Numerical investigation of cavitating flow behind the cone of a poppet valve in water hydraulic system

Computational Fluid Dynamics (CFD) simulations of cavitating flow through water hydraulic poppet valves were performed using advanced RNG k-epsilon turbulence model. The flow was turbulent, incompressible and unsteady, for Reynolds numbers greater than 43 000. The working fluid was water, and the structure of the valve was simplified as a two dimensional axisymmetric geometrical model. Flow field visualization was numerically achieved. The effects of inlet velocity, outlet pressure, opening size as well as poppet angle on cavitation intensity in the poppet valve were numerically investigated. Experimental flow visualization was conducted to capture cavitation images near the orifice in the poppet valve with 30° poppet angle using high speed video camera. The binary cavitating flow field distribution obtained from digital processing of the original cavitation image showed a good agreement with the numerical result.

Detached-eddy Simulation for Time-dependent Turbulent Cavitating Flows

The Reynolds-averaged Navier-Stokes（RANS）,such as the original k-ω two-equation closures,have been very popular in providing good prediction for a wide variety of flows with presently available computational resource.But for cavitating flows,the above equations noticeably over-predict turbulent production and hence effective viscosity.In this paper,the detached eddy simulation（DES） method for time-dependent turbulent cavitating flows is investigated.To assess the state-of-the-art of computational capabilities,different turbulence models including the widely used RANS model and DES model are conducted.Firstly,in order to investigate the grid dependency in computations,different grid sizes are adopted in the computation.Furthermore,the credibility of DES model is supported by the unsteady cavitating flows over a 2D hydrofoil.The results show that the DES model can effectively reduce the eddy viscosities.From the experimental validations regarding the force analysis,frequency and the unsteady cavity visualizations,more favorable agreement with experimental visualizations and measurements are obtained by DES model.DES model is better able to capture unsteady phenomena including cavity length and the resulting hydrodynamic characteristics,reproduces the time-averaged velocity quantitatively around the hydrofoil,and yields more acceptable and unsteady dynamics features.The DES model has shown to be effective in improving the overall predictive capability of unsteady cavitating flows.

PIV analysis and high-speed photographic observation of cavitating flow field behind circular multi-orifice plates

Based on a self-developed hydrodynamic cavitation device with different geometric parameters for circular multi-orifice plates,turbulence characteristics of cavitating flow behind multi-orifice plates,including the effects of orifice number and orifice layout on longitudinal velocity,turbulence intensity,and Reynolds stress,were measured with the particle image velocimetry(PIV)technique.Flow regimes of the cavitating flow were also observed with high-speed photography.The experimental results showed the following:(1)high-velocity multiple cavitating jets occurred behind the multi-orifice plates,and the cavitating flow fields were characterized by topological structures;(2)the longitudinal velocity at each cross-section exhibited a sawtooth-like distribution close to the multi-orifice plate,and each sawtooth indicated one jet issuing from one orifice;(3)there were similar magnitudes and forms for the longitudinal and vertical turbulence intensities at the same cross-section;(4)the variation in amplitude of Reynolds stress increased with an increase in orifice number;and(5)the cavitation clouds in the flow fields became denser with the increase in orifice number,and the clouds generated by the staggered layout of orifices were greater in number than those generated by the checkerboard-type one for the same orifice number.The experimental results can be used to analyze the mechanism of killing pathogenic microorganisms through hydrodynamic cavitation.

Experimental Investigation on Cavitating Flow Shedding over an Axisymmetric Blunt Body

