture model. The decrease of the kinematic eddy viscosity in the region of high volume fraction of water vapor was considered in the calculation. The flow and external characteristic in the hump region were analyzed. Results show that the hump characteristic of a pump–turbine might be related to the cavity flow in the pump–turbine. It is the appearance of the cavitation that reduces the head of the pump–turbine. The cavitation incipience is thought to occur when the pump–turbine runs at the peak head and the cavitation is worse at 80% discharge of the pump–turbine. The cavitation regions locate at the inlet of the suction side. Calculation results are in good agreement with experimental data. The pressure fluctuation at the wave trough of hump characteristic is determined by the rotational speed. Numerical study of hump characteristics can provide a basic understanding for the improvement of stable operation of a pump–turbine.

Assessment of the Improved Cavitation Model and Modified Turbulence Model for Ship Propeller Cavitation Simulation

To assess the effectiveness of the adopted improved Sauer cavitation model and modified shear stress transport turbulence model for ship propeller cavitation simulation,and verify the applicability of the rule when σσi,the pressure coefficient of the blade tip section is relative unaltered to determine the cavitation inception,comprehensive validation and analysis of E779A propeller’s sheet cavitation pattern,cavity area,pressure coefficient distribution of the blade section,thrust and torque breakdown performance curves and its inception cavitation index are conducted under lightly,moderately and heavily cavitation levels.Results show that,under moderately cavitation level condition(0.1 ≤Ac/A00.25),simulated cavity area agrees very well the experiment and being better than that in opened research papers,while a little smaller than the test for the lightly cavitation level(Ac/A00.1) due to wall roughness effect,and over-prediction for heavily cavitation(0.25≤Ac/A00.5) because of the bubble cavitation area included.Under both of the design and un-design conditions,the predicted beginning points of thrust decline induced by cavitation are the same as experiment,while the slope indexes of thrust and torque are bigger.Under J=0.77 condition,the calculated cavitation inception number determined by the rule is 3.25 and just differs by 0.6% to its experiment.All the results above are concluded that the adopted numerical models are absolutely valuable for propeller cavitation simulation under moderately cavitation level associated with satisfactory results.Additionally,the inception rule is positively useful to determine the cavitaion inception and predict the inception bucket next after back inception index of the 0.88R section(for low skew angles) or 0.7R section(for highly-skewed propeller) being obtained.With this method,the critical inception speed prediction of warships is no more difficult.

Intense laser beam guiding in self-induced electron cavitation channel in underdense plasmas

In underdense plasmas, the transverse ponderomotive force of an intense laser beam with Gaussian transverse profile expels electrons radially, and it can lead to an electron cavitation. An improved cavitation model with charge conservation constraint is applied to the determination of the width of the electron cavity. The envelope equation for laser spot size derived by using source-dependent expansion method is extended to including the electron cavity. The condition for self-guiding is given and illuminated by an effective potential for the laser spot size. The effects of the laser power, plasma density and energy dissipation on the self-guiding condition are discussed.

Numerical Analysis of Cavitating Centrifugal Pump (1st Report, Validation of Model and Pump Steady Performance)

An improved cavitation model and treatment has been developed for the prediction of the flow field resulting from an attached cavitation region. The cavitation model is implemented in a viscous calculation basing on a Reynolds Averaged Navier-Stokes (RANS) equations solver with the effect of turbulence taken into account. A priori knowledge of the wall detachment point and bubble length is not required but naturally a part of the solution by this cavitation model. The liquid/vapor interface is tracked and obtained by an iteration procedure between the flow field computation and interface updating. An improved interface updating technique has been proposed to speed up and stabilize the iteration process. A series of computation has been carried out for internal and external flows of different configurations. The code and the cavitation model have been well validated by comparison of the computations against the experimental data available. The computations also demonstrate the feasibility of the improved cavitation model and treatment to flows in complicated configurations.

Numerical Analysis of Cavitating Centrifugal Pump (2nd Report, Pump Unsteady Characteristics)

An improved cavitation model described in the 1st report was applied to study the frequency response of a cavitating centrifugal pump to rotational speed. The responses of flow rate and total head rise across the pump were calculated by a liquid/vapor interface tracking method coupled with the unsteady Reynolds Averaged Navier-Stokes equation. Calculated responses of flow rate and total head rise were compared with the corresponding experimental ones, and showed reasonable agreement with measured data. Frequency response of the cavitating pump to rotational speed was discussed based on the calculated and measured characteristics.

Axial magnetic fields in relativistic self-focusing channels.

Based on an improved cavitation model for the electron dynamics, an exact analysis is presented of the generation of axial magnetic fields in the relativistic self-focusing channels produced by circularly polarized light in plasmas. Two kinds of waveguiding structures are considered: single-channel waveguides and plasma filaments surrounded by a light field. It is found that due to large electron density gradients in the cavitation plasma, magnetic fields of megagauss values with opposite directions separated by a neutral sheet, where the magnetic field passes through zero, can be produced.

Axisymmetric relativistic self-channeling of laser light in plasmas.

By using an improved cavitation model, relativistic self-channeling structures are derived, which make it possible to propagate laser powers exceeding the critical one for self-focusing. A propagation mode for high laser power is also presented which is qualitatively different from those in the weakly relativistic case. Structural stability analysis shows that stable self-wave-guide propagation can take place.

Electron cavitation and relativistic self-focusing in underdense plasma

An improved cavitation model shows that stable beam channeling and electron cavitation occur for relativistic laser intensities even at powers hundreds of times larger than the critical power for self-focusing.

A Moving Spectral Element Approach to the Dynamically Loaded Journal Bearing Problem

A moving spectral element method is described for solving the dynamically loaded journal bearing problem. The journal bearing geometry comprises two eccentric cylinders with a lubricant occupying the region between them. The inner cylinder (the journal) rotates and is also free to move under a time-dependent load, while the outer cylinder (the bearing) is stationary. Lubrication engineers are interested in the dependence of the minimum oil film thickness on viscosity and viscoelasticity. The numerical method is validated by comparing the paths with those generated from lubrication theory. A study of the effect the choice of cavitation model has upon the journal's locus is made and is found to be critical. The possibility of an improved cavitation model is discussed.