Nowadays,most researchers focus on the cavity shedding mechanisms of unsteady cavitating flows over different objects,such as 2D/3D hydrofoils,venturi-type section,axisymmetric bodies with different headforms,and so on.But few of them pay attention to the differences of cavity shedding modality under different cavitation numbers in unsteady cavitating flows over the same object.In the present study,two kinds of shedding patterns are investigated experimentally.A high speed camera system is used to observe the cavitating flows over an axisymmetric blunt body and the velocity fields are measured by a particle image velocimetry（PIV）technique in a water tunnel for different cavitation conditions.The U-type cavitating vortex shedding is observed in unsteady cavitating flows.When the cavitation number is 0.7,there is a large scale cavity rolling up and shedding,which cause the instability and dramatic fluctuation of the flows,while at cavitation number of 0.6,the detached cavities can be conjunct with the attached part to induce the break-off behavior again at the tail of the attached cavity,as a result,the final shedding is in the form of small scale cavity and keeps a relatively steady flow field.It is also found that the interaction between the re-entrant flow and the attached cavity plays an important role in the unsteady cavity shedding modality.When the attached cavity scale is insufficient to overcome the re-entrant flow,it deserves the large cavity rolling up and shedding just as that at cavitation number of 0.7.Otherwise,the re-entrant flow is defeated by large enough cavity to induce the cavity-combined process and small scale cavity vortexes shedding just as that of the cavitation number of0.6.This research shows the details of two different cavity shedding modalities which is worthful and meaningful for the further study of unsteady cavitation.

Dynamic Characteristics of High-speed Water-Lubricated Spiral Groove Thrust Bearing Based on Turbulent Cavitating Flow Lubrication Model

The water-lubricated bearings are usually the state of turbulent cavitating flow under high-speed conditions. And the distribution of cavitation bubbles and the interface effect between the two phases have not been included in previous studies on high-speed water-lubricated bearings. In order to study the influence of interface effect and cavitation bubble distribution on the dynamic characteristics of high-speed water-lubricated spiral groove thrust bearings(SGTB).A turbulent cavitating flow lubrication model based on two-phase fluid and population balance equation of bubbles was established in this paper. Stiffness and the damping coefficients of the SGTB were calculated using the perturbation pressure equations. An experimental apparatus was developed to verify the theoretical model. Simulating and experimental results show that the small-sized bubbles tend to generate in the turbulent cavitating flow when at a high rotary speed, and the bubbles mainly locate at the edges of the spiral groove. The simulating results also show that the direct stiffness coefficients are increased due to cavitation effect, and cross stiffness coefficients and damping coefficients are hardly affected by the cavitation effect. Turbulent effect on the dynamic characteristics of SGTB is much stronger than the cavitating effect.

Passive control of cavitating flow around an axisymmetric projectile by using a trip bar

Quasi-periodical evolutions such as shedding and collapsing of unsteady cloud cavitating flow, induce strong pressure fluctuations, what may deteriorate maneuvering stability and corrode surfaces of underwater vehicles. This paper analyzed effects on cavitation stability of a trip bar arranged on high-speed underwater projectile. Small scale water tank experiment and large eddy simulation using the open source software Open FOAM were used, and the results agree well with each other. Results also indicate that trip bar can obstruct downstream re-entrant jet and pressure wave propagation caused by collapse, resulting in a relatively stable sheet cavity between trip bar and shoulder of projectiles.

Dynamic mode decomposition and reconstruction of transient cavitating flows around a Clark-Y hydrofoil

The transient cavitating flow around the Clark-Y hydrofoil is numerically investigated by the dynamic mode decomposition with criterion.Based on the ranking dominant modes,frequencies of the first four modes are in good accordance with those obtained by fast Fourier transform.Furthermore,the cavitating flow field is reconstructed by the first four modes,and the dominant flow features are well captured with the reconstructed error below 12%when compared to the simulated flow field.This paper offers a reference for observing and reconstructing the flow fields,and gives a novel insight into the transient cavitating flow features.

Simulation of Cavitating Flow around a 2-D Hydrofoil

In order to predict the effects of cavitation on a hydrofoil, the state equations of the cavitation model were combined with a linear viscous turbulent method for mixed fluids in the computational fluid dynamics (CFD) software FLUENT to simulate steady cavitating flow. At a fixed attack angle, pressure distributions and volume fractions of vapor at different cavitation numbers were simulated, and the results on foil sections agreed well with experimental data. In addition, at the various cavitation numbers, the vapor fractions at different attack angles were also predicted. The vapor region moved towards the front of the airfoil and the length of the cavity grew with increased attack angle. The results show that this method of applying FLUENT to simulate cavitation is reliable.

Numerical Study of Cavitating Flows around a Hydrofoil with Deep Analysis of Vorticity Effects

This paper aims to numerically explore the characteristics of unsteady cavitating flow around a NACA0015 hydrofoil,with a focus on vorticity attributes.The simulation utilizes a homogeneous mixture model coupled with a filter-based density correction turbulence model and a modified Zwart cavitation model.The study investigates the dynamic cavitation features of the thermal fluid around the hydrofoil at various incoming flow velocities.It systematically elucidates the evolution of cavitation and vortex dynamics corresponding to each velocity condition.The results indicate that with increasing incoming flow velocity,distinct cavitation processes take place in the flow field.

NUMERICAL SIMULATIONS OF CAVITATING FLOWS

A new model, which involves viscous and multi-phase effects, was given to study cavitating flows. A local compressible model was established by introducing a density-pressure function to account for the two-phase flow of water/vapor and the transition from one phase to the other. An algorithm for calculating variable-density N-S equations of cavitating flow problem was put forward. The present method yields reasonable results for both steady and unsteady cavitating flows in 2D and 3D cases. The numerical results of unsteady character of cavitating flows around hydrofoils coincide well with experimental data. It indicates the feasibility to apply this method to a variety of cavitating flows of practical problems.

Experimental and numerical investigation of unsteady cavitating flows through a 2D hydrofoil

In the present study, firstly, the unsteady cavitating flows around a hydrofoil are studied based on the flow visualization and detail velocity measurement, a high-speed video camera is used to visualize the flow structures, and a particle image velocimetry （PIV） technique is applied to the measurement of the time-averaged and instantaneous velocity and vorticity fields. The results show that the unsteadiness of mass transfer process between the vapor and the two-phase regions is substantial, a self-oscillatory behavior of the whole sheet cavitation is obtained, with large length fluctuations and vapor cloud shedding, and also the cavitation structure depends on the interaction of the water-vapor mixture and the periodic vortex shedding. The main purpose of this experimental study is to offer information for validating computational models, and shed light on the unsteady multiphase transport process of cavitating flows. Furthermore, with an emphasis on the dynamics of the attached turbulent cavitating flows, a filter-based model （FBM） is derived from the k-6 two-equation model, a conditional averaging method aimed at improving unsteady simulation is applied to computation. In comparison to the standard k-ε model, overall, the filter-based model is shown to improve the predictive capability considerably.

Numerical simulation unsteady cloud cavitating flow with a filter-based density correction model

In this paper, various turbulence closure models for unsteady cavitating flows are investigated. The filter-based model （FBM） and the density correction model （DCM） were proposed to reduce the turbulent eddy viscosities in a turbulent cavitating flow based on the local meshing resolution and the local fluid density, respectively. The effects of the resolution control parameters in the FBM and DCM models are discussed. It is shown that the eddy viscosity near the cavity closure region can significantly influence the cavity shapes and the unsteady shedding pattern of the cavitating flows. To improve the predictions, a Filter-Based Density Cor-rection model （FBDCM） is proposed, which blends the FBM and DCM models according to the local fluid density. The new FBDCM model can effectively represent the eddy viscosity, according to the multi-phase characteristics of the unsteady cavitating flows. The experimental validations regarding the force analysis and the unsteady cavity visualization show that good agreements with experimental visualizations and measurements are obtained by the FBDCM model. For the FBDCM model, the attached cavity length and the resulting hydrodynamic characteristics are subsequently affected by the detail turbulence modeling parameters, and the model is shown to be effective in improving the overall predictive capability.

Physical and numerical investigation on transient cavitating flows

The objective of this paper is to investigate transient cavitating flows around a hydrofoil via combined physical and numerical studies. The aims are to 1) investigate the periodic formation, breakup, shedding, and collapse of the sheet/cloud cavities, 2) provide a better insight in the physical mechanism that governs the dynamics and structures of the sheet/cloud cavitation, 3) quantify the influence of cavitation on the surrounding flow structures. Results are presented for a Clark-Y hydrofoil fixed at an angle of attack of a=8° at a moderate Reynolds number, Re=7×105 , for sheet/cloud cavitating conditions. The experimental studies were conducted in a cavitation tunnel at Beijing Institute of Technology, China. The numerical simulations are performed by solving the incompressible, multiphase unsteady Reynolds-averaged Navier-Stokes (URANS) equations via the commercial code CFX using a transport equation-based cavitation model; a filter-based density corrected model (FBDCM) is used to regulate the turbulent eddy viscosity in both the cavitation regions near the foil and in the wake. The results show that numerical predictions are capable of capturing the initiation of the cavity, growth toward the trailing edge, and subsequent shedding in accordance with the quantitative features observed in the experiment. Regarding vapor shedding in the cavitating flow around the three-dimensional foil, it is primarily attributed to the effect of the re-entrant flow, which is formed due to the strong adverse pressure gradient. The results show strong correlation between the cavity and vorticity structures, demonstrating that the inception, growth, shedding, and collapse of sheet/cloud cavities are important mechanisms for vorticity production and modification.

PARTIALLY AVERAGED NAVIER-STOKES METHOD FOR TIME-DEPENDENT TURBULENT CAVITATING FLOWS

Cavitation typically occurs when the fluid pressure is lower than the vapor pressure in a local thermodynamic state,and the flow is frequently unsteady and turbulent.The Reynolds-Averaged Navier-Stokes（RANS）approach has been popular for turbulent flow computations.The most widely used ones,such as the standard k-εmodel,have well-recognized deficiencies when treating time dependent flow field.To identify ways to improve the predictive capability of the current RANS-based engineering turbulence closures,conditional averaging is adopted for the Navier-Stokes equation,and one more parameter,based on the filter size,is introduced into the k-εmodel.In the Partially Averaged Navier-Stokes（PANS）model,the filter width is mainly controlled by the ratio of unresolved-to-total kinetic energy1f.This model is assessed in unsteady cavitating flows over a Clark-Y hydrofoil.From the experimental validations regarding the forces,frequencies,cavity visualizations and velocity distributions,the PANS model is shown to improve the predictive capability considerably,in comparison to the standard k-ε model,and also,it is observed the value of1f in the PANS model has substantial influence on the predicting result.As the filter width1f is decreased,the PANS model can effectively reduce the eddy viscosity near the closure region which can significantly influence the capture of the detach cavity,and this model can reproduce the time-averaged velocity quantitatively around the hydrofoil.

A modified PANS model for computations of unsteady turbulence cavitating flows

A modification to the PANS(partially averaged Navier-Stokes) model is proposed to simulate unsteady cavitating flows. In the model, the parameter fk is modified to vary as a function of the ratios between the water density and the mixture density in the local flows. The objective of this study is to validate the modified model and further understand the interaction between turbulence and cavitation around a Clark-Y hydrofoil. The comparisons between the numerical and experiment results show that the modified model can be improved to predict the cavity evolution, vortex shedding frequency and the lift force fluctuating in time fairly well, as it can effectively modulate the eddy viscosity in the cavitating region and various levels of physical turbulent fluctuations are resolved. In addition, from the computational results, it is proved that cavitation phenomenon physically influences the turbulent level, especially by the vortex shedding behaviors. Also, the mean u-velocity profiles demonstrate that the attached cavity thickness can alter the local turbulent shear layer.

Numerical simulation of transient turbulent cavitating flows with special emphasis on shock wave dynamics considering the water/vapor compressibility

The objective of this paper is to investigate the compressible turbulent cavitating flows with special emphasis on shock wave dynamics, with the water/vapor compressibility taken into account. The simulations are performed by solving the compressible, multiphase unsteady Reynolds-averaged Navier-Stokes equations with Saito cavitation model and SST-SAS turbulence model. The compressibility of both the pure water and vapor is considered by employment of the Tait equation of state for water and ideal gas equation of state for vapor. Results are presented for a 3-D NACA66 hydrofoil fixed at ？= 6？ and ？= 1.25 in partial cavitating flows. Cavity collapse induced shock wave formation and propagation, which is closely related to the compressibility characteristics of cavitating flows, are well predicted. Good performance has been obtained for both the cavity evolution process and cavitation induced pressure signals, especially the cavity collapse induced shock wave emission and its interaction with the attached cavity sheet. The pressure peaks in microseconds accompanying the shock wave are captured. The typical quasi-periodic sheet/cloud cavitation evolution is characterized by the following four stages：（1） the growth of the attached cavity sheet,（2） development of re-entrant flow and attached cavity sheet breakup,（3） attached cavity sheet rolling up and cavity cloud shedding, and（4） cloud cavity collapse, shock wave emission and propagation. The cloud cavity collapse induced shock wave dynamics is supposed to be the major origin of cavitation instabilities.

Dynamic behaviors of cavitation bubble for the steady cavitating flow

In this paper, by introducing the flow velocity item into the classical Rayleigh-Plesset dynamic equation, a newequation, which does not involve the time term and can describe the motion of cavitation bubble in the steadycavitating flow, has been obtained. By solving the new motion equation using Runge-Kutta fourth order methodwith adaptive step size control, the dynamic behaviors of cavitation bubble driven by the varying pressure fielddownstream of a venturi cavitation reactor are numerically simulated. The effects of liquid temperature (correspondingto the saturated vapor pressure of liquid), cavitation number and inlet pressure of venturi on radial motionof bubble and pressure pulse due to the radial motion are analyzed and discussed in detail. Some dynamicbehaviors of bubble different from those in previous papers are displayed. In addition, the internal relationshipbetween bubble dynamics and process intensification is also discussed. The simulation results reported in thiswork reveal the variation laws of cavitation intensity with the flow conditions of liquid, and will lay a foundationfor the practical application of hydrodynamic cavitation technology.

NUMERICAL SIMULATIONS OF 2D PERIODIC UNSTEADY CAVITATING FLOWS

A two-phase mixture model was established to study unsteady cavitating flows. A local compressible system of equations was derived by introducing a density-pressure function to account for the two-phase flow of water/vapor and the transition from one phase to the other. An algorithm for solving the variable-density Navier-Stokes equations of cavitating flow problem was put forward. The numerical results for unsteady characteristics of cavitating flows on a 2D NACA hydrofoil coincide well with experimental data.

Large eddy simulation of cavitating flows with dynamic adaptive mesh refinement using OpenFOAM

Cavitating flows are dominated by large gradients of physical properties and quantities containing complicated interfacial structures and lots of multi-scale eddies that need to be accurately characterized using a high-resolution mesh.The present work,within OpenFOAM,proposes an effective modeling framework using the large eddy simulation(LES)approach along with the volume of fluid(VOF)method to simulate the two-phase flow system and applies the Schnerr-Sauer model to calculate the mass-transfer rate between water and vapor.The adaptive mesh refinement(AMR)which is a powerful tool for allocating high-resolution grids only to the region of the greatest concern is adopted for improving the solution of interfacial structures.The effect of grid size is firstly investigated and the time-averaged quantities are verified against the experimental data,and then simulations of cavitating flows are successfully achieved to precisely characterize the features of cavitation with automatically and dynamically refining the mesh.As the refinement only takes place in the interfacial region,high-precision simulations can be achieved with limited computational resources,and the method shows promising prospects for modeling of the multi-scale,time-critical and computationally intensive cavitating flows.

Measurement and prediction of cavitating flow-induced vibrations

The objective of this paper is to investigate the unsteady cavitation behaviors and the corresponding cavitating flow-induced vibrations. Results are presented for the modified NACA66 hydrofoils made of stainless steel and POM Polyacetate respectively at Re= 6.0×105for various cavitation regimes. The high-speed camera and the single point laser Doppler vibrometer(LDV) are used to observe the transient cavitating flow patterns and measure the vibration velocities. The results showed that the vibration amplitude increases dramatically for the cloud cavitation due to the development of large-scale cloud cavity. The main flow-induced frequencies, which are in accordance with the cavity shedding frequency, decrease with the decrease of the cavitation number. As for the effect of the hydroelastic response on the vibration behavior, the lift coefficient for the POM Polyacetate hydrofoil fluctuates more significantly with a larger mean value than that for the stainless steel hydrofoil. Compared with the vaporous cavity along the suction side of the stainless steel hydrofoil, the cavity for POM Polyacetate hydrofoil appears to be fragmentized. The main vibration frequencies for the POM Polyacetate hydrofoil are larger than that for the stainless steel hydrofoil, with the chaotic hydroelastic response with high frequency